The convergence coefficient across political systems

Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 653035 28 pageshttpdxdoiorg1011552013653035

Research ArticleThe Convergence Coefficient across Political Systems

Maria Gallego12 and Norman Schofield1

1 Center in Political Economy Washington University 1 Brookings Drive Saint Louis MO 63130 USA2Department of Economics Wilfrid Laurier University 75 University Avenue West Waterloo ON Canada N2L 3C5

Correspondence should be addressed to Norman Schofield schofieldnormangmailcom

Received 4 August 2013 Accepted 21 August 2013

Academic Editors M Kohl and J Pacheco

Copyright copy 2013 M Gallego and N SchofieldThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Formal work on the electoral model often suggests that parties or candidates should locate themselves at the electoral mean Recentresearch has found no evidence of such convergence In order to explain nonconvergence the stochastic electoral model is extendedby including estimates of electoral valence We introduce the notion of a convergence coefficient 119888 It has been shown that highvalues of 119888 imply that there is a significant centrifugal tendency acting on partiesWe used electoral surveys to construct a stochasticvalence model of the the elections in various countries We find that the convergence coefficient varies across elections in a countryacross countries with similar regimes and across political regimes In some countries the centripetal tendency leads parties toconverge to the electoral mean In others the centrifugal tendency dominates and some parties locate far from the electoral meanIn particular for countries with proportional electoral systems namely Israel Turkey and Poland the centrifugal tendency is veryhigh In the majoritarian polities of the United States and Great Britain the centrifugal tendency is very low In anocracies theautocrat imposes limitations on how far from the origin the opposition parties can move

1 Introduction

Work on modeling elections has often assumed that the pol-icy space was restricted to one dimension or that there wereat most two parties [1 2] The extensive formal literature onelectoral competition has typically been based on the assump-tion that parties or candidates adopt positions in orderto win and has inferred that parties will converge to the elec-toral median under deterministic voting in one dimensionor to the electoral mean in stochastic models

In this paper we offer a formal stochastic model of ele-ctions that emphasizes the importance of the idea of valenceand use this notion to provide an explanation of why votemaximizing political leaders in some countries will not adoptconvergent policy positions at the mean of the electoral dis-tribution In the standard spatial model candidate positionsmatter to voters However as Stokes [3 4] has emphasizedthe nonpolicy evaluations or valences of candidates by theelectorate are just as important (See also Clarke et al [5 6]Scotto et al [7] and Clarke et al [8])

The main objective of this paper is to examine whetherparties locate close to or far from the electoral mean

(the electoral mean is the mean of voters ideal policiesdimension by dimension) of various countries We useSchofieldrsquos [9] stochastic electoral model as a unifying frame-work that allows us to compare parties positions acrossdifferent political systems In this model parties respondto their partisan constituencies after taking into accountthe anticipated electoral outcome and the positions of otherparties Voters decisions depend on partiesrsquo locations and onthe partyrsquos valence the votersrsquo overall common evaluation ofthe ability of a party leader to provide good governanceUsingthis model we examine whether parties converge to electoralmean in several elections in various countries under differentpolitical systems and use convergence or the lack thereof toclassify political systems

To examine whether parties converge to the electoralmean in each country in a particular election we test whetherany party has an incentive to stay or move away from theelectoral mean to increase its vote share In formal votingtheory it is usual to define a ldquoNash equilibriumrdquo as a vector ofparty positions with the property that no party may make aunilateral move so as to increase its vote share We use avariant of this concept that is a ldquolocal Nash equilibriumrdquo

2 The Scientific World Journal

(LNE) where we consider only marginal moves from theposition One of the standard results in formal theory is themean voter theorem where the ldquoNash equilibriumrdquo of a spatialvoting game under votemaximization is one where all partiesposition themselves at the electoral mean (For variants ofthe theorem see Enelow and Hinich [10ndash12]) We call such avector the electoral mean

To study each partyrsquos best response to the electoral situ-ation they face we use the results presented in Schofield [9]Schofield identifies a convergence coefficient denoted 119888 whosevalue determines whether vote maximizing parties convergeor not to the electoral mean This coefficient depends onvarious parameters of the model In particular it dependson the competence valences of the party leaders Using 119895 isin

119875 = 1 119901 to denote the parties the valence of party 119895 120582119895essentially measures the electoral perception of the ldquoqualityrdquoof 119895 the votersrsquo overall common evaluation of the ability of119895rsquos leader to provide good governance The valence terms120582 = (1205821 120582119901) are assumed to be independent of the partyrsquospositions and can be estimated as the intercept term in theappropriate stochastic model of the voter utility function AsSanders et al [13] comment valence theory is based on theassumption that ldquovoters maximize their utilities by choosingthe party that is best able to deliver policy successrdquo Thesevalence terms measure the bias in favor of one another of theparty leaders [14]

The convergence coefficient 119888 also depends on theweight that voters give to the policy differences they havewith the various parties 120573 Lastly 119888 depends on the vari-ancecovariance matrix of the electoral distribution 1205902 Byits construction 119888 equiv 119888(120582 120573 120590

2) is dimensionless and thus

independent of the units of measurement of the variousparameters We use the convergence coefficient to compareresults across elections and countries and to classify politicalsystems

The convergence coefficient is a summary measure thatprovides an estimate of the centrifugal or centripetal forcesacting on the parties The Valence Theorem presented inSection 2 (see Schofield [9] for the proof of this result) showsthat if the policy space is two-dimensional and if 119888(120582 120573 120590

2) lt

1 then the sufficient condition for convergence to the meanhas been met and the ldquolocal Nash Equilibriumrdquo (LNE) (theset of such local Nash Equilibria contains the set of NashEquilibria) is one where all parties locate at the electoralmean On the other hand if 119908 is the dimension of the policyspace and 119888(120582 120573 120590

2) ge 119908 then the LNE if it exists will be

one where at least one party will have an incentive to divergefrom the electoral mean in order to maximize its vote shareThus the necessary condition for convergence to the mean isthat 119888(120582 120573 120590

2) lt 119908

In essence a high empirical convergence coefficient of anelection is a convenient measure of the electoral incentive ofa small or low valence party tomove away from the electoralmean to its core constituency position We can interpreta high value of the convergence coefficient as a measureof the centrifugal tendency exerted on parties pulling themaway from the electoral mean The convergence coefficient istherefore a convenient simple and intuitive way to examine

whether parties will have an incentive to locate close to or farfrom the electoral mean We will show that there is a strongconnection between the values of the convergence coefficientand the nature of the political system under which partiesoperate

We used preelection polls to study elections in severalcountries operating under different political regimes Thefactor analysis done on preelection surveys showed that forall elections the policy space was two-dimensional exceptin Azerbaijan were it was one-dimensional The position ofvoters along this two-dimensional space were then estimatedand their voting intentions used to estimate party positionsWe then ran a multinomial logit (MNL) model for theelection using the estimated party and voter positions Theintercept of the MNL model gives the valences of eachpartyleader Following Schofieldrsquos [9] formal model we rankparties according to their valenceUsing theseMNL estimateswe calculate the convergence coefficient of the election andexamine whether the party with the lowest valence has anincentive to locate close to or far from the electoral origin

When comparing the convergence coefficients acrosscountries we observe that in countries with proportionalrepresentation the convergence coefficient is high and that incountries with plurality systems or in anocracies it is lowThus suggesting that we can use the valence theorem and itsassociated convergence result to classify electoral systems

The convergence coefficients for the 2005 and 2010elections in the UK were not significantly different from 1meeting the necessary condition for convergence to themeanFor the 2000 2004 and 2008 US presidential elections theconvergence coefficient is significantly below 1 in 2000 and2004 thusmeeting the sufficient and thus necessary conditionfor convergence and not significantly different from 1 in2008 only meeting the necessary condition for convergenceWe suggest that the centrifugal tendency in the majoritarianpolities like the United States and theUnited Kingdom is verylow

In contrast the convergence coefficient gives an indi-cation that the centrifugal tendency in Israel Poland andTurkey is very high In these proportional representationsystems with highly fragmented polities the convergencecoefficients are significantly greater than 2 failing to meet thenecessary condition for convergence to the electoral mean

In the anocracies of Georgia Russia and Azerbaijanwhere the Presidentautocrat dominates and controls whocan run in legislative elections the convergence coefficient isnot significantly different from the dimension of the policyspace (2 for Georgia and Russia and 1 for Azerbaijan) failingthe necessary condition for convergence While the analysisGeorgia and Azerbaijan show that not all parties convergeto the mean in Russia it is likely that they did Thus inRussia opposition parties found it difficult to diverge from themean Note that convergence in anocracies may not generatea stable equilibrium as any change in the valence of theautocrat and the oppositionmay cause parties to diverge fromthe mean and may even lead to popular uprising that bringabout changes in the governing parties such as in Georgia inprevious elections or in the Arab revolutions

The Scientific World Journal 3

We can also classify polities using the effective votenumber and the effective seat number (Fragmentation canbe identified with the effective number That is let 119867V (theHerfindahl index) be the sum of the squares of the relativevote shares and let 119890119899V = 119867

minus1V be the effective number of

party vote strength In the same way we can define ens asthe effective number of party seat strength using shares ofseats See Laakso and Taagepera [15]) We examine how thesetwo measures of fragmentation relate to the convergencecoefficient for the polities we consider The effective voteor seat numbers give an indication of the difficulty inher-ent in interparty negotiation over government These twomeasures do not however address the fundamental aspectof democracy namely the electoral preferences for policySince convergence involves both preferences in terms of theelectoral covariance matrix and the effect of the electoralsystemwe argue that theValenceTheorem and the associatedconvergence coefficient allow for a more comprehensive wayof classifying polities and political systems precisely becauseit is derived from the fundamental characteristics of theelectorateThat is while we can use the effective vote and seatnumber to identifywhich polities are fragmented theValenceTheorem and the convergence result can help us understandwhy parties locate close to or far from the electoral mean andhow under some circumstances these considerations lead topolitical fragmentation

The next section presents Schofieldrsquos [9] stochastic formalmodel of elections and implications it has for convergenceto the mean Section 31 applies the model to the electionsto two plurality polities The United States and the UnitedKingdom In Section 32 we apply the model to polities usingproportional electoral systems namely Israel Turkey andPoland Section 33 considers the convergence coefficients forthree ldquoanocraciesrdquo Azerbaijan Georgia and Russia Com-parisons between different fragmentation measures and theconvergence coefficient are examined in Section 4 Section 5concludes the paper In the appendix we estimate the con-fidence intervals for the convergence coefficient as well asdetermining whether the low valence party has an incentiveto deviate from the electoral mean

2 The Spatial Voting Model with Valence

Recent research on modelling elections has followed earlierwork by Stokes [3 4] and emphasized the notion of valence ofpolitical candidates As Sanders et al [13] comment valencetheory extends the spatial or Downsian model of elections byconsidering not just the policy positions of parties but also thepartiesrsquo rival attractions in terms of their perceived ability tohandle themost serious problems that face the countryThusvoters maximize their utilities by choosing the party that theythink is best able to deliver policy success

Schofield and Sened [16] have also argued that Valencerelates to votersrsquo judgments about positively or negativelyevaluated conditions which they associate with particularparties or candidates These judgements could refer to partyleadersrsquo competence integrity moral stance or ldquocharismardquoover issues such as the ability to deal with the economy andpolitics

Valence theory has led to a considerable theoretical liter-ature on voting based on the assumption that valence playsan important role in the relationship between party posi-tioning and the votes that parties receive (Ansolabare andSnyder [17] Groseclose [18] Aragones and Palfrey [19 20]Schofield [21] Schofield et al [22] Miller and Schofield [23]Schofield and Miller [24] Peress [25]) Empirical work basedon multinomial logit (MNL) methods has also shown theimportance of electoral judgements in analyses of electionsin the United States and the United Kingdom (Clarke et al[8 26ndash28] Schofield [29] Schofield et al [30 31] Scotto et al[7])These empiricalmodels of elections have a ldquoprobabilisticrdquocomponent That is they all assume that ldquovoter utilityrdquo ispartly ldquoDownsianrdquo in the sense that it is based on the distancebetween party positions and voter preferred positions andpartly due to valence The estimates of a partyrsquos valence isassumed to be subject to a ldquostochastic errorrdquo In this paper weuse the same methodology

The pure ldquoDownsianrdquo spatial model of voting tends topredict that parties will converge to the center of the electoraldistribution [10ndash12] However when valence is included theprediction is very different To see this suppose there are twoparties A and B and both choose the same position at theelectoral center but A has much higher valence than B Thishigher valence indicates that voters have a bias towards partyA and as a consequence more voters will choose A over BThe question for B is whether it can gain votes by movingaway from the center It should be obvious that the optimalposition of bothA andBwill depend on the various estimatedparameters of the model To answer this question we nowpresent the details of the spatial model

21 The Theoretical Model To find the optimal party posi-tions to the anticipated electoral outcome we use a Downsianvote model that has a valence component as presented inSchofield [9] Let the set of parties be denoted by119875 = 1 119901The positions of the 119901 parties (We will use candidate partyand agents interchangeably throughout the paper) in119883 sube R119908

where119908 is the dimension of the policy space it is given by thevector

z = (1199111 119911119895 119911119901) isin 119883119901 (1)

Denote voter 119894rsquos ideal policy be 119909119894 isin 119883 and her utility by119906119894(119909119894 119911) = (1199061198941(119909119894 1199111) 119906119894119901(119909119894 119911119901)) where

119906119894119895 (119909119894 119911119895) = 120582119895 minus 120573

10038171003817100381710038171003817119909119894 minus 119911119895

10038171003817100381710038171003817

2+ 120598119895 = 119906

lowast119894119895 (119909119894 119911119895) + 120598119895

(2)

Here 119906lowast119894119895(119909119894 119911119895) is the observable component of the utility

voter 119894 derived from party 119895 The competence valence ofcandidate 119895 is 120582119895 and the competence valence vector 120582 =

(1205821 1205822 120582119901) is such that 120582119901 ge 120582119901minus1 ge sdot sdot sdot ge 1205822 ge 1205821so that party 1 has the lowest valence Note that 120582119895 is the samefor all voters and provides an estimate of the ldquoqualityrdquo of party119895 or its ability to govern The term 119909119894 minus 119911119895 is simply theEuclidean distance between voter 119894rsquos position119909119894 and candidate119895rsquos position 119911119895 The coefficient 120573 is the weight given to thispolicy difference The error vector 120598 = (1205981 120598119895 120598119901) hasa Type I extreme value distribution where the variance of 120598119895


is fixed at 12058726 Note that 120573 has dimension 11198712 where 119871 is

whatever unit of measurement used in 119883Since voter behavior is modeled by a probability vector

the probability that voter 119894 chooses party 119895 when partiesposition themselves at z is

120588119894119895 (z) = Pr [119906119894119895 (119909119894 119911119895) gt 119906119894119897 (119909119894 119911119897) forall119897 = 119895]

= Pr [120598119897 minus 120598119895 lt 119906lowast119894119895 (119909119894 119911119895) minus 119906

lowast119894119897 (119909119894 119911119895) forall119897 = 119895]

(3)

Here Pr stands for the probability operator generated bythe distribution assumption on 120598 Thus the probability that119894 votes for 119895 is given by the probability that 119906119894119895(119909119894 119911119895) gt

119906119894119895(119909119894 119911119897) for all 119897 = 119895 isin 119875 that is that 119894 gets a higher utilityfrom 119895 than from any other party

Train [32] showed that when the error vector 120598 has aType I extreme value distribution the probability 120588119894119895(119911) has aMultinomial Logit (MNL) specification and can be estimatedThus for each voter 119894 and party 119895 the probability that voter 119894

chooses party 119895 at the vector z is given by

120588119894119895 (z) =

exp [119906lowast119894119895 (119909119894 119911119895)]

sum119901

119896=1exp 119906lowast119894119896(119909119894 119911119896)

(4)

Voters decisions are stochastic in this framework (Seefor example the models of McKelvey and Patty [14] Notethat there is a problem with the independence of irrelevantalternatives assumption (IIA) which can be avoided using aprobit model [33] However Quinn et al [34] have shownthat probit and logit models tend to give very similar resultsIndeed the results given here for the logit model carrythrough for probit though they are less elegant) Even thoughparties cannot perfectly anticipate how voters will vote theycan estimate the expected vote share of party 119895 as the averageof these probabilities as follows

119881119895 (z) =

1

119899

sum

119894isin119873

120588119894119895 (z) (5)

We assume a partyrsquos objective is to find the position thatmaximizes its expected vote share as desired by ldquoDownsianrdquoopportunists On the other hand the party may desire toadopt a position that is preferred by the base of the partysupporters namely the ldquoguardiansrdquo of the party as suggestedby Roemer [35]

We assume that parties can estimate how their vote shareswould change if they marginally move their policy positionThe Local Nash Equilibrium (LNE) is that vector z of partypositions such that no party may shift position by a smallamount to increase its vote share More formally a LNE isa vector z = (1199111 119911119895 119911119901) such that each vote share119881119895(z) is weakly locally maximized at the position 119911119895 To avoidproblems with zero eigenvalues we also define a SLNE to be avector that strictly locally maximizes 119881119895(z)

Using the estimated MNL coefficients we simulate thesemodels and then relate any vector of party positions z toa vector of vote share functions 119881(z) = (1198811(z) 119881119901(z))predicted by the particular model with 119901 parties Moreoverwe can examine whether in equilibrium parties position

themselves at the electoral mean (The electoral mean or ori-gin is the mean of all votersrsquo positions (1119899)sum119909119894 normalizedto zero so that (1119899)sum119909119894 = 0)We call this vector the electoralmean

Given the vector of policy position z and since theprobability that voter 119894 votes for party 119895 is given by (4) theimpact of amarginal change in 119895rsquos position on the probabilitythat 119894 votes for 119895 is then

119889120588119894119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816zminus119895

= 2120573120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) (6)

where zminus119895 indicates that we are holding the positions of allparties but 119895 is fixedThe effect that 119895rsquos change in position hason the probability that 119894 votes for 119895 depends on the weightgiven to the policy differences with parties 120573 on how likelyis 119894 to vote for 119895 120588119894119895 and for any other party (1 minus 120588119894119895) and onhow far apart 119894rsquos ideal policy is from 119895rsquos (119909119894 minus 119911119895)

From (5) party 119895 adjusts its position to maximize itsexpected vote share that is 119895rsquos first order condition is

119889119881119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816119911minus119895

=

1

119899

sum

119894isin119873

119889120588119894119895

119889119911119895

=

1

119899

sum

119894isin119873

2120573120588119894119895 (1minus120588119894119895) (119909119894minus119911119895) = 0

(7)

where the third term follows after substituting in (6) TheFOC for party 119895 in (7) is satisfied when

sum

119894isin119873

120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) = 0 (8)

so that the candidate for party 119895rsquos votemaximizing policy (SeeSchofield [36] for the proof) is

119911119862119895 = sum

119894isin119873

120572119894119895119909119894 where 120572119894119895 equiv

120588119894119895 (1 minus 120588119894119895)

sum119894isin119873 120588119894119895 (1 minus 120588119894119895)

(9)

where 120572119894119895 represents the weight that party 119895 gives to voter119894 when choosing its candidate vote maximizing policy Thisweight depends on how likely is 119894 to vote for 119895 120588119894119895 and for anyother party (1 minus 120588119894119895) relative to all voters (For example if allvoters are equally likely to vote for 119895 say with probability Vthen the weight party 119895 gives to voter 119894 in its vote maximizingpolicy is 1119899 that is the weight 119895 gives each voter is justthe inverse of the population size) Note that 120572119894119895 may benonmonotonic in 120588119894119895 To see this exclude voter 119894 from thedenominator of 120572119894119895 When sum119886isin119873minus119894 120588119886119895(1 minus 120588119886119895) lt 23 then120572119894119895 (120588119894119895 = 0) lt 120572119894119895 (120588119894119895 = 1) lt 120572119894119895 (120588119894119895 = 12) Thus if 119894 willfor sure vote for 119895 119894 receives a lower weight in 119895rsquos candidateposition than a voter who will only vote for 119895with probability12 (an ldquoundecidedrdquo voter) Party 119895 caters then to ldquoundecidedrdquovoters by giving them a higher weight in 119895rsquos policy weight andthus a higher weight on its positionThis is themost commoncase When sum119886isin119873minus119894 120588119886119895(1 minus 120588119886119895) gt 23 then 120572119894119895 increases in120588119894119895 If 119895 expects a large enough vote share (excluding voter119894) it gives a core supporter (a voter who votes for sure for119895) a higher weight in its policy position than it gives other


voters as there is no risk of doing so The weights 120572119894119895 areendogenously determined in the model

Note that since voter 119894rsquos utility depends on how far 119894 isfrom party 119895 the probability that 119894 votes for 119895 given in (4) andthe expected vote share of the party given in (5) are influencedby the voters and parties positions in the policy space Thatis in the empirical models estimated below the positionsof voters and parties in the policy space together with thevalence estimates influence voters electoral choices

Recall that we are interested in finding whether partiesconverge to or diverge from the electoral mean Suppose thatall parties locate at the same position 119911119896 = 119911 for all 119896 isin 119875Thus from (2) we see that

[119906lowast119894119896 (119909119894 119911) minus 119906

lowast119894119895 (119909119894 119911)] = (120582119896 minus 120582119895) (10)

so the probability that 119894 votes for 119895 in (4) is given by

120588119894119895 (z) =

1

sum119901

119896=1exp [119906

lowast119894119896(119909119894 119911119896) minus 119906

lowast119894119895 (119909119894 119911119895)]

= [

119901

sum

119896=1

exp (120582119896 minus 120582119895)]

minus1

(11)

Clearly in this case 120588119894119895(z) = 120588119895(z) is independent of voter 119894rsquosideal pointThus from (9) the weight given by 119895 to each voteris also independent of voter 119894rsquos position and given by

120572119895 equiv

120588119895 (1 minus 120588119895)

sum119894isin119873 120588119895 (1 minus 120588119895)

=

1

119899

(12)

so that 119895 gives each voter equal weight in its policy positionIn this case from (9) 119895rsquos candidate position is

119911119862119895 =

1

119899

sum

119894isin119873

119909119894 (13)

that is 119895rsquos candidate position is to locate at the electoralmean which we have placed at the electoral origin Let z0 =

(0 0) be the vector of party positions when all parties areat the electoral mean

Moreover as (11) indicateswhenparties locate at themeanz0 only valence differences between parties matter in votersrsquochoices The probability that a generic voter votes for party 1(the party with the lowest valence) is

1205881 equiv 1205881(z0) = [

119901

sum

119896=1

exp (120582119896 minus 1205821)]

minus1

(14)

Using this spatial model Schofield [9] proved a ValenceTheoremdeterminingwhether votemaximizing parties locateat the mean The theorem showed that the spatial model ischaracterized by a convergence coefficient given by

119888 equiv 119888 (120582 120573 1205902) = 2120573 [1 minus 21205881] 120590

2 (15)

The convergence coefficient depends on120573 theweight given topolicy differences on 1205881 the probability that a generic voter

votes for the lowest valence party at the vector z0 and on 1205902

the electoral variance given by

1205902equiv trace (nabla) (16)

where nabla is the symmetric 119908 times 119908 electoral covariance matrix(nabla is simply a description of the distribution of voter preferredpoints taken about the electoral mean)

The convergence coefficient increases in 120573 and 1205902 (and

on its product 1205731205902) and decreases in 1205881 As (14) indicates 1205881

decreases if the valence differences between party 1 and theother parties increases that is when the difference between1205821 and 1205822 120582119901 increases

The Valence Theorem allows us to characterize politiesaccording to the value of their convergence coefficientThe theorem states that when the sufficient condition forconvergence to the electoral mean is met that is when 119888 lt 1the LNE is onewhere all parties adopt the same position at themean of the electoral distribution A necessary condition forconvergence to the electoralmean is that 119888 lt 119908 where119908 is thedimension of the policy space If 119888 ge 119908 then theremay exist anonconvergent LNE Note that in this case there may indeedbe no LNE However there will exist a mixed strategy Nashequilibrium (MNE) In either of these two cases we expect atleast one party will diverge from the electoral mean

Note that 119888 is dimensionless because 1205731205902 has no dimen-

sion In a sense 1205731205902 is a measure of the polarization of the

preferences of the electorateMoreover 1205881 in (14) is a functionof the distribution of beliefs about the competence of partyleaders which is a function of the difference (120582119896 minus 1205821)

When some parties have a low valence so the probabilitythat a generic voter votes for party 1 (with the lowest valencewhen all parties locate at the origin) 1205881 in (14) will tend tobe small because the valence differences between party 1 andthe other parties is sufficiently large Thus vote maximizingparties will not all converge to the electoral mean In thiscase 119888 will be close to 2120573120590

2 If 21205731205902 is large because for

example the electoral variance is large then 119888 will be largesuggesting 119888 gt 119908 In this case the low valence party has anincentive to move away from the origin to increase its voteshare This implies the existence of a centrifugal force pullingsome parties away from the origin

Thus for 1205731205902 sufficiently large so that 119888 ge 119908 we expect

parties to diverge from the electoral center Indeed we expectthose parties that exhibit the lowest valence to move furtheraway from the electoral center implying that the centrifugalforce on parties will be significant Thus in fragmented poli-ties with a polarized electorate the nature of the equilibriumtends to maintain this centrifugal characteristic

On the contrary in a polity where there are no very smallor low valence parties 1205881 will tend to 12 and so 119888 willbe small In a polity with small 120573120590

2 and with low valencedifferences so that 119888 lt 1 we expect all parties to convergeto the center In this case we expect this centripetal tendencyto be maintained

The convergence coefficient is a way of characterizing theHessian (the 119908 by 119908 second derivatives of the vote sharefunction) of party 1 with the lowest valence The Hessian of


the vote share function of party 1 is given by the characteristicmatrix

1198621 = 2120573 (1 minus 21205881) nabla minus 119868 (17)

Here 119868 is a 119908 by 119908 identity matrix and the other terms areas before The eigenvalues of 1198621 determine whether the voteshare function of party 1 will be at a maximum minimum orat a saddlepoint at the electoral mean If 1198621 shows that party1 is at a minimum or at a saddlepoint at the mean then party 1has an incentive to locate away from the mean to increase itsvote share When all parties are at the mean and 119888 lt 1 thenall eigenvalues of the Hessian of the vote share function ofthe lowest valence party are negative indicating that the voteshare function is at a maximumThe LNEmust then be at theelectoral mean

For an arbitrary dimension 119908 if 119888(120582 120573 1205902) le 1 in

(15) then trace (1198621) lt 0 In the two-dimensional case if119888(120582 120573 120590

2) lt 1 then det (1198621) must be positive implying

that both eigenvalues of 1198621 are negative It then follows thatall 119862119895 have negative eigenvalues giving a SLNE and thusan LNE at the electoral mean (This result follows from theapplication of the triangle inequality to the determinant Aparallel result can be obtained inmore than two dimensions)

The Valence Theorem asserts that if 119888(120582 120573 1205902) gt 119908

then the party with the lowest valence has an incentive tomove away from the electoral mean to increase its vote shareWhen this is the case then other low valence parties mayalso find it advantageous to vacate the center The value ofthe convergence coefficient together with the analysis of theHessians of the low valence parties allows us to identifywhich parties have an incentive to move away from theelectoralmeanThe convergence coefficient then gives an easyand intuitive way to identify whether a low valence partyshould vacate the electoral mean

In the next section we estimate the convergence coeffi-cient of various elections in different countries

3 MNL Models of the Elections ofVarious Countries

We use the framework of the spatial model presented inSection 2 as a unifying methodology that allows us tostudy convergence across elections countries and politicalregimes The Valence Theorem leads to the convergencecoefficient of the election a summary statistic that determineswhether parties converge to or diverge from the electoralmean Using this formal multinomial (MNL) spatial modelwe now estimate the convergence coefficient for the electionsin various countries For each MNL estimation we choosea baseline party and normalize its coefficients to zero thenestimate the coefficients of all other parties relative to those ofthe base party Using these coefficients we estimate the con-vergence coefficient and the characteristic matrix of the lowvalence parties to determine whether these parties convergeto or diverge from the electoralmean in each election for eachcountry (These elections were studied in depth elsewhereIn this paper we present only the calculations leading to theconvergence coefficient and estimate the confidence intervals

for the convergence coefficients that were not provided inearlier work)

We study convergence under three political regimes(plurality proportional representation and anocracy) andgroup countries according to the similarities of their politicalregimes Under plurality rule we examine elections in twoAnglo-Saxon countries the US and the UK under propor-tional representation we study Israel Turkey and Polandand under anocracy Georgia Russia and Azerbaijan Sincewe use the same unifying methodology for all countrieswe present the methodology for the first elections in detailthen condense the analysis to its basic components for theremaining countries For each country we give a generaldescription of the analysis and direct the reader to the fullanalysis of each election in the detailed country paper Wesummarize the results across countries in various tables

31 Convergence in Plurality Systems We begin our analysisby examining the United States and the United KingdomElections in these countries are carried out under pluralityrule We show that the electoral system in these countriesproduces relatively low convergence coefficients (Relative tothe convergence coefficient of other countries included inthis study In Section 4 we discuss how the values of theconvergence coefficient are related to the political systemsunder which the countries operate)

311 The 2000 2004 and 2008 Elections in the United StatesWe construct stochastic models of the 2000 2004 and 2008US presidential elections using survey data taken from theAmerican National Election Surveys (ANES) The factoranalysis done on ten survey questions taken from the ANES(See Schofield et al [30 31] for the list of survey questions andthe factor loadings and the full analysis of the US elections)led us to conclude that voters preferences can be representedalong the economic (119864 = 119909-axis) and social (119878 = 119910-axis)dimensions for all three elections Voters located on the leftof the economic axis are pro-redistributionThe social axis isdetermined by attitudes to abortion and gays We interpretedgreater values along this axis to mean more support forcertain civil rights Using the factor loadings we estimatedeach voterrsquos position in these two dimensions Figures 1 2and 3 give a smoothing of the estimated voter distribution ofthe 2000 2004 and 2008 elections respectively

Votersrsquo ideal points in the 2000 US election are character-ized by the following electoral covariance matrix

nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)

The trace of electoral covariance matrix is 1205902US 2000 equiv

trace (nabla2000US ) = 1205902119864 + 1205902119878 = 117 Given the negative covariance

between these two dimensions 120590119864119878 = minus020 the correlationbetween these two factors is minus0344

Using the spatial model presented in Section 2 we esti-mated the MNL model of the 2000 election The coefficientsfor the US 2000 shown in Table 1 are

120582US2000rep = minus043 120582

US2000dem equiv 00 120573

US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Redistributive Policy

Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05

Figure 1 Distribution of voter ideal points and candidate positionsin the 2000 US election

minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05


Bushrsquos competence valence 120582US2000rep = minus043 measures the

common perception that voters in the sample have on Bushrsquosability to govern and represents the nonpolicy componentin the voterrsquos utility function in (2) As seen in Table 1for the 2000 election Bush has a statistically significantlower valence thanGore the democratic (baseline) candidateBushrsquos negative valence is an indication that voters regardedhim as less able to govern than Gore once policy differencesare taken into account

To find the convergence coefficient for this election weassume that all parties locate at the electoral mean so thatparties differ only in their valence terms (see Section 2)We can use (14) and the coefficients in (19) to estimate theprobability that a typical US voter chooses to vote for thelow valence Republican candidate when both Bush and Gorelocate at origin z0 that is

120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y


We found the estimate for 120588US2000rep using the MNL valence

estimates Note that since the central estimates of 120582 =

(1205821 120582119901) given by the MNL regressions depend on thesample of voters surveyed then so does 1205881 Thus to makeinferences from empirical models we need the 95 confi-dence bounds of 1205881 In the introduction of the appendix wederive the methodology used to find the confidence boundsof 1205881 The bounds of 1205881 are calculated in Appendix A1

The results indicate that in the 2000 election bothcandidates found it in their best interest to locate at theelectoral mean To see this we compute the convergencecoefficient using (15) and the electoral covariance matrix in(18) nabla2000US to determine whether the two parties converge toor diverge from the electoral mean

Using (19) and (20) we have that 2120573US2000(1 minus 2120588

US2000rep ) =

2 times 082 times 02 = 0328 and from (18) the trace is 1205902US2000 =

117 so that using (15) the convergence coefficient for 2000US election is

1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)

Appendix A1 shows that 1198882000US is significantly less than 1

implying that 1198882000US meets the sufficient and thus necessary

condition for convergence to the electoral mean given inSection 2

To check whether Bush the low valence candidate hasan incentive to stay at the electoral origin z0 that is whetherBushrsquos vote share function is at a maximum at z0 we use theHessian or characteristic matrix (of second order conditions)of Bushrsquos vote share function using (17) at z0 as follows

119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)

Because the characteristic matrix for Bush 119862US2000rep is esti-

mated using the MNL coefficients of the 2000 US sample


Table 1 MNL spatial model for countries with plurality systems

United Statesb United Kingdomc

Party 2000 2004 2008 Party 2005 2010

Var Esta|119905 minus value|

Esta|119905 minus value|




120573

082lowastlowastlowast(149)





Valence 120582repminus043lowastlowastlowast(505)

minus043lowastlowastlowast(505)

minus084lowastlowastlowast(764) 120582Lab


minus004(131)

120582Con027lowastlowastlowast(322)


Base party Demb Demb Repb Libc Libc

119899 1238 935 788 1149 6218119871119871 minus708 minus501 minus298 minus1136 minus5490alowastprob lt 005 lowastlowastprob lt 001 lowastlowastlowastprob lt 0001bUS Rep Republican Dem DemocratscUK Lab Labour Con Conservatives Lib Liberal Democrats

Table 2 The convergence coefficient in plurality systems

United States United Kingdom2000 2004 2008 2005 2010

Weight of policy differences (120573)Est 120573(conf Inta)

082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)

Electoral variance (tracenabla = 1205902)

1205902 117 117 163 5607 1462

Probability of voting for lowest valence party (party 1 1205881 = [sum119901

119896=1exp(120582119896 minus 1205821)]

minus1)Demb Demb Repb LibDemc Labourc

Est 1205881(conf Inta)

120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)

Convergence coefficient (119888 equiv 119888(120582 120573 1205902) = 2120573[1 minus 21205881]120590

2)Est 119888(conf Inta)

038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)

aConf Int confidence intervalsbUS Dem Democrats Rep RepublicancUK LibDem Liberal Democrats

119862US2000rep depends on the sample of voters surveyed The

confidence bounds on 119862US2000rep in Appendix A1 suggest that

if Bush positions himself at the electoral origin then withprobability exceeding 95 his vote share function would beat amaximumWe infer that with probability exceeding 95the origin is an LNE for the spatial model for the 2000 USelection The valence differences between Bush and Gore arenot large enough to cause either of them to move from theorigin The unique local Nash equilibrium was one whereboth candidates converge to the electoral origin in order tomaximize their vote shares

All the components needed to derive the convergencecoefficient for 2000US election and its confidence bounds aresummarized in Table 2

Bush faced Kerry as the democratic candidate in the2004 US election The distribution of voters in 2004 gives

the following electoral covariance matrix along the economicand social dimensions

nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)

While the covariance between economic and social axesdiffers the trace 120590

2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117

is similar to that in the 2000 US electionFrom Table 1 the MNL estimates of the spatial model for

the 2004 US election are

120582US2004rep = minus043 120582


US2004 = 095

(24)

Bush has a significantly lower valence (120582US2004rep = minus043) than

Kerry (120582US2004dem equiv 00) the baseline candidate


From (14) the probability that a US voter chooses Bushthe low valence candidate when both Bush and Kerry are atthe electoral origin z0 is

120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)

The confidence bounds for 120588US2004rep are given in Appendix A1

Since Bushrsquos valence relative to that of his opponent wassimilar in the two elections it is not surprising that theprobability of voting Republican is similar in the two elec-tions compare (20) and (25) From (15) 2120573US

2004(1minus2120588US2004rep ) =

2 times 095 times 02 = 038 and 1205902US2004 = 117 so that the

convergence coefficient of the 2004 election is

1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)

Since 1198882004US = 045 is significantly less than 1 (see

Appendix A1) the sufficient condition for convergence givenin Section 2 is met Moreover from (17) Bushrsquos characteristicmatrix is

119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)

If Bush positions himself at the electoral origin then withprobability exceeding 95 (see Appendix A1) his vote sharefunction would be at a maximum Bush the low valencecandidate has then no incentive to move from the originz0 With probability exceeding 95 the mean is an LNE formodel of the 2004 US election

Our analysis suggests that Obamarsquos victory over McCainin the 2008 US election was the result of an overall shiftin the relative valences of the Democratic and Republicancandidates as compared to those of the candidates in the 2000and 2004 elections The electoral covariance matrix for thesample in 2008 along the economic and social dimensions is

nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)

Relative to the two previous elections the ldquovariancerdquo of theelectoral distribution 120590

2US2008 = trace (nablaUS

2008) = 1205902119864 +1205902119878 = 163

increased while the covariance between these dimensions120590119864119878 = minus0127 decreased

The MNL estimates of the spatial model given in Table 1for the 2008 US election are

120582US2008rep = minus084 120582


US2008 = 085

(29)

Obama the baseline candidate has a significantly highervalence than McCain

From (14) the probability that a voter chooses McCainwhen both candidates are at the origin z0 is

120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)

From (15) 21205732008US (1 minus 2120588US2008dem ) = 2 times 085 times 04 = 068 and

1205902US2008 = 163 so the convergence coefficient is

1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)

Appendix A1 shows that 1198882008US = 111 is significantly greaterthan 1 and significantly less than 2 The Valence Theoremthen states that the necessary but not the sufficient conditionfor convergence has been met To check whether the lowvalence candidateMcCain has an incentive tomove from theelectoral mean we examine McCainrsquos characteristic matrixusing (17) to get

119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)

With probability exceeding 95 (see Appendix A1)McCainrsquosvote share function is at a maximum when he locates at theorigin and thus has no incentive to move Thus with pro-bability exceeding 95 the electoral origin is an LNE for thespatial model for the 2008 US election

In conclusion Table 2 illustrates that the convergencecoefficient varies across elections in the same country evenwhen there are only two parties This is to be expected asfrom (15) the convergence coefficient depends on the ldquovari-ancerdquo of the electoral distribution 120590

2= trace(nabla) on the

weight voters give to differences with partyrsquos policies 120573 andon the probability that a voter chooses the party with thelowest valence 1205881 The electoral distributions of the 2000and 2004 are quite similar as can be seen by comparing(18) and (23) Votersrsquo preferences had however substantiallychanged by 2008 see (28) The electoral variance along bothaxes increased relative to 2000 and 2004 While the 2000and 2004 convergence coefficients are indistinguishable fromeach other the 2008 coefficient is significantly different fromthat in 2000 and 2004 In spite of these differences candidatesin all three elections had no incentive to move from theorigin

312 The 2005 and 2010 Elections in Great Britain We studythe 2005 and 2010 elections in the UK using the British


minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib

Figure 4 Electoral distribution and estimated party positions inBritain in 2005

Election Study (BES) (The full analysis of the 2005 and 2010elections in Great Britain can be found in Schofield et al[37]) The factor analysis conducted on the questions of thetwo surveys led us to conclude that the same two dimensionsmattered in voter choices in the two elections The firstfactor deals with issues on ldquoEU membershiprdquo ldquoImmigrantsrdquoldquoAsylum seekersrdquo and ldquoTerrorismrdquo A voter who feels stronglyabout nationalism has a high value in the nationalism dimen-sion (Nat = 119909-axis) Items such as ldquotaxspendrdquo ldquofree marketrdquoldquointernational monetary transferrdquo ldquointernational companiesrdquoand ldquoworry about job loss overseasrdquo have strong influencein the economic (119864 = 119910-axis) dimension with higher valuesindicating a promarket attitude Figures 4 and 5 present thesmoothed electoral distribution obtained from these analysesfor the 2005 and 2010 elections

The electoral covariance matrix for the 2005 UK electionis

nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)

where 1205902UK2005 equiv trace(nablaUK

2005) = 1205902Nat + 120590

2119864 = 5607

From Table 1 the MNL estimates of the spatial model forthe 2005 UK are

120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)

Both the Labour (Lab) and the Conservative (Con) partieshad a significantly higher valence than the Liberal Democrats(Lib) the baseline party

minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib

Figure 5 Voter and party positions in Britain in 2010

From (14) the probability that a voter chooses the LiberalDemocratic Party the lowest valence party when all partieslocate at the origin z0 is

120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)

Given that 2120573UK2005(1 minus 2120588

UK2005Lib ) = 2 times 015 times 05 = 015

and since 1205902UK2005 = 5607 in (33) from (15) the convergence

coefficient in Table 2 is

1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)

Appendix A1 shows that 1198882005UK is significantly less than 1 andthusmeets the sufficient and necessary conditions for conver-gence given in Section 2 From (17) the characteristic matrixof the Liberal Democratic Party is

1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)

From the 95 confidence bounds in Appendix A1 we con-clude that if the LibDem locates at the origin it is maximizingits vote share and has no incentive to vacate the center Thuswith probability exceeding 95 the origin is an LNE for the2005 UK election



nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)


2010) = 1462 lower than in 2005From Table 1 the MNL estimates of the spatial model of

the 2010 election are

120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)

Given the great popular discontent with Gordon Brownthe Labour leader heading into the 2010 election it isnot surprising to find that both Conservatives and LiberalDemocrats (the base party) had significantly higher valencesthan Labour

From (14) the probability that a voter chooses Labourwhen all parties locate at the origin z0 is

120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588

UK2010Lab ) = 2 times 086 times 0362 = 0622 and

1205902UK2010 = 1462 in (38) from (15) the convergence coefficient

in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)

The convergence coefficient 1198882010UK = 091 is significantly lessthan 1 (see Appendix A1) meeting the sufficient and thusnecessary condition for convergence From (17) Labourrsquoscharacteristic matrix is

119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)

If Labour the low valence party locates at the origin thenwith probability exceeding 95 its vote share function is at amaximum (see Appendix A1) giving it no incentive to movefrom the mean Thus with probability exceeding 95 theelectoral origin is an LNE for the 2010 UK election

The major shift in votersrsquo preferences between the twoelections led to very different electoral outcomes as evidencedby the electoral covariance matrices in (33) and (38) Voterdissatisfaction with the governing Labour leader led to adramatic decrease in his competence valence and on theprobability of voting Labour Even though the electoral

variance fell in 2010 relative to 2005 the increase in theconvergence coefficient meant that this lower variance wasmore than compensated by the lower probability of votingLabour in 2010 The analysis for the UK elections showsthat the convergence coefficient reflects not only changes inthe electoral distribution but also changes in votersrsquo valencepreferences as the convergence coefficient of the 2005 electionis substantially lower than the one for the 2010 election

The analysis of these twoAnglo-Saxon countries illustratethat even under plurality rule the convergence coefficientvaries from election to election and from country to countryThe analysis for the 2010 UK election highlights that candi-datesrsquo valences matter and that parties understand how theirvalence affects their electoral prospects and may adjust theirpositions to increase their votes This section illustrates thatunder plurality the convergence coefficient has low valuesthat generally satisfy the necessary condition for convergenceto the mean and is thus below the dimension of the policyspace

32 Convergence in Proportional Systems We now estimatethe convergence coefficients for three parliamentary coun-tries using proportional representation Israel Turkey andPoland As is well known these countries are characterizedby multiparty elections in which generally no party wins alegislative majority leading then to coalitions governmentsThis section shows that these countries are characterized byvery high convergence coefficients

321 The 1996 Election in Israel In the 1996 as in previouselections Israel had approximately nineteen parties attainingseats in the Knesset (These include parties on the left onthe center on the right as well as religious parties Onthe left there is Labor Merets Democrat Communists andBalad those on the center include Olim Third Way CenterShinui those on the right Likud Gesher Tsomet and YisraelThe religious parties are Shas Yahadut NRP Moledet andTechiya) There were small parties with 2 seats to moderatelylarge parties such as Likud and Labor whose seat strengthslie in the range 19 to 44 out of a total of 120 Knesset seatsSince Likud and Labour compete for dominance of coalitiongovernment these large parties must maximize their seatstrengthMoreover Israel uses a highly proportional electoralsystem with close correspondence between seat and voteshares Thus one can consider vote shares as the maximandand for these parties

Schofield et al [30] performed a factor analysis of thesurveys conducted by Arian and Shamir [38] for the 1996Israeli election The two dimensions identified by the factoranalysis were Security (119878 = 119909-axis) and Religion (119877 = 119910-axis) ldquoSecurityrdquo refers to attitudes toward peace initiativesldquoreligionrdquo to the significance of religious considerations ingovernment policy A voter on the left of the security axis isinterpreted as supporting negotiations with the PLO whilehigher values on the religious axis indicates support for theimportance of the Jewish faith in Israel The distribution ofvoters is shown in Figure 6


Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2

minus2 minus1 0 1Security

Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists

Figure 6 Party positions and voter distribution in Israel in the 1996election

Voter distribution along these two axes gives the follow-ing covariance matrix

nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)

giving a ldquovariancerdquo of 1205902I1996 equiv trace(nablaI996) = 1732

Only the seven largest parties are included in the MNLestimationThese include Likud Labor NRP Moledat ThirdWay (TW) and Shas with Meretz being the base party FromTable 2 the MNL coefficients for the 1996 election in Israel(I) are

120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582

I1996Shas = minus2023

120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)

The 120573-coefficient and the valence estimates for all partiesare significantly nonzero The two largest parties Likud andLabour have significantly higher valences than the othersmaller parties with Third Way (TW) having the smallestvalence

From (14) the probability that an Israeli votes for TWwhen all parties locate at the mean is

120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)

Given that 2120573I1996(1 minus 2120588

I1996TW ) = 2 times 1207 times 0972 = 2346

and since 1205902I1996 = 1732 from (43) then using (15) we com-

pute the convergence coefficient for Israel in Table 4 as

119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)

The 95 confidence intervals for 119888I1996 = 406 in

Appendix A2 confirm that the necessary condition is notsatisfied as 119888

I1996 = 406 is significantly higher than 2 the

dimension of the policy space Moreover at the electoralmean the vote share function of Third Way is not at amaximum since its Hessian from (17)

119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)

shows that if TW locates at the mean its vote share functionis at a saddlepoint since 119862

I1996TW has one positive (2453) and

one negative (minus039) eigenvalue Appendix A2 confirms that119862I1996TW has one negative and one positive eigenvalue at both its

lower and upper boundsThus with a high degree of certaintyTW deviates from the mean to maximize its votes and theelectoral mean is not a LNE for the 1996 Israeli election

322 The 1999 and 2002 Elections in Turkey We used factoranalysis of electoral survey data of Veri Arastima for TUSESto study the 1999 and 2002 Turkish elections (See Schofieldet al [39] for details of the estimation)The analysis indicatesthat voters made decisions in a two-dimensional spaceduring the two elections Voters who support secularism orldquoKemalismrdquo are placed on the left of the Religious (119877 = 119909)axis and those supporting Turkish nationalism (119873 = 119910) tothe north Figures 7 and 8 give the distribution of voters alongthese two dimensions surveyed in these two elections

Minor differences between these two figures include thedisappearance of the Virtue Party (FP) which was bannedby the Constitutional Court in 2001 and the change of thename of the pro-Kurdish party fromHADEP toDEHAP (Forsimplicity the pro-Kurdish party is denoted HADEP in thevarious figures and tables Notice that theHADEP position inFigures 8 and 9 is interpreted as secular andnonnationalistic)The most important change is the emergence of the newJustice and Development Party (AKP) in 2002 essentiallysubstituting for the outlawed Virtue Party

The parties included in the analysis of the 1999 electionare the Democratic Left Party (DSP) the National Actionparty (MHP) the Vitue Party (VP) the Motherland Party(ANAP) the True Path Party (DYP) the Republican PeoplersquosParty (CHP) and the Peoplersquos Democratic Party (HADEP)A DSP minority government formed supported by ANAPand DYP This only lasted about 4 months and was replacedby a DSP-ANAP-MHP coalition indicating the difficulty


0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism

minus3 minus2 minus1

Figure 7 Party positions and voter distribution in the 1999 Turkishelection

Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1

minus22 310minus1minus2minus3

Figure 8 Party positions and voter distribution in Turkey in 2002

of negotiating a coalition compromise across the disparatepolicy positions of the coalition members

In the 1999 election the electoral covariance matrix alongthe Religious (119877) and Nationalism (119873) axes is

nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)

with 1205902T1999 equiv trace(nablaT

999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al

Figure 9 Voter distribution and party-positions in Poland in 1997

Using DYP as the base party from Table 3 the 1999MNLcoefficients are

120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582

T1999HADEP = minus0071

120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)

The 120573-coefficient and the valence estimates of DSP andMHPand CHP are significantly nonzero The probability that aTurkish voter chooses FP with lowest valence in 1999 whenall parties locate at the mean 120588T1999

FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)

Given that 2120573T1999(1 minus 2120588

T1999FP ) = 2 times 038 times 084 = 064

and since 1205902T1999 = 234 in (48) then using (15) Turkeyrsquos

convergence coefficient in 1999 in Table 4 is

119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)

The convergence coefficient is significantly higher that 1 andsignificantly lower than 2 (see Appendix A2) From (17) FPrsquosHessian at the origin is

119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)


Table 3 MNL spatial model for countries with proportional systems

Var Israelb Turkeyd Polandc

Party 1996 Party 1999 2002 Party 1997

Distance Esta|119905 minus value|




120573





Valence

120582Lik0777lowastlowastlowast(412) 120582DSP

0724lowastlowastlowast(473) 120582SLD


120582Lab0999lowastlowastlowastlowast(606) 120582MHP


minus012(066) 120582PSL

0073(033)

120582NRPminus0626lowastlowastlowast(253) 120582FP

minus0159(090) 120582AWS


120582MOminus1259lowastlowastlowast(438) 120582ANAP


minus031(163) 120582UW


120582TWminus2291lowastlowastlowast(830) 120582CHP


133lowastlowastlowast(740) 120582UP


120582Shasminus2023lowastlowastlowast(645) 120582HADEP

minus0071(030)

043lowast(20) 120582UPR


120582AKP078lowastlowastlowast(52)

Base party Meretz DYPd DYPd ROPc

119899 922 635 483 660119871119871 minus777 minus1183 minus737 minus855alowastprob lt 005 lowastlowastprob lt 001 lowastlowastlowastprob lt 0001bIsrael Lik Likud Lab Labor NRP Mafdal Mo Moledet TWThird WaycPoland SLD Democratic Left Alliance PSL Polish Peoplersquos Party UW Freedom Union AWS Solidarity ElectionAction UP Labor Party UPR Union of Political Realism ROP Movement for Reconstruction of Poland SO Self Defense PiS Law and Justice PO CivicPlatform LPR League of Polish Families DEM Democratic Party SDP Social Democracy of PolanddTurkey DSP Democratic Left Party MHP Nationalist Action Party FP Virtue Party ANAP Motherland Party CHP Republican Peoplersquos Party HADEPPeoplersquos Democracy Party DYP True Path Party

Table 4 The convergence coefficient in proportional systems

Israel Turkey Poland1996 1999 2002 1997

Weight of policy differences (120573)Central Esta of 120573(conf Intb)

1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]

minus1)TWc FPd ANAPd ROPe

Central Esta of 1205881(conf Intb)

120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007

(0002 0022)Convergence coefficient (119888 equiv 119888(120582 120573 120590

2) = 2120573[1 minus 21205881]120590

2)Central Esta of 119888(conf Intb)

406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)

aCentral Est central estimatebConf Int confidence intervalscIsrael TWThird WaydTurkey DYP True Path PartyePoland ROP Movement for Reconstruction of Poland


When at the electoral origin FPrsquos characteristic functionshows that its vote share function is at a saddlepoint asthe eigenvalues of 119862

T1999FP are minus074 with minor eigenvector

(+1 minus 1116) and +023 with major eigenvector (+1 +0896)Moreover as seen in Appendix A2 the 95 confidencebounds show that at the lower bound of 119862

T1999FP FP has no

incentive to move but it does at the upper bound Since FPwants to move at the central estimate of 119862

T1999FP in (52) it

is probable that in general FP wants to move away fromthe mean to increase its vote share Moreover since theconvergence coefficient is significantly greater than 2 thenwith a high degree confidence the electoral mean cannot bea LNE for Turkey in 1999

The electoral covariance matrix of the 2002 Turkishelection is

nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)

with 1205902T2002 = trace (nablaT

2002) = 233Note that the covariance matrix of 1999 in (48) and that

of 2002 in (53) suggest few changes in the distribution ofvoters between these two election Figures 8 and 9 suggest thatthere were few changes in party positions between these twoelections The basis of support for the AKP may be regardedas similar to that of the banned FP suggesting that the leaderof this party changed the partyrsquos position on the religion axisadopting amuch less radical positionOnewould think of thisas generating political stability in Turkey Yet between 1999and 2002 Turkey experienced two severe economic crises andin 2002 a 10 electoral cut-off rule was instituted The crisesand the cut-off rule changed the political landscape in TurkeyIn the 2002 election seven parties obtained less than 10 ofthe vote and won no seatsThe AKPwon 34 of the vote anddue to the cut-off rule obtained a majority of the seats (363out of 550)

Our analysis reflects this change in the political landscapeUsing DYP as the base party from Table 3 the 2002 MNLcoefficients are

120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)

The 120573-coefficient and the valences of AKP and CHP aresignificantly nonzero with ANAP having the lowest valenceThe probability of voting ANAP when parties locate at themean 120588T20029

ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)

Given that 2120573T2002(1minus2120588

T2002ANAP) = 2times152times084 = 255 and

since 1205902T2002 = 233 from (53) then using (15) we find that the

2002 convergence coefficient for Turkey in Table 4 is

119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)

The political changes induced by the cut-off rule led toa higher convergence coefficient in 2002 relative to 1999(increasing from a low of 119888T1999 = 149 in (51) to a high 119888

T2002 =

594 in (56)) An indication that a more fractionalized polityemerged from this reformThe convergence coefficient of the2002 election is significantly above 2 the dimension of thepolicy space (see Appendix A2) giving ANAP an incentive tolocate far from the mean ANAPrsquos characteristic matrix using(17) is

119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)

When at the origin 119862T2002ANAP indicates that ANAP is minimiz-

ing its vote share since its eigenvalues are both positive (0090and 3850) This together with the 95 confidence boundsin Appendix A2 implies that there is a high probability thatANAP will vacate the center and that the mean is not an LNEfor Turkey in 2002

323 The 1997 Polish Election In the election held in Polandin 1997 (In this election Poland used an open-list propor-tional representation electoral system with a threshold of 5nationwide vote for parties and 8 for electoral coalitionsVotes are translated into seats using the DrsquoHondt method)the following five parties won seats in the Sejm (lowerhouse)The left-wing excommunist Democratic Left Alliance(SLD) and the agrarian Polish Peoplesrsquo Party (PSL) bothof which have been the most frequent governing parties inthe postcommunist period The Freedom Union (UW) andthe Solidarity Election Action (AWS) had grown out of theSolidarity movement AWS combined various mostly rightwing and Christian groups under one label while UW wasformed based on the liberal wing of SolidarityThe remainingparty is the Movement for Reconstruction of Poland (ROP)

Applying factor analysis to questions from the PolishNational Election Survey an economic and a social valuedimensions were identified (see [40]) The economic dimen-sion is influenced by issues such as privatization versusstate ownership of enterprises fighting unemployment ver-sus keeping inflation and government expenditure undercontrol proportional versus flat income tax support versusopposition to state subsidies to agriculture and state versusindividual social responsibilityThe separation of church andstate versus the influence of church over politics completedecommunization versus equal rights for former nomencla-ture and abortion rights regardless of situation versus nosuch rights regardless of situation are the most influential


issues in this social values dimension The distribution ofvoters along these dimensions is seen in Figure 9 (SeeSchofield et al [40] for details of the estimation)

The covariance matrix for the 1997 Polish (P) election is

nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)

with variance 1205902P1997 = trace(nablaP

1997) = 200From Table 3 the MNL coefficients for the 1997 election

are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)

The 120573-coefficient and valence estimates for all parties exceptUP and PSL are significantly nonzero The probability ofvoting UPR with lowest valence in 1997 when parties locateat the mean 120588P1997

TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)

Given that 2120573P1997(1minus2120588

P1997UPR ) = 2times174times098 = 341 and

since 1205902P1997 = 2 from (58) then using (15) the convergence

coefficient for Poland in Table 4 is

119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)

Appendix A2 shows that 119888P1997 = 682 is significantly greaterthan 2 and thus fails the necessary condition for convergenceto the mean UPRrsquos Hessian from (17) is

119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)

The trace (= 382) the determinant (= 580) and the eigen-values of 119862I

UPR (241 141) are positive The 95 confidencebound of 119862

IUPR in Appendix A2 also shows positive eigen-

values at the lower and upper bounds of 119862IUPR Thus with a

high degree of certainty UPR locates far from the origin tomaximize its votes and the electoral mean is not a LNE for1997 Polish election

Summarizing in this section we examined three coun-tries that use proportional representationTheir convergencecoefficients are significantly higher than 2 the dimension ofthe policy space and are also much higher than that of theUS and the UK A high convergence coefficient signals then ahigh degree of political fractionalization in these multi-partyparliamentary democracies

33 Convergence in Anocracies We now study elections inGeorgia Russia and Azerbaijan In these partial democ-racies or anocracies (The term ldquopartial democracyrdquo hasbeen applied to new democracies lacking the full array ofdemocratic institutions present in western democracies (see[41])) the Presidentautocrat holds regular presidential andlegislative elections while exerting undue influence on theelections Anocracies lack important democratic institutionssuch as freedom of the press Autocrats hold regular electionsin an attempt to give their regime legitimacy The autocratldquobuysrdquo legitimacy by rewarding their supporters and oppo-sition members with well-paid legislative positions and givelegislators the ability to influence policies Opposition partiesparticipate in elections to become known political entitiesThis allows them to regularly communicate with votersTheirobjective is to oust the autocrat either in a future electionor through popular uprisings We assume that oppositionparties maximize their vote share even when understandingthat there is little chance of ousting the autocrat in theelection

331 The 2008 Georgian Election We use the postelectionsurvey conducted by GORBI-GALLUP International fromMarch 19 through April 3 2008 to built a formal model ofthe 2008 election in Georgia (see [42]) The factor analysisdone on the survey questions determined that there were twodimensions describing votersrsquo attitudes towards democracyand the west One dimension is strongly related with therespondentsrsquo attitude toward the US the EU and NATO withlarger values in the West (119882 = 119910-axis) dimension implying astronger anti-western attitude Along the democracy (119863 = 119909-axis) dimension larger values are associated with negativejudgements on the current state of democratic institutions inGeorgia coupled with a demand for more democracy Theelectoral distribution along these two dimensions is given inFigure 10 The points (S G P N) in Figure 10 represent theestimated positions of the four candidates Saakashvili (S)Gachechiladze (G) Patarkatsishvili (P) and Natelashvili (N)(See Schofield et al [39] for details of the estimation)

The 2008 electoral covariance matrix in the Democracy(119863) and West (119882) axes is

nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)

with 1205902G2008 equiv trace (nablaG

2008) = 173From Table 5 the MNL estimates of the 2008 election

with Natelashvili as the base candidate are120582G2008S = 256 120582

G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Demand for more democracy

Wes

tern

izat

ion

SG

P N

Figure 10 Voter distribution and candidate positions in the 2008Georgian election

All coefficients are significantly nonzero showingNatelashvilias having the lowest valence

The probability that a Georgian votes for Natelashviliwhen all candidates locate at the mean is

120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)

Given that 2120573G2008(1 minus 2120588

G2008N ) = 2 times 078 times 09 = 14 and

since 1205902G2008 = 173 from (63) then using (15) Georgiarsquos the

convergence coefficient in Table 6 is

119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)

As shown in Appendix A3 119888G2008 is not significantly

different from 2 and thus fails the necessary condition forconvergence to the mean Natelashvilirsquos Hessian or character-istic matrix from (17) is

119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)

Since the eigenvalues of 119862G2008N are both positive (+0139

+0291) Natelashvilirsquos vote share function is at a minimumwhen he is at the mean and has an incentive to move toincrease his vote share This together with the analysis of

the 95 confidence intervals of 119862G2008N in Appendix A3

shows that with a high degree of certainty Natelashvili willlocate far from the mean This is not surprising since Geor-gians managed to induce three major changes in governmentthroughmass protests prior to this electionThus with a highdegree of certainty Natelashvili locates far from the origin inthis election and the electoral mean cannot be an LNE for the2008 Georgian election

332 The 2007 Russian Election The analysis of the 2007Russian election concentrates on four parties the pro-Kremlin United Russia party (ER) Liberal Democratic Party(LDPR) Communist Party (CPRF) and Fair Russia (SR)Votersrsquo ideological preferences were measured according totwo questions taken from the survey conducted by VCIOM(Russian Public Opinion Research Center) in May 2007 (see[43]) The first dimension gives a measure of voters general(dis)satisfaction (119863 = 119909-axis) High values in this dimensioncorrespond to negative feelings toward ldquojusticerdquo ldquolaborrdquo andto a lesser extent ldquoorderrdquo ldquostaterdquo ldquostabilityrdquo and ldquoequalityrdquoAlso those with high values of the first axis tend to feelneutral toward order elite West and non-Russians Thesecond dimension measures the voterrsquos degree of economicliberalism (119864 = 119910-axis) High values correspond to positivefeelings to ldquofreedomrdquo ldquobusinessrdquo ldquocapitalismrdquo ldquowell-beingrdquoldquosuccessrdquo and ldquoprogressrdquo and to negative feelings towardldquocommunismrdquo ldquosocialismrdquo ldquoUSSRrdquo and related conceptsThedistribution of voter preferences along these two dimensionscan be seen in Figure 11 (See Schofield and Zakharov [43] fordetails of the estimation)

The 2007 electoral covariance matrix along the (dis)satisfaction (119863) and economic liberalism (119864) axes is

nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)

with 1205902R2007 equiv trace(nablaR

2007) = 59From Table 5 the MNL estimates of the spatial model for

Russia are120582R2007SR = minus04 120582

R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)

Distance and all valences except for that of the LDPR partyare significantly nonzero When parties locate at the meanthe probability that a Russian votes for Fair Russia (SR) withlowest valence from (14) is

120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)

Given that 2120573R2007(1 minus 2120588

R2007SR ) = 2 times 0181 times 086 = 031

and since 1205902R2007 = 59 from (68) then using (15) Russiarsquos


119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)


Table 5 MNL spatial model in anocracies

Georgiac Russiab Azerbaijand

Party 2008 Party 2007 Party 2010




120573




Valance

120582S256lowastlowastlowast(1366) 120582CPRF

1971lowastlowastlowast(1779) 120582YAP

130lowast(214)

120582G150lowastlowastlowast(796) 120582LDRP

0153(109)

120582P053lowast(251) 120582SR


Base party N ER AXCP-MP119899 676 1004 149119871119871 minus533 minus797 minus115alowastprob lt 005 lowastlowastprob lt 001 lowastlowastlowastprob lt 0001bGeorgia S Saakashvili G Gachechiladze P Patarkatsishvili and N NatelashvilicRusia ER United Russia CPRF Communist Party SR Fair Russia LDPR Liberal Democratic PartydAzerbaijan YAP Yeni Azerbaijan Party AXCP-MP Azerbaijan Popular Front Party (AXCP)-and Musavat (MP)

Table 6 The convergence coefficient in anocracies

Georgia Russia Azerbaijand

2008 2007 2010Weight of policy differences (120573)


078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]

minus1)Nc SRb AXCP-MPd


120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)

aConf Int confidence intervalsbGeorgia N NatelashvilicRussia SR Fair RussiadAzerbaijan AXCP-MP Azerbaijan Popular Front Party (AXCP) and Musavat (MP)The estimates for Azerbaijan are less precise because the sample is small

Since 119888R2007 is not significantly different from 2 (see Appendix

A3) the necessary condition for convergence is notmetThecharacteristic matrix or Hessian of Fair Russia (SR) from (17)is

119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)

The eigenvalues are both negative (minus0126 minus0046) implyingthat at this central estimate Fair Russia is maximizing itsvote share and thus has no incentive to vacate the originThis conclusion holds at the lower 95 bound of 119862

R2007SR in

Appendix A3 However at the upper bound of 119862R2007SR Fair

Russia is minimizing its vote share It seems then that withthe Russian President and his party exerting much influenceover the election and Putin being so popular that Fair Russiais more likely to remain at the origin (This result howeverhighlights that unexpected political events could prompt FairRussia to move from the origin) It is then likely that theelectoral mean is a LNE for the 2007 Russian election


minus4 minus3 minus2 minus1 0 1 2 3 4 5

minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR

Figure 11 Party positions and voters distribution in the 2007Russian election

333 The 2010 Election in Azerbaijan In the 2010 electionin Azerbaijan 2500 candidates filed application to run inthe election but only 690 were given permission by theelectoral commission The parties that competed in theelection were the Yeni Azerbaijan Party (the party of thePresident YAP) Civic Solidarity Party (VHP) MotherlandParty (AVP) Azerbaijan Popular Front Party (AXCP) andMusavat (MP) Various small parties formed political blocks

President Ilham Aliyevrsquos ruling Yeni Azerbaijan Partytook a majority of 72 out of 125 seats Nominally independentcandidates who were aligned with the government received38 seats and 10 small opposition or quasiopposition partiestook 10 seatsTheDemocratic Reforms party Great Creationthe Movement for National Rebirth Umid Civic WelfareAdalet (Justice) and the Popular Front of United Azerbaijanmost of which were represented in the previous parliamentwon one seat a piece Civic Solidarity retained its 3 seats andAnaVaten kept the 2 seats they had in the previous legislatureFor the first time not a single candidate from the oppositionAzerbaijan Popular Front (AXCP) or Musavat were elected

We organized a small preelection survey of 2010 electionin Azerbaijan allowing us to construct a model of the election(see [42]) For VHP and AVP the estimation of their partypositions was very sensitive to inclusion or exclusion of onerespondentThus we used only the small subset of 149 voterswho completed the factor analysis questions and intended tovote for YAP or the AXCP+MP coalition

The factor analysis showed that voters were only con-cerned with one dimension the ldquodemand for democracyrdquowith higher values being associated with voters who had anegative evaluation of the current democratic situation inAzerbaijan who did not think that free opinion is allowedhad a low degree of trust in key national political institutionsand expected that the 2010 parliamentary election would beundemocratic Figure 12 shows the distribution of voters andthe party positions at the mean of their supporters (See [42]

minus2 minus1 0 1 2

00

01

02

03

04

05

Demand for democracy

Den

sity

YAP AXCP-MP

YAP activist AXCP-MP activist

Figure 12 Voter distribution and activist positions in the 2010Azerbaijani election

for details of the estimation) In this one dimensional modelthe variance is

1205902A2010 equiv trace (nabla2010G ) = 093 (73)

The binomial logit estimates for the 2010 election withAXCP-MP as the base party in Table 5 are

120582A2010YAP = 130 120582

A2010AXCP-MP equiv 00 120573

A2010 = 134

(74)

All coefficients are significantly nonzero with AXCP-MPhaving the lowest valence If these two parties locate at themean the probability that an Azerbaijani votes AXCP-MPfrom (14) is

120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)

Given that 2120573A2010(1 minus 2120588

A2010AXCP-MP) = 2 times 134 times 058 =

1554 and since 1205902A2010 = 093 from (73) then using (15) the

convergence coefficient for Azerbaijan in Table 6 is

119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)

Given that 119888A2010 is not significantly different from 1 the

dimension of the policy space (see Appendix A3) and thenecessary condition for convergence is not met The onedimensional Hessian of AXCP-MP from (17) is

119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)


Clearly 119862A2010AXCP-MP has a single positive eigenvalue indicating

the AXCP+MP is minimizing its vote share at the originThe 95 bounds of 119862

A2010AXCP-MP in Appendix A3 shows that

this matrix has positive eigenvalues at the lower and upperbounds of the confidence interval Thus with a high degreeof certainty AXCP+MP will deviate from the origin andthe electoral mean is not a LNE for the 2010 election inAzerbaijan

This section illustrates that for the three anocracies thatwe consider the convergence coefficient does not satisfy thenecessary condition for convergence to the mean That isthese convergence coefficients are not significantly differentfrom the dimension of the policy space As a consequenceparties are at a knife-edge equilibrium Under some con-ditions parties converge to the mean under others theydiverge Which equilibrium materializes depends on howpopular or unpopular the Presidentautocrat and his partyare and so depends on the valence of all parties and on howdispersed voters are in the policy space Thus any change invalence can substantially affect party positions

4 Convergence across Political Systems

In the previous sections we used the unifying framework ofSchofieldrsquos [9] stochastic electoralmodel outlined in Section 2to study whether parties locate near or far from the electoralmean for countries with plurality and proportional represen-tation systems and in anocracies Using this framework weestimated the convergence coefficient for various electionsin different countries We will now use this dimensionlesscoefficient to compare convergence to the electoral meanacross elections countries and political systems We canthen illustrate the use of the convergence coefficient toclassify political systems Table 7 presents a summary ofthe convergence coefficients across elections countries andpolitical systems that we now discuss

As Table 7 indicates the two countries using pluralitysystems (the US and the UK) studied in Section 31 meet theconditions for convergence to the mean Thus suggestingthat plurality rule imposes a strong centripetal tendency thatkeeps parties close to the mean Our analysis suggests that incountries with plurality systems the convergence coefficientwill be low at or below the dimension of the policy space

Of the anocratic countries that we studied in Section 33Georgia seems to have the highest convergence coefficient119888G2008 = 242 in (66) which is not different from 2 suggestingthat parties can diverge from the mean (Note that priorto 2008 Georgians had already brought about three majorpolitical changes throughmass popular revoltThis rebelliousldquotraditionrdquo may give opposition candidates the ability toposition themselves away from the mean) The convergencecoefficient of all three anocracies was not significantly dif-ferent than the dimension of the policy space [2 for Georgiaand Russia and 1 for Azerbaijan 119888G2008 = 242 given in (66)119888Ru2007 = 183 in (71) and 119888

A2010 = 144 in (76)] These results

suggest that convergence in anocracies is fragile and dependson the distribution of votersrsquo preferences as well as on thevalences of the autocrat and the opposition parties

The countries with proportional systems studied inSection 32 have convergence coefficients that are signifi-cantly above their two-dimensional policy space signallingthe lack of convergence of small valence parties to the elec-toral mean (fromTable 7 Israelrsquos 119888I1996 = 406 in (46) Turkeyrsquos119888T1999 = 149 in (51) in 1999 and 119888

T2002 = 594 in (56) in 2002 and

Polandrsquos 119888P1997 = 682 in (61)) Having no possibility of forminggovernment these small parties maximize their vote sharesby locating closer to their core supporters Elections lead tomultiparty legislatures producing a highly fragmented partysystem where coalition governments are the norm Note thatchanges to the electoral process in Turkey between 1999 and2002 forced parties to move from locating close to the meanin 1999 to diverging towards their partisan constituencies soas to increase their vote shares in 2002 These results suggestthat in countries with proportional systems with highlyfragmented political parties divergence from the mean is thenorm

We can explain the lack of convergence to the meanin proportional systems with multiparty (gt3) legislatures bynoting that the convergence coefficient 119888 equiv 119888(120582 120573 120590

2) =

2120573[1minus21205881]1205902 in (15) depends on fundamental characteristics

of the electorate These characteristics include the weightgiven by voters to the distance to the partiesrsquo positions 120573 theelectoral variance 1205902 in (16) and the probability that a voterchooses the lowest valence party 1205881 in (14)Thus in countrieswith many parties the smallest low valence parties have littlechance of receiving much support a low 1205881 If in additionvoters care a lot about policy differences (a high 120573) and if theelectorate is very dispersed (a high 120590

2) then small parties willhave an incentive to move towards their core supporters andaway from the mean That is in highly fragmented politieswhere voters and correspondingly parties are very dispersedwe observe high convergence coefficients

In essence Schofieldrsquos [9] Valence theorem gives a simplesummary statistic the convergence coefficient that measuresthe degree of fragmentation or lack thereof in each polityPoland is an extreme case of this fragmentation and cor-respondingly has a very high convergence coefficient (seeTable 7)

The are other measures of political fragmentation in theliterature The effective number of party vote strength (env)used by Laakso and Taagepera [15] serves to measure howmany dominant parties there are in a polity a given electionTo find the env let the Herfindahl index of the election begiven by

119867V =

119901

sum

119895=1

V2119895 (78)

where V119895 is the vote share of party 119895 for 119895 = 1 119901 ThisHerfindahl index 119867V gives a measure of the party size inan election and measures how competitive the election wasLaakso and Taageperarsquos effective number of party vote strengthis then the inverse of 119867V that is

119890119899V = 119867minus1V (79)


Table 7 Convergence and fragmentation

Plurality systemsVariable US BritainPolitical system Presidential ParliamentaryElection year 2000 2004 2008 2005 2010Conv Coefa(conf Intb) 038 (02 07) 045 (02 08) 111 (07 15) 084 (05 13) 095 (09 11)

Converge to mean Yes Yes Yes Yes YesNumber of partiesc 2 2 2 9 9

Presidentenvc 216 205 205

House ofRepresentatives House of Commons

envd 225 218 218 361 374ensd 202 200 200 247 258

Proportional RepresentationIsrael Turkey Poland

Political system Fragmented Fragmented Cut off FragmentedElection year 1996 1999 2002 1997Conv Coefa(conf Intb) 398 (35 46) 149 (07 22) 594 (44 74) 682 (58 78)

Converge to mean No Likely No NoNumber of partiesb 11 9 10 7

Prime Ministerse

envc 200Knesset Parliament Sejm

envc 584 691 562 499ensc 589 635 229 677

AnocraciesmdashpluralityGeorgia Russia Azerbaijan

Political system Presidential Presidential PresidentialElection year 2008 2007 2010Conv Coefa(conf Intb) 242 (20 29) 183 (14 23) 144 (01 30)

Converge to mean No Likely NoPresident President (2008) President (2008)

Number of partiesc 8 4 7

envd 276 188 131Parliamentary Duma (2007) National assembly (2010)

Number of partiesa 5 7 12

envd 256 222 474

ensd 155 194 227aThis is the central estimate of the convergence coefficientbConf Int confidence interval rounded to the nearest tenthcNumber of parties who won votes in the electiondBased on the number of parties who obtained seats in the electioneThis was the first time the Prime Minister was elected on a ballot separate from the Knesset

In the same way we can define the effective number of partyseat strength (119890119899119904) using seat shares instead of vote sharesgiving us a measure of the strength of parties in a legislature

We calculate the 119890119899V and 119890119899119904 for each electionwe consider(see Table 7) using all the parties that obtained votes in eachelection and exclude parties that ran in the election but that


got no votes We now compare the level of fragmentationgiven by the 119890119899V and 119890119899119904 with that given by the convergencecoefficient for each country and each election under the threepolitical systems that we studied

We first examine countries with plurality rule In Table 7we see that for the US the 119890119899V and the 119890119899119904 at the Presidentialand House levels are closely aligned There is little variationbetween the 119890119899V and 119890119899V indices in the three electionsAccording to these indices there is essentially no changein political fragmentation across these three elections Theconvergence coefficient however rises in 2008 relative to2000 and 2004 indicating that in 2008 the dispersion amongvoters was higher than in the previous two elections For theUS the convergence coefficient provides more informationthan do 119890119899V or 119890119899V For the UK the convergence coefficientshows that the electorate was more dispersed in 2010 thanin 2005 (see Tables 2 and 7) This dispersion led to the firstminority government since 1974 which resulted in highereffective number of parties as measured by the 119890119899V and 119890119899VAll three measures 119888 119890119899V and 119890119899119904 indicate that the UnitedKingdom became more fragmented in 2010 Thus in thecountries using plurality the convergence coefficient tends toprovide more information than the 119890119899V and 119890119899119904 numbers doas the convergence coefficient takes into account the degreeof dispersion among the electorate and the valence of parties

Polities with high convergence coefficients (Israel Turkeyin 2002 and Poland in Table 7) had a large number of partiescompeting in these elections The greater the number ofparties obtaining votes and thus effectively competing in theelection led to large 119890119899V values These elections producedhighly fragmented legislatures leading to very high 119890119899119904

values Having a large number of effective parties competingin the election and greater effective number of parties inthe legislature does not necessarily translate into a higherconvergence coefficient The convergence coefficient is lowerfor Israel with a larger number of effective parties (higher 119890119899Vand 119890119899119904) than for Poland with fewer parties Changes in theTurkish electoral system between 1999 and 2002 in which aminimum cut-off rule has instituted led to a high 119890119899V but alow 119890119899119904 Small parties were however able to gain enough votesleading to a high convergence coefficient an indication thatthese parties would disperse themselves in the policy spaceThe 119890119899V and 119890119899119904 values of the 2002 Turkish election show highparty fragmentation but no legislative fragmentation Thisshows that these three measures of fragmentation providedifferent information about a particular election

The convergence coefficient suggests that a way of inter-preting the arguments of Duverger [44] and Riker [45] onthe effects of proportional electoral methods on electoraloutcomes the strong centrifugal tendency pulling all partiesaway from the electoralmean towards their core constituencyThis tendency will be particularly strong for small or lowvalence parties In particular even small parties in such apolity can assign a nonnegligible probability to becoming amember of a coalition government and it is this phenomenonthat maintains the fragmentation of the party system Forexample in Poland no party can obtain a majority andparties and coalitions regularly form and dissolve In general

the convergence coefficients in Poland were of the order of60 in the elections in the 1990rsquos

For countries using proportional representation whilethe 119890119899V and 119890119899119904 give a measure of electoral and legislativedispersion the convergence coefficient provides a measurethat summarizes dispersion across voters and parties in thepolicy space

In the anocratic countries studied the convergence coef-ficient seems in line with the 119890119899V in presidential electionsbut going in the opposite direction in parliamentary elections(see Table 7) In these countries the convergence coefficientdoes not meet the necessary condition for convergence tothe mean These countries that we study show that partiescould either converge to or diverge from the mean underanocracy as the equilibrium is fragile Changes in valencesfor example of the autocrat or in votersrsquo preferences can leadsmall valence opposition parties to diverge from the meanand to mount popular uprisings as happened in previouselections in Georgia or in recent Arab uprisings

The convergence coefficient reflects information that the119890119899V and 119890119899119904 cannot capture as it reflects the preferences ofthe electorate through the policy weight 120573 the perceivedability of parties or candidates to govern as captured by theirvalences 120582 = (1205821 120582119901) and the dispersion of votersrsquopreferences in the policy space 120590

2 All of which are nottaken into account in the 119890119899V and 119890119899119904 Moreover 119890119899V and 119890119899119904

have nothing to say about the dispersion in partiesrsquo positionsrelative to the mean

The analysis carried out in this section suggests that thereis an inverse relationship between the degree of fractionaliza-tion in a polity and the convergence coefficient By our inter-pretation of the nature of the convergence coefficient the con-vergence effect in presidential elections in the United Statesis stronger than in parliamentary elections in Great BritainThat is our results suggest that democratic presidentialsystems have fewer parties and a low convergence coefficientParliamentary democracies operating under plurality ruletend to have more parties than presidential democracies anda somewhat higher convergence coefficient Parliamentarydemocracies operating under proportional representationtend to have multiparty legislatures and high convergencecoefficients Anocratic countries tend to havemultiple partiescompeting in the election but low convergence coefficients asopposition parties remain close to the electoral mean whenPresidentsautocrats have high valences and diverge whenthey do not

5 Conclusion

In this paper Schofieldrsquos [9] Valence Theorem together withmultinomial logit models of elections are used as a unifyingframework to compare the convergence properties of partiesacross elections countries and political systems We foundevidence to support the hypothesis that in countries withproportional representation parties located away from theelectoral mean

We relate the convergence coefficient to the effectivenumber of parties according to both vote (env) and seat (ens)


shares and showed how the characteristics of the electorateand the political regime under which parties operate Thencompare the convergence coefficient to the fractionalizationmeasures provided by the env and ens The advantage of theconvergence coefficient is that it is a summary statistic thatincorporates the preferences of voters the valence of partiesand the dispersion of voters and parties in the policy space

Appendix

A Confidence Intervals

Schofieldrsquos [9] Valence Theorem presented in Section 2perfectly predicts whether parties converge to or diverge fromthe electoral origin Convergence or divergence depends onthe value of the convergence coefficient 119888 equiv 2120573[1 minus 21205881]120590

2 in(15) and on the Characteristic matrix of party 1 with lowestvalence 1198621 = 2120573(1 minus 21205881)nabla minus 119868 in (17) Both 119888 and 1198621 dependon 120573 and on 1205881 = [sum

119901

119896=1exp(120582119896 minus 1205821)]

minus1 in (14)The central estimate of 120573 and of 120582 = (1205821 120582119901) given

by the MNL regressions depend on the sample of voterssurveyed as do 1205881 119888 and 1198621 Thus to make inferences fromempirical models we need the 95 confidence bounds ofthese estimates Using these bounds we assert with somedegree of certainty whether parties converge to or divergefrom the electoral mean or if there is a knife-edge unstableequilibrium

To build these bounds we could perform simulations ofthe election For each simulation we could generate the valueof 120573 120582 = (1205821 120582119901) 1205881 119888 and 1198621 Repeating the simulationmany times would generate their distribution from whichwe could derive their 95 confidence bounds Note that 119888

and 1198621 increase in 120573 and decrease in 1205881 So that given theelectoral covariance matrix nabla and variancetrace 120590

2 in (16) ofan election when in a simulation 120573 has a low value and 1205881

a high one the values of 119888 and 1198621 are low with the oppositebeing true when 120573 is high and 1205881 is low Since we have notperformed simulations for the elections in this study we usethese features of 119888 and 1198621 to generate our confidence bounds

Let 119871 identify the lower and 119880 the upper bounds ofthe 95 confidence intervals of any estimate The MNLestimation for an election gives the confidence bounds of 120573and 1205821 (120573

119871 120573119880) and [120582

1198711 1205821198801 ] To estimate the bounds on 1205881 in

(14) [1205881198711 1205881198801 ] we use the bounds on 1205821 and TaylorrsquosTheorem

which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)

Using (15) and the bounds on 120573 and 1205881 we build theconfidence intervals for the convergence coefficient 119888 asfollows In (15) use 120573

119871 and 1205881198801 to get the lower bound of 119888

119888119871 and use 120573

119880 and 1205881198711 for the upper bound of 119888 119888119880 The 95

confidence interval of the convergence coefficient is then

[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)

Following a similar procedure we estimate the bounds for1198621 using (17) and the corresponding bounds of120573 and 1205881 to getthe bounds for the Hessian of the lowest valence party

[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)

Clearly the bounds for 119888 and 1198621 must be similar to thosegenerated by repeated simulations

Using these procedures we now derive the 95 confi-dence intervals for the central estimates of 1205881 119888 and 1198621 foreach of the elections studied (see summary in Tables 2 4 and6) We first derive the detail of the confidence bounds for the2000 US election then in less detail those of other electionsTable 7 gives the values needed to derive the confidenceintervals for the convergence coefficient of the election

A1 Convergence in Plurality Systems

A11 Confidence Bounds for the 2000 2004and 2008 US Elections

US 2000 Election From Table 1 the 95 confidence intervalfor 120573

US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =

[071 093] Using (A1) the bounds for 120588US2000rep = 04 in (20)

are [120588US2000119871rep 120588

US2000119880rep ] = [035 044] Using these bounds

and (18) the bounds for the convergence coefficient for the2000 US election in (21) from (A2) are

[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)

With 95 confidence the convergence coefficient is below1 meeting the sufficient and thus necessary condition forconvergence to themeanThe bounds on Bushrsquos characteristicmatrix in (22) from (A3) are

[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003

minus003 minus090] [

minus068 minus011

minus011 minus067]]

(A5)

Since the eigenvalues of the lower and upper bounds of119862US2000rep are negative [119862

US2000119871rep = (minus087 minus093) 119862

US2000119880Bush =

(minus079 minus057)] with 95 confidence Bushrsquos vote share is at amaximum when all parties locate at the mean Thus with ahigh degree of certainty the origin is a LNE for the 2000 USelection

US 2004 Election From Table 1 the 95 confidence boundsof 120573

US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =


[082 108] Using (A1) the bounds of 120588US2004rep = 04 in (25)

are [120588US2004119871rep 120588

US2004119880rep ] = [035 044] The bounds for 119888US2004 =

038 in (21) from (A2) and for the characteristic matrix ofBush 119862

2004rep in (27) from (A3) are

[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)

The convergence coefficient is significantly below 1 Bushmaximizes his vote share when located at the origin since theeigenvalues of the lower and upper bounds of119862US2004

rep are neg-ative [119862


US2004119880rep = (minus079 minus057)]

Thus with 95 confidence Bush does not want to move fromthe mean implying that with a great certainty the origin is aLNE for the 2004 US election

US 2008 Election FromTable 1 the bounds of 120573US2008 = 085 are

[120573US1198712008 120573

US1198802008] = [085plusmn196times006] = [073 097] Using (A1)

those of 120588US2008rep in (30) are [120588

US2008119871rep 120588

US2080119880rep ] = [026 035]

So that the bounds for cUS2008 = 11 in (31) from (A2) and forMcCainrsquos characteristic matrix CUS2008

rep in (32) from (A3) are

[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)

The convergence coefficient is not statistically different from 1and thus meets the necessary but not the sufficient conditionfor convergence Since the eigenvalues of the lower andupper bounds of 119862

US2008rep are negative [119862

US2008119871rep = (minus075

minus059) 119862US2008119880rep = (minus037 minus012)] then with 95 confi-

dence McCain stays at the origin With a high degree ofcertainty the mean is an LNE for the 2008 US election

A12 Confidence Bounds for the 2005 and 2010 UK Elections

UK 2005 Election From Table 1 the bounds of 120573UK2005 = 015

are [120573UK1198712005 120573

UK1198802005 ] = [015 plusmn 196 times 001] = [013 017] Using

(A1) those for 120588UK2005lib in (35) are [120588

UK2005119871lib 120588

UK2005119880lib ] =

[018 032] so that those for 119888UK2005 in (36) from (A2) and for

the Liberal Democratsrsquo characteristic matrix 119862UK2005lib in (37)

from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)

With 119888UK2005 not significantly different from 1 the necessary

but not the sufficient condition for convergence to the meanhas been met The eigenvalues of the bounds on 119862

UK2005lib

are negative [119862UK2005119871lib = (minus085 minus064) 119862

UK2005119880lib =

(minus037 minus012)] With 95 confidence the LibDem locate atthe origin and the mean is an LNE of the 2005 UK election


are [120573UK1198712010 120573


(A1) those for 120588UK2010lab in (40) are [120588

UK2010119871lab 120588

UK2010119880lab ] =

[029 032] So that those for 1198882010UK in (41) from (A2) and for

Labourrsquos characteristic matrix 119862UK2010lab in (42) from (A3) are

[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)

The convergence coefficient meets the necessary but not thesufficient condition for convergence to the mean as is notsignificantly different from 1The eigenvalues of the bounds of119862UK2010lib are negative [119862UK2010119871

lab = (minus066 minus048) 119862UK2015119880lab =

(minus056 minus034)] Thus with 95 confidence Labour does not


want to move from the origin and the origin is an LNE of themodel of the 2010 UK election

A2 Convergence in Proportional Systems

A21 Confidence Bounds for the 1996 Israeli Election FromTable 3 the bounds of 120573

I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =

[1207 plusmn 196 times 0065] = [1076 1338] Using (A1) those for120588I1996TW in (45) are [120588

I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying

that those of 119888I1996 in (46) from (A2) and for the TWrsquos

characteristic matrix 119862I1996TW in (47) from (A3) are

[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)

Since 119888I1996 is significantly greater than 2 the necessary

condition for convergence to the electoral mean is not metThe lower and upper bounds of 119862I1996

TW have one negative andone positive eigenvalue [119862I1996119871

119879119882 = (minus048 195) 119862I1996119880TW =

(minus0313 2892)] TW is at a saddle point at both boundsThus with 95 confidence TW locates away from the originand the origin fails to be a LNE for the 1996 Israeli election

A22 Confidence Bounds for the 1999 and2002 Turkish Elections

1999 Turkish Election From Table 3 the bounds of 120573T1999 =

0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =

[0203 0547] Using (A1) those for 120588T1999FP in (50) are

[120588T1999119871FP 120588

T1999119880FP ] = [0046 0145] so that those of 119888

T1999 in

(51) from (A2) and for the FPrsquos characteristic matrix 119862T1999FP

in (52) from (A3) are

[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)

Since 119888T1999 is significantly greater than 2 the necessary

condition for convergence to the mean is not met 119862T1999119871FP

has two negative eigenvalues [119862T1999119871FP = (minus0888 minus0437)]

indicating that at the lower bound FP has no incentive tomove from the origin However119862T1999119880

FP has one negative andone positive eigenvalue 119862

T1999119880FP = (minus0614 0938) thus FP is

at a saddlepoint at the upper bound and wants to move fromthe mean At the central estimate of 119862T1999

FP given in (52) FPis also at a saddlepoint It is more probable that FP wants tomove and that the electoralmean is not a LNE of 1999 Turkishelection


152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]

Using (A1) those for 120588T2002ANAP in (55) are [120588

T2002119871ANAP 120588

T2002119880ANAP ] =

[0038 0133] implying that those of 119888T2002 in (56) from (A2)and for the ANAPrsquos characteristic matrix 119862

T2002ANAP in (57) from

(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)


condition for convergence to the mean has not been metTheeigenvalues of 119862

T2002119871ANAP are all negative 119862T2002119871

ANAP = (minus0878

minus0451) so that at the lower boundANAP remain at themeanHowever at 119862

T2002119880ANAP there is one negative and one posi-

tive eigenvalue 119862T2002119880ANAP = (minus0578 0892) ANAP is at a

saddlepoint and wants to move At the central estimate of119862T2002ANAP in (57) the eigenvalues are both positive and ANAP

is minimizing its vote share There is a high likelihood thatANAP wants to move from the origin and that the electoralmean is not a LNE of 2002 Turkish election

A23 Confidence Bounds for the 1997 Polish Election FromTable 3 the bounds of 120573

P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =

[1739 plusmn 196 times 012] = [1512 1966] Using (A1) thosefor 120588

P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that

those of 119888P1997 in (61) from (A2) and for the UPRrsquos character-istic matrix 119862

P1997UPR in (62) from (A3) are

[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)

With 119888P1997 significantly greater than 2 the necessary con-

dition for convergence to the mean is not met The eigen-values of the bounds of 119862

P1997 are positive [119862

P1997119871UPR =

(1891 1891) 119862P1997119871UPR = (2916 2916)] as are those of the

central estimate of119862P1997 in (62)Thus with a high probability

UPR will not locate at the mean and the electoral mean is nota LNE of 1997 Polish election

A3 Convergence in Anocracies

A31 Confidence Bounds for the 2008 Georgian ElectionFrom Table 5 the bounds of 120573G

2008 = 078 are [120573G1198712008 120573

G1198802008] =

[078 plusmn 196 times 006] = [066 089] Using (A1) those for120588G2008N = 005 in (65) are [120588

G2001198718N 120588

G2008119880N ] = [003 007] So

that those of 119888G2008 in (66) from (A2) and for Natelashvilirsquos

characteristic matrix 119862G2008N in (67) from (A3) are

[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)

Since 119888G2008 is not statistically different from 2 the necessary

condition for convergence is not met The lower boundof 119862

G2008N has one negative and one positive eigenvalue

[119862G2008119871N = (minus0068 0058)] so that at the lower bound Nate-

lashvilirsquos vote share function is at a saddlepoint The upperbound has two positive eigenvalues [119862G200119880

N = (0355 0535)]

so that at the upper boundNatelashvili is minimizing his voteshare At the central estimate of 119862G2008

N in (67) Natelashvili isalso minimizing his vote share Thus with a high probabilityNatelashvili diverges from the mean and the mean cannot bea LNE of the 2008 Georgian election

A32 Confidence Bounds for the 2007 Russian ElectionFromTable 5 the bounds of 120573R

2007 = 0181 are [120573R1198712007 120573

R1198802007] =

[018 plusmn 196 times 001] = [015 020] Using (A1) those for120588R2007SR = 007 in (70) are [120588

R2007LSR 120588

R2007119880SR ] = [004 012] So

that those of 119888R2007 in (71) from (A2) and for SRrsquos characteristicmatrix 119862

R2007SR in (72) from (A3) are

[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)

With 119888R2007 not significantly different from 2 the necessary for

convergence is not met The lower bound of 119862R2007SR has two

negative eigenvalues [119862R2007119871SR = (minus030 minus036)] implying

that at lower bound SRrsquos vote share is at a maximum and SRstays at the origin However at the upper bound there aretwo positive eigenvalues [119862R2007119880

SR = (009 019)] Thus at theupper bound SRrsquos vote share is at minimum and SR wants tomove At the central estimate of119862R2007

SR in (72) SR also has twonegative eigenvalues suggesting that SRwants to remain at theorigin So it seems more likely that SR will stay at the originand that the mean is a LNE of the 2007 Russian election

A33 Confidence Bounds for the 2010 Azerbaijani ElectionFrom Table 5 the bounds for 120573A

2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =

[008 047] So that those of 119888A2010 in (76) from (A2) and forAXCP-MPrsquos characteristicmatrix119862

A2010AXCP-MP in (77) from (A3)

are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]

= [2 (077) (1 minus 2 times 047) (0445) minus 1

2 (191) (1 minus 2 times 008) (0445) minus 1]

= [0037 1428]

(A16)

With 119888A2010 not significantly different from 1 the dimension of

the policy space the necessary and the sufficient (in this case


the same) conditions for convergence are not met This one-dimensional characteristic matrix has positive eigenvalues atthe lower and upper bounds as does the central estimate of119862A2010AXCP-MP = 0445 in (77) It is then very likely that AXCP-

MP locates far from the origin and that the electoral mean isnot an LNE for the 2010 election in Azerbaijan

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

Prepared for presentation at the Journees Louis-AndreGerard-Varet 24-28 June Marseille and for presentation atthe joint LSE-WashU workshop on Comparative politicaleconomy September 2013 This paper is based on worksupported by NSF grant 0715929 and a Weidenbaum Centergrant Earlier versions were completed while Gallego was avisitor at the Center and later while Schofield was the GlennCampbell and Rita Ricardo-Campbell National Fellow at theHoover Institution Stanford

References

[1] A DownsAn EconomicTheory of Democracy Harper and RowNew York NY USA 1957

[2] W H Riker and P C Ordeshook An Introduction to PositivePoliticalTheory Prentice-Hall EnglewoodCliffs NJ USA 1973

[3] D Stokes ldquoSpatial models and party competitionrdquo The Ameri-can Political Science Review vol 57 pp 368ndash377 1963

[4] D Stokes ldquoValence politicsrdquo in Electoral Politics D KavanaghEd pp 141ndash164 Clarendon Press Oxford UK 1992

[5] H Clarke D Sanders M Stewart and P Whiteley OxfordUniversity Press Oxford UK 2005

[6] H Clarke D Sanders M Stewart and PWhiteley PerformancePolitics and the British Voter Cambridge University PressCambridge UK 2009

[7] T J Scotto H D Clarke A Kornberg et al ldquoThe dynamicpolitical economyof support for BarackObamaduring the 2008presidential election campaignrdquo Electoral Studies vol 29 no 4pp 545ndash556 2010

[8] H D Clarke T J Scotto and A Kornberg ldquoValence politicsand economic crisis electoral choice in Canada 2008rdquo ElectoralStudies vol 30 no 3 pp 438ndash449 2011

[9] N Schofield ldquoThemean voter theorem necessary and sufficientconditions for convergent equilibriumrdquo Review of EconomicStudies vol 74 no 3 pp 965ndash980 2007

[10] J M Enelow andM J Hinich ldquoNonspatial candidate character-istics and electoral competitionrdquo Polish Journal of Ecology vol44 pp 115ndash131 1982

[11] J M Enelow and M J Hinich The Spatial Theory of VotingCambridge University Press Cambridge UK 1984

[12] J M Enelow and M J Hinich ldquoA general probabilistic spatialtheory of electionsrdquo Public Choice vol 61 no 2 pp 101ndash1131989

[13] D Sanders H D Clarke M C Stewart and P WhiteleyldquoDowns stokes and the dynamics of electoral choicerdquo BritishJournal of Political Science vol 41 no 2 pp 287ndash314 2011

[14] R D McKelvey and J W Patty ldquoA theory of voting in largeelectionsrdquoGames and Economic Behavior vol 57 no 1 pp 155ndash180 2006

[15] M Laakso and R Taagepera ldquoEffective number of parties ameasure with applications to West Europerdquo Competition andPolitical Science vol 12 pp 3ndash27 1979

[16] N Schofield and I SenedMultiparty Democracy Elections andLegislative Politics Cambridge University Press CambridgeUK 2006

[17] S Ansolabare and J M Snyder ldquoValence politics and equilib-rium in spatial election modelsrdquo Public Choice vol 103 no 3-4pp 327ndash336 2000

[18] T Groseclose ldquoA model of candidate location when onecandidate has a valence advantagerdquoAmerican Journal of PoliticalScience vol 45 no 4 pp 862ndash886 2001

[19] E Aragones and T R Palfrey ldquoMixed equilibrium in a Down-sian model with a favored candidaterdquo Journal of EconomicTheory vol 103 no 1 pp 131ndash161 2002

[20] E Aragones and T R Palfrey ldquoElectoral competition betweentwo candidates of different quality the effects of candidateideology and private informationrdquo Social Choice and StrategicDecisions Studies in Choice and Welfare pp 93ndash112 2005

[21] N Schofield ldquoValence competition in the spatial stochasticmodelrdquo Journal of Theoretical Politics vol 15 no 4 pp 371ndash3832003

[22] N Schofield G Miller and A Martin ldquoCritical elections andpolitical realignments in the USA 1860ndash2000rdquo Political Studiesvol 51 no 2 pp 217ndash442 2003

[23] G Miller and N Schofield ldquoActivists and partisan realignmentin the United Statesrdquo American Political Science Review vol 97no 2 pp 245ndash260 2003

[24] N Schofield and G Miller ldquoElections and activist coalitions inthe United Statesrdquo American Journal of Political Science vol 51no 3 pp 518ndash531 2007

[25] M Peress ldquoThe spatial model with non-policy factors a theoryof policy-motivated candidatesrdquo Social Choice and Welfare vol34 no 2 pp 265ndash294 2010

[26] HD Clarke A Kornberg JMacLeod andT Scotto ldquoToo closeto call political choice in Canada 2004rdquo Political Science andPolitics vol 38 no 2 pp 247ndash253 2005

[27] H D Clarke A Kornberg T Scotto and J Twyman ldquoFlawlesscampaign fragile victory voting in Canadarsquos 2006 federalelectionrdquo Political Science and Politics vol 39 no 4 pp 815ndash8192006

[28] H D Clarke A Kornberg and T Scotto Making PoliticalChoices Toronto University Press Toronto Canada 2009

[29] N Schofield ldquoA valence model of political competition inBritain 1992ndash1997rdquo Electoral Studies vol 24 no 3 pp 347ndash3702005

[30] N Schofield C Claassen U Ozdemir and A ZakharovldquoEstimating the effects of activists in two-party and multi-partysystems comparing the United States and Israelrdquo Social Choiceand Welfare vol 36 no 3 pp 483ndash518 2011

[31] N Schofield C Claassen M Gallego and U Ozdemir ldquoEmpir-ical and formal models of the US presidential elections in 2004and 2008rdquo in The Political Economy of Institutions Democracyand Voting N Schofield and G Caballero Eds pp 217ndash258Springer Berlin Germany 2011

[32] K Train Discrete Choice Methods for Simulation CambridgeUniversity Press Cambridge UK 2003


[33] J K Dow and JW Endersby ldquoMultinomial probit andmultino-mial logit a comparison of choice models for voting researchrdquoElectoral Studies vol 23 no 1 pp 107ndash122 2004

[34] K M Quinn A D Martin and A B Whitford ldquoVoter choicein multi-party democracies a test of competing theories andmodelsrdquo American Journal of Political Science vol 43 no 4 pp1231ndash1247 1999

[35] J E Roemer ldquoA theory of income taxation where politiciansfocus upon core and swing votersrdquo Social Choice and Welfarevol 36 no 3 pp 383ndash421 2011

[36] N Schofield ldquoEquilibria in the spatial stochastic model ofvoting with party activistsrdquo Review of Economic Design vol 10no 3 pp 183ndash203 2006

[37] N Schofield M Gallego and J Jeon ldquoLeaders voters andactivists in the elections in Great Britain 2005 and 2010rdquoElectoral Studies vol 30 no 3 pp 484ndash496 2011

[38] A Arian and M Shamir The Election in Israel 1996 SUNYPress Albany NY USA 1999

[39] N Schofield M Gallego U Ozdemir and A Zakharov ldquoCom-petition for popular support a valence model of elections inTurkeyrdquo Social Choice and Welfare vol 36 no 3 pp 451ndash4822011

[40] N Schofield J S Jeon M Muskhelishvili U Ozdemir andM Tavits ldquoModeling elections in post-communist regimesvoter perceptions political leaders and activistsrdquo inThePoliticalEconomy of InstitutionsDemocracy andVoting N Schofield andG Caballero Eds pp 259ndash301 Springer Berlin Germany 2011

[41] D L Epstein R Bates J Goldstone I Kristensen and SOrsquoHalloran ldquoDemocratic transitionsrdquo American Journal ofPolitical Science vol 50 no 3 pp 551ndash569 2006

[42] N Schofield M Gallego J Jeon and M MuskhelishvilildquoModelling elections in the Caucasusrdquo Journal of ElectionsPublic Opinion and Parties vol 22 no 2 pp 187ndash214 2012

[43] N Schofield and A Zakharov ldquoA stochastic model of the 2007Russian Duma electionrdquo Public Choice vol 142 no 1-2 pp 177ndash194 2010

[44] M Duverger Political Parties Their Organization and Activityin the Modern State John Wiley amp Sons New York NY USA1954

[45] W H Riker Democracy in the United States Macmillan NewYork NY USA 1953


(LNE) where we consider only marginal moves from theposition One of the standard results in formal theory is themean voter theorem where the ldquoNash equilibriumrdquo of a spatialvoting game under votemaximization is one where all partiesposition themselves at the electoral mean (For variants ofthe theorem see Enelow and Hinich [10ndash12]) We call such avector the electoral mean

To study each partyrsquos best response to the electoral situ-ation they face we use the results presented in Schofield [9]Schofield identifies a convergence coefficient denoted 119888 whosevalue determines whether vote maximizing parties convergeor not to the electoral mean This coefficient depends onvarious parameters of the model In particular it dependson the competence valences of the party leaders Using 119895 isin

119875 = 1 119901 to denote the parties the valence of party 119895 120582119895essentially measures the electoral perception of the ldquoqualityrdquoof 119895 the votersrsquo overall common evaluation of the ability of119895rsquos leader to provide good governance The valence terms120582 = (1205821 120582119901) are assumed to be independent of the partyrsquospositions and can be estimated as the intercept term in theappropriate stochastic model of the voter utility function AsSanders et al [13] comment valence theory is based on theassumption that ldquovoters maximize their utilities by choosingthe party that is best able to deliver policy successrdquo Thesevalence terms measure the bias in favor of one another of theparty leaders [14]

The convergence coefficient 119888 also depends on theweight that voters give to the policy differences they havewith the various parties 120573 Lastly 119888 depends on the vari-ancecovariance matrix of the electoral distribution 1205902 Byits construction 119888 equiv 119888(120582 120573 120590

2) is dimensionless and thus

independent of the units of measurement of the variousparameters We use the convergence coefficient to compareresults across elections and countries and to classify politicalsystems

The convergence coefficient is a summary measure thatprovides an estimate of the centrifugal or centripetal forcesacting on the parties The Valence Theorem presented inSection 2 (see Schofield [9] for the proof of this result) showsthat if the policy space is two-dimensional and if 119888(120582 120573 120590

2) lt

1 then the sufficient condition for convergence to the meanhas been met and the ldquolocal Nash Equilibriumrdquo (LNE) (theset of such local Nash Equilibria contains the set of NashEquilibria) is one where all parties locate at the electoralmean On the other hand if 119908 is the dimension of the policyspace and 119888(120582 120573 120590

2) ge 119908 then the LNE if it exists will be

one where at least one party will have an incentive to divergefrom the electoral mean in order to maximize its vote shareThus the necessary condition for convergence to the mean isthat 119888(120582 120573 120590

2) lt 119908

In essence a high empirical convergence coefficient of anelection is a convenient measure of the electoral incentive ofa small or low valence party tomove away from the electoralmean to its core constituency position We can interpreta high value of the convergence coefficient as a measureof the centrifugal tendency exerted on parties pulling themaway from the electoral mean The convergence coefficient istherefore a convenient simple and intuitive way to examine

whether parties will have an incentive to locate close to or farfrom the electoral mean We will show that there is a strongconnection between the values of the convergence coefficientand the nature of the political system under which partiesoperate

We used preelection polls to study elections in severalcountries operating under different political regimes Thefactor analysis done on preelection surveys showed that forall elections the policy space was two-dimensional exceptin Azerbaijan were it was one-dimensional The position ofvoters along this two-dimensional space were then estimatedand their voting intentions used to estimate party positionsWe then ran a multinomial logit (MNL) model for theelection using the estimated party and voter positions Theintercept of the MNL model gives the valences of eachpartyleader Following Schofieldrsquos [9] formal model we rankparties according to their valenceUsing theseMNL estimateswe calculate the convergence coefficient of the election andexamine whether the party with the lowest valence has anincentive to locate close to or far from the electoral origin

When comparing the convergence coefficients acrosscountries we observe that in countries with proportionalrepresentation the convergence coefficient is high and that incountries with plurality systems or in anocracies it is lowThus suggesting that we can use the valence theorem and itsassociated convergence result to classify electoral systems

The convergence coefficients for the 2005 and 2010elections in the UK were not significantly different from 1meeting the necessary condition for convergence to themeanFor the 2000 2004 and 2008 US presidential elections theconvergence coefficient is significantly below 1 in 2000 and2004 thusmeeting the sufficient and thus necessary conditionfor convergence and not significantly different from 1 in2008 only meeting the necessary condition for convergenceWe suggest that the centrifugal tendency in the majoritarianpolities like the United States and theUnited Kingdom is verylow

In contrast the convergence coefficient gives an indi-cation that the centrifugal tendency in Israel Poland andTurkey is very high In these proportional representationsystems with highly fragmented polities the convergencecoefficients are significantly greater than 2 failing to meet thenecessary condition for convergence to the electoral mean

In the anocracies of Georgia Russia and Azerbaijanwhere the Presidentautocrat dominates and controls whocan run in legislative elections the convergence coefficient isnot significantly different from the dimension of the policyspace (2 for Georgia and Russia and 1 for Azerbaijan) failingthe necessary condition for convergence While the analysisGeorgia and Azerbaijan show that not all parties convergeto the mean in Russia it is likely that they did Thus inRussia opposition parties found it difficult to diverge from themean Note that convergence in anocracies may not generatea stable equilibrium as any change in the valence of theautocrat and the oppositionmay cause parties to diverge fromthe mean and may even lead to popular uprising that bringabout changes in the governing parties such as in Georgia inprevious elections or in the Arab revolutions













z = (1199111 119911119895 119911119901) isin 119883119901 (1)


119906119894119895 (119909119894 119911119895) = 120582119895 minus 120573

10038171003817100381710038171003817119909119894 minus 119911119895

10038171003817100381710038171003817

2+ 120598119895 = 119906

lowast119894119895 (119909119894 119911119895) + 120598119895

(2)








120588119894119895 (z) = Pr [119906119894119895 (119909119894 119911119895) gt 119906119894119897 (119909119894 119911119897) forall119897 = 119895]


lowast119894119897 (119909119894 119911119895) forall119897 = 119895]

(3)





120588119894119895 (z) =

exp [119906lowast119894119895 (119909119894 119911119895)]

sum119901

119896=1exp 119906lowast119894119896(119909119894 119911119896)

(4)


119881119895 (z) =

1

119899

sum

119894isin119873

120588119894119895 (z) (5)






119889120588119894119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816zminus119895

= 2120573120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) (6)



119889119881119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816119911minus119895

=

1

119899

sum

119894isin119873

119889120588119894119895

119889119911119895

=

1

119899

sum

119894isin119873

2120573120588119894119895 (1minus120588119894119895) (119909119894minus119911119895) = 0

(7)


sum

119894isin119873

120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) = 0 (8)


119911119862119895 = sum

119894isin119873

120572119894119895119909119894 where 120572119894119895 equiv

120588119894119895 (1 minus 120588119894119895)

sum119894isin119873 120588119894119895 (1 minus 120588119894119895)

(9)






[119906lowast119894119896 (119909119894 119911) minus 119906

lowast119894119895 (119909119894 119911)] = (120582119896 minus 120582119895) (10)


120588119894119895 (z) =

1

sum119901

119896=1exp [119906

lowast119894119896(119909119894 119911119896) minus 119906

lowast119894119895 (119909119894 119911119895)]

= [

119901

sum

119896=1

exp (120582119896 minus 120582119895)]

minus1

(11)


120572119895 equiv

120588119895 (1 minus 120588119895)

sum119894isin119873 120588119895 (1 minus 120588119895)

=

1

119899

(12)


119911119862119895 =

1

119899

sum

119894isin119873

119909119894 (13)




1205881 equiv 1205881(z0) = [

119901

sum

119896=1

exp (120582119896 minus 1205821)]

minus1

(14)


119888 equiv 119888 (120582 120573 1205902) = 2120573 [1 minus 21205881] 120590

2 (15)







































nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)





120582US2000rep = minus043 120582


US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References



























































z = (1199111 119911119895 119911119901) isin 119883119901 (1)


119906119894119895 (119909119894 119911119895) = 120582119895 minus 120573

10038171003817100381710038171003817119909119894 minus 119911119895

10038171003817100381710038171003817

2+ 120598119895 = 119906

lowast119894119895 (119909119894 119911119895) + 120598119895

(2)








120588119894119895 (z) = Pr [119906119894119895 (119909119894 119911119895) gt 119906119894119897 (119909119894 119911119897) forall119897 = 119895]


lowast119894119897 (119909119894 119911119895) forall119897 = 119895]

(3)





120588119894119895 (z) =

exp [119906lowast119894119895 (119909119894 119911119895)]

sum119901

119896=1exp 119906lowast119894119896(119909119894 119911119896)

(4)


119881119895 (z) =

1

119899

sum

119894isin119873

120588119894119895 (z) (5)






119889120588119894119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816zminus119895

= 2120573120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) (6)



119889119881119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816119911minus119895

=

1

119899

sum

119894isin119873

119889120588119894119895

119889119911119895

=

1

119899

sum

119894isin119873

2120573120588119894119895 (1minus120588119894119895) (119909119894minus119911119895) = 0

(7)


sum

119894isin119873

120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) = 0 (8)


119911119862119895 = sum

119894isin119873

120572119894119895119909119894 where 120572119894119895 equiv

120588119894119895 (1 minus 120588119894119895)

sum119894isin119873 120588119894119895 (1 minus 120588119894119895)

(9)






[119906lowast119894119896 (119909119894 119911) minus 119906

lowast119894119895 (119909119894 119911)] = (120582119896 minus 120582119895) (10)


120588119894119895 (z) =

1

sum119901

119896=1exp [119906

lowast119894119896(119909119894 119911119896) minus 119906

lowast119894119895 (119909119894 119911119895)]

= [

119901

sum

119896=1

exp (120582119896 minus 120582119895)]

minus1

(11)


120572119895 equiv

120588119895 (1 minus 120588119895)

sum119894isin119873 120588119895 (1 minus 120588119895)

=

1

119899

(12)


119911119862119895 =

1

119899

sum

119894isin119873

119909119894 (13)




1205881 equiv 1205881(z0) = [

119901

sum

119896=1

exp (120582119896 minus 1205821)]

minus1

(14)


119888 equiv 119888 (120582 120573 1205902) = 2120573 [1 minus 21205881] 120590

2 (15)







































nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)





120582US2000rep = minus043 120582


US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References



















































120588119894119895 (z) = Pr [119906119894119895 (119909119894 119911119895) gt 119906119894119897 (119909119894 119911119897) forall119897 = 119895]


lowast119894119897 (119909119894 119911119895) forall119897 = 119895]

(3)





120588119894119895 (z) =

exp [119906lowast119894119895 (119909119894 119911119895)]

sum119901

119896=1exp 119906lowast119894119896(119909119894 119911119896)

(4)


119881119895 (z) =

1

119899

sum

119894isin119873

120588119894119895 (z) (5)






119889120588119894119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816zminus119895

= 2120573120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) (6)



119889119881119895 (z)119889119911119895

1003816100381610038161003816100381610038161003816100381610038161003816119911minus119895

=

1

119899

sum

119894isin119873

119889120588119894119895

119889119911119895

=

1

119899

sum

119894isin119873

2120573120588119894119895 (1minus120588119894119895) (119909119894minus119911119895) = 0

(7)


sum

119894isin119873

120588119894119895 (1 minus 120588119894119895) (119909119894 minus 119911119895) = 0 (8)


119911119862119895 = sum

119894isin119873

120572119894119895119909119894 where 120572119894119895 equiv

120588119894119895 (1 minus 120588119894119895)

sum119894isin119873 120588119894119895 (1 minus 120588119894119895)

(9)






[119906lowast119894119896 (119909119894 119911) minus 119906

lowast119894119895 (119909119894 119911)] = (120582119896 minus 120582119895) (10)


120588119894119895 (z) =

1

sum119901

119896=1exp [119906

lowast119894119896(119909119894 119911119896) minus 119906

lowast119894119895 (119909119894 119911119895)]

= [

119901

sum

119896=1

exp (120582119896 minus 120582119895)]

minus1

(11)


120572119895 equiv

120588119895 (1 minus 120588119895)

sum119894isin119873 120588119895 (1 minus 120588119895)

=

1

119899

(12)


119911119862119895 =

1

119899

sum

119894isin119873

119909119894 (13)




1205881 equiv 1205881(z0) = [

119901

sum

119896=1

exp (120582119896 minus 1205821)]

minus1

(14)


119888 equiv 119888 (120582 120573 1205902) = 2120573 [1 minus 21205881] 120590

2 (15)







































nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)





120582US2000rep = minus043 120582


US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References



















































[119906lowast119894119896 (119909119894 119911) minus 119906

lowast119894119895 (119909119894 119911)] = (120582119896 minus 120582119895) (10)


120588119894119895 (z) =

1

sum119901

119896=1exp [119906

lowast119894119896(119909119894 119911119896) minus 119906

lowast119894119895 (119909119894 119911119895)]

= [

119901

sum

119896=1

exp (120582119896 minus 120582119895)]

minus1

(11)


120572119895 equiv

120588119895 (1 minus 120588119895)

sum119894isin119873 120588119895 (1 minus 120588119895)

=

1

119899

(12)


119911119862119895 =

1

119899

sum

119894isin119873

119909119894 (13)




1205881 equiv 1205881(z0) = [

119901

sum

119896=1

exp (120582119896 minus 1205821)]

minus1

(14)


119888 equiv 119888 (120582 120573 1205902) = 2120573 [1 minus 21205881] 120590

2 (15)







































nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)





120582US2000rep = minus043 120582


US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

































































nablaUS2000 = [

1205902119864 = 058 120590119864119878 = minus020

120590119864119878 = minus020 1205902119878 = 059

] (18)





120582US2000rep = minus043 120582


US2000 = 082

(19)


minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































minus2 minus1 0 1 2

minus2

minus1

0

1

2


Soci

al p

olic

y

Democrats

Republicans

Bush

Gore

median

005

015

02

02

03025

01

119901(vo

te de

m)

=05


minus2 minus1 0 1 2

minus2

minus1

0

1

2

Economic policy

Soci

al p

olic

y

Bush

Kerry

Median

Democrats

Republicans

005

02

025

01501

119901(vo

te de

m)

=05





120588US2000rep = [

2

sum

119896=1

exp(120582US2000119896 minus 120582

US2000rep )]

minus1

= [1 + exp(043)]minus1 = 040

(20)

minus2 minus1 0 1 2

0

2

1

3

minus2

minus1

Obama

McCain

Economic policy

Soci

al p

olic

y







US2000rep ) =



1198882000US equiv 2120573

US2000 (1 minus 2120588

US2000rep ) 120590

2US2000 = 0328 times 117 = 0384

(21)





119862US2000rep = [2120573

US2000 (1 minus 2120588

US2000rep )] nabla

US2000 minus 119868

= 0328 [

058 minus020

minus020 059] minus 119868

= [

minus081 minus006

minus006 minus081]

(22)






Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References


















































Party 2000 2004 2008 Party 2005 2010






120573










minus004(131)








082(071 093)

095(082 108)

085(073 097)

015(013 017)

086(081 090)


1205902 117 117 163 5607 1462


119896=1exp(120582119896 minus 1205821)]



120588Dem = 04(035 044)

120588Dem = 04(035 044)

120588rep = 03(026 035)

120588Lib = 025(018 032)

120588Lab = 032(029 032)



038(02 065)

045(023 076)

11(071 152)

084(051 125)

098(086 110)








nablaUS2004 = [

1205902119864 = 058 120590119864119878 = minus0177

120590119864119878 = minus0177 1205902119878 = 059

] (23)


2US2004 = trace (nabla2004US ) = 120590

2119864 + 120590

2119878 = 117



120582US2004rep = minus043 120582


US2004 = 095

(24)





120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

















































120588US2004rep = [

2

sum

119896=1

exp (120582US2004119896 minus 120582

US2004rep )]

minus1

= [1 + exp (043)]minus1

= 040

(25)



2004(1minus2120588US2004rep ) =



1198882004US = 2120573

US2004 [1 minus 2120588

US2004rep ] 120590

2US2004 = 038 times 119 = 045

(26)



119862US2004rep = [2120573

US2004 (1 minus 2120588

US2004rep )] nabla

US2004 minus 119868

= 038 [

053 minus018

minus018 066] minus 119868

= [

minus080 minus006

minus006 minus075]

(27)



nablaUS2008 = [

1205902119864 = 080 120590119864119878 = minus0127

120590119864119878 = minus0127 1205902119878 = 083

] (28)



2008) = 1205902119864 +1205902119878 = 163



120582US2008rep = minus084 120582


US2008 = 085

(29)



120588US2008rep = [

2

sum

119896=1

exp(120582US2008119896 minus 120582

US2008rep )]

minus1

= [1 + exp(084)]minus1 = 030

(30)



1198882008US = 2120573

US2008 [1 minus 2120588

US2008dem ] 120590

2US2008

= 068 times 163 = 111

(31)


119862US2008rep = [2120573

US2008 (1 minus 2120588

US2008rep )] nabla

US2008 minus 119868

= 068 [

080 minus0127

minus0127 083] minus 119868

= [

minus046 minus0086

minus0086 minus044]

(32)







minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































minus4 minus2 0 2

0

2

4

minus4

minus2

4

Party positions

Economy

Nat

iona

lism

Lab

Con

Lib




nablaUK2005 = [

1205902Nat = 1646 120590Nat119864 = 000

120590119864Nat = 0067 1205902119864 = 3961

] (33)


2005) = 1205902Nat + 120590

2119864 = 5607


120582UK2005Lab = 052 120582

UK2005Con = 027

120582UK2005Lib equiv 00 120573

UK2005 = 015

(34)


minus2 minus1 0 1 2

0

1

2

minus2

minus1

Voter distribution

Economy

Nat

iona

lism

Lab

Con

Lib



120588UK2005Lib = [

3

sum

119896=1

exp (120582UK2005119896 minus 120582

UK2005Lib )]

minus1

= [1 + exp (052) + exp (027)]minus1

= 025

(35)





1198882005UK = 2120573

UK2005 [1 minus 2120588

UK2005Lib ] 120590

2UK2005

= 015 times 5607 = 084

(36)


1198622005UKLib = [2120573

UK2005 (1 minus 2120588

UK2005Lib )] nabla

UK2005 minus 119868

= 015 [

1646 00

0067 3961] minus 119868

= [

minus075 00

001 minus0406]

(37)




nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

















































nablaUK2010 = [

1205902Nat = 0601 120590Nat119864 = 0067

120590119864Nat = 0067 1205902119864 = 0861

] (38)




120582UK2010Lab = minus004 120582

UK2010Con = 017

120582UK2010Lib equiv 00 120573

UK2010 = 086

(39)



120588UK2010Lab = [

3

sum

119896=1

exp (120582UK2010119896 minus 120582

UK2010Lab )]

minus1

= [1 + exp (021) + exp (004)]minus1

= 0319

(40)

Since 2120573UK2010(1 minus 2120588



in Table 2 is

1198882010UK = 2120573

UK2010 [1 minus 2120588

2010Lab ] 120590

2UK2010

= 0622 times 1462 = 091

(41)


119862UK2010Lab = [2120573

UK2010 (1 minus 2120588

UK2010Lab )] nabla

UK2010 minus 119868

= 0622 [

0601 0067

0067 0861] minus 119868

= [

minus063 0042

0042 minus046]

(42)









Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































Meretz

Labor Olim

Likud

Shas NRP

Moledet

lll Way

0

1

2

minus2


Relig

ion

2

minus1

Gesher

Yahadut

Tzomet

Dem-ArabCommunists



nablaI996 = [

1205902119878 = 100 120590119878119877 = 0591

120590119877119878 = 0591 1205902119877 = 0732

] (43)



120582I1996Lik = 078 120582

I1996Lab = 0999

120582I1996NRP = minus0626 120582

I1996MO = minus1259

120582I1996TW equiv minus2291 120582


120582I1996Merezt equiv 00 120573

I1996 = 1207

(44)



120588I1996TW = [

7

sum

119896=1

exp [120582I1996119895 minus 120582

I1996TW ]]

minus1

= [1 + 1198903071

+ 119890329

+ 1198901665

+ 1198901032

+ 1198900268

+ 1198902291

]

minus1≃ 0014

(45)


I1996TW ) = 2 times 1207 times 0972 = 2346



119888I1996 = 2120573

I1996 (1 minus 2120588

I1996TW ) 120590

2I1996

= 2346 times 1732 = 406

(46)





119862I1996TW = 2120573

I1996 (1 minus 2120588

I1996TW ) nabla

I996 minus 119868

= 2346 [

100 0591

0591 0732] minus 119868

= [

1346 1386

1386 0717]

(47)









0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































0 1 2 3

0

1

2

Religion

ANAP

CHPDSP DYP

FP

HADEP

MHP

minus2

minus1

Nat

iona

lism



Religion

AKP

DYPCHP

HADEP

MHP

ANAPNat

iona

lism

2

1

0

minus1





nablaT999 = [

1205902119877 = 120 120590119877119873 = 078

120590119873119877 = 078 1205902119873 = 114

] (48)


999) = 234


minus1

0 1 2 3

0

1

2

Economic

UPUW

AWS

SLD

PSL UPR

ROP

Soci

al



120582T1999FP = minus016 120582

T1999MHP = 066

120582T1999DYP equiv 00 120582


120582T1999ANAP = 034 120582

T1999CHP equiv 073

120582T1999DSP = 072 120573

T1999 = 038

(49)


FP in (14) is

120588T1999FP = [

7

sum

119896=1

exp [120582T1999119895 minus 120582

T1999FP ]]

minus1

= [1 + 119890082

+ 119890016

+ 119890009

+ 11989005

+ 119890089

+ 119890088

]

minus1≃ 008

(50)


T1999FP ) = 2 times 038 times 084 = 064



119888T1999 = 2120573

T1999 (1 minus 2120588

T1999FP ) 120590

2T1999

= 064 times 234 = 149

(51)


119862T1999FP = 2120573

T1999 (1 minus 2120588

T1999FP ) nabla

T999 minus 119868

= 064 [

120 078

078 114] minus 119868

= [

minus024 0448

0448 minus027]

(52)









120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References























































120573





Valence






minus012(066) 120582PSL

0073(033)


minus0159(090) 120582AWS




minus031(163) 120582UW







minus0071(030)

043lowast(20) 120582UPR








1207(1076 1338)

0375(0203 0547)

1520(1285 1755)

1739(1512 1966)


1205902 1732 234 233 200


119896=1exp(120582119896 minus 1205821)]



120588ITW = 0014

(0006 0034)120588FP = 008

(0046 0145)120588TANAP = 008

(0038 0133)120588PROP = 0007


2) = 2120573[1 minus 21205881]120590


406(3474 4579)

149(0675 2234)

575(4388 7438)

599(5782 7833)






T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References



















































T1999FP FP has no


T1999FP in (52) it



nablaT2002 = [

1205902119877 = 118 120590119877119873 = 074

120590119873119877 = 074 1205902119873 = 115

] (53)





120582T2002ANAP = minus031 120582

T2002MHP = minus012

120582T2002DYP equiv 00 120582

T2002HADEP = 043

120582T2002AKP = 078 120582

T2002CHP equiv 133 120573

T2002 = 152

(54)


ANAP in (14) is

120588T2002ANAP = [

6

sum

119896=1

exp [120582T2002119895 minus 120582

T2002ANAP]]

minus1

= [1 + 119890019

+ 119890031

+ 119890074

+ 119890109

+ 1198901164

]

minus1≃ 008

(55)





119888T2002 = 2120573

T2002 (1 minus 2120588

T20029ANAP ) 120590

2T2002 = 255 times 233 = 594

(56)


T2002 =


119862T2002ANAP = 2120573

T2002 (1 minus 2120588

T2002ANAP) nabla

T2002 minus 119868

= 255 [

118 074

074 115] minus 119868

= [

201 188

188 193]

(57)








nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References


















































nablaP1997 = [

1205902119864 = 100 120590119864119878 = 00

120590119878119864 = 00 1205902119878 = 100

] (58)



are

120582P1997UPR = minus23 120582

P1997UP = minus056

120582P1997ROP equiv 00 120582

P1997PSL = 007

120582P1997UW equiv 073 120582

P1997SLD = 140

120582P1997AWS = 192 120573

P1997 = 174

(59)


TW in (14) is

120588P1997UPR = [

6

sum

119896=1

exp [120582P1997119895 minus 120582

P1997UPR ]]

minus1

= [1 + 1198900048

+ 119890308

+ 119890427

+ 119890377

+ 119890242

]

minus1≃ 001

(60)





119888P1997 = 2120573

P1997 (1 minus 2120588

P1997UPR ) 120590

2P1997

= 341 times 2 = 682

(61)


119862P1997UPR = 2120573

P1997 (1 minus 2120588

P1997UPR ) nabla

P1997 minus 119868

= 341 [

10 00

00 10] minus 119868

= [

241 00

00 241]

(62)










nablaG2008 = [

1205902119863 = 082 120590119863119882 = 003

120590119882119863 = 003 1205902119882 = 091

] (63)




G2008G = 150 120582

G2008P = 053

120582G2008N equiv 00 120573

G2008 = 078

(64)


minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































minus2 minus1 0 1 2

0

1

2

minus2

minus1


Wes

tern

izat

ion

SG

P N




120588G2008N = [

4

sum

119896=1

exp [120582G2008119895 minus 120582

G2008N ]]

minus1

= [1 + 119890256

+ 119890150

+ 119890053

]

minus1≃ 005

(65)





119888G2008 = 2120573

G2008(1 minus 2120588

G2008N ) 120590

2G2008

= 14 times 173 = 242

(66)



119862G2008N = 2120573

G2008 (1 minus 2120588

G2008N ) nabla

G2008 minus 119868

= 14 [

082 003

003 091] minus 119868

= [

015 004

004 028]

(67)







nablaR2007 = [

1205902119863 = 295 120590119863119864 = 013

120590119864119863 = 013 1205902119864 = 295

] (68)




R2007119864119877 equiv 0 120582

R2007LDPR = 0153

120582R2007CPRF = 1971 120573

R2007 = 0181

(69)


120588R2007SR = [

4

sum

119896=1

exp[120582R2007119895 minus 120582

R2007SR ]]

minus1

= [1 + 11989004

+ 1198900553

+ 1198902371

]

minus1≃ 007

(70)


R2007SR ) = 2 times 0181 times 086 = 031



119888R2007 = 2120573

R2007 (1 minus 2120588

R2007SR ) 120590

2R2007

= 031 times 59 = 183

(71)








120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References






















































120573




Valance



130lowast(214)


0153(109)

120582P053lowast(251) 120582SR







078(066 089)

0181(015 020)

134(077 191)


1205902 173 590 093


119896=1exp(120582119896 minus 1205821)]



120588GN = 005

(003 007)120588RSR = 007

(004 012)120588AXCP-MP = 021


2) = 2120573[1 minus 21205881]120590


242(199 289)

183(135 228)

144(0085 2984)




119862R2007SR = 2120573

R2007 (1 minus 2120588

R2007SR ) nabla

R2007 minus 119868

= 031 [

295 013

013 295] minus 119868

= [

minus0086 004

004 minus0086]

(72)


R2007SR in





minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

















































minus4

minus2

0

2

4

6

CPRFSR

ER

LDPR






minus2 minus1 0 1 2

00

01

02

03

04

05


Den

sity

YAP AXCP-MP






120582A2010YAP = 130 120582


A2010 = 134

(74)


120588A2010AXCP-MP = [

2

sum

119896=1

exp [120582A2010119895 minus 120582

A2010AXCP-MP]]

minus1

= [1 + 11989013

]

minus1≃ 021

(75)





119888A2010 = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010

= 1554 times 093 = 1445

(76)



119862A2010AXCP-MP = 2120573

A2010 (1 minus 2120588

A2010AXCP-MP) 120590

2A2010 minus 119868

= 1554 times 093 minus 1 = 0445

(77)














T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References




























































T2002 = 594 in (56) in 2002 and



2) =






119867V =

119901

sum

119895=1

V2119895 (78)


119890119899V = 119867minus1V (79)







envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References





















































envd 225 218 218 361 374ensd 202 200 200 247 258




Prime Ministerse


envc 584 691 562 499ensc 589 635 229 677







envd 256 222 474

















5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References




























































5 Conclusion





Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

















































Appendix




119901

119896=1exp(120582119896 minus 1205821)]








119871 120573119880) and [120582



which asserts that

1205881(1205821 plusmn ℎ) = 1205881 (1205821) plusmn ℎ

1198891205881

1198891205821

= 1205881 (1205821) plusmn ℎ1205881(1205821) [1 minus 1205881(1205821)]

= 1205881 (1205821) [1 plusmn ℎ (1 minus 1205881(1205821))] = [1205881198711 1205881198801 ]

(A1)



119888119871 and use 120573



[119888119871 119888119880] = [2120573

119871[1 minus 2120588

1198801 ] 1205902 2120573119880[1 minus 2120588

1198711 ] 1205902] (A2)


[1198621198711 1198621198801 ] = [2120573

119871[1 minus 2120588

1198801 ] nabla minus 119868 2120573

119880[1 minus 2120588

1198711 ] nabla minus 119868]

(A3)






US2000 = 082 are [120573

US1198712000 120573

US1198802000] = [082 plusmn 196 times 006] =


are [120588US2000119871rep 120588



[119888US1198712000 119888

US1198802000 ]

= [2 (071) (1 minus 2 times 044) (117)

2 (093) (1 minus 2 times 035) (117)]

= [020 065]

(A4)


[119862US2000119871rep 119862

US2000119880rep ]

= [2 (071) (1 minus 2 times 044) [

058 minus020

minus020 059] minus 119868

2 (093) (1 minus 2 times 035) [

058 minus020

minus020 059] minus 119868]

= [[

minus090 minus003


minus068 minus011

minus011 minus067]]

(A5)



US2000119880Bush =



US2004 = 095 is [120573

US1198712004 120573

US1198802004] = [095 plusmn 196 times 007] =



are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References

















































are [120588US2004119871rep 120588




[119888US1198712004 119888

US1198802004 ] = [2 (082) (1 minus 2 times 044) (117)

2 (108) (1 minus 2 times 035) (117)]

= [023 076]

[119862US2004119871rep 119862

US2004119880rep ]

= [2 (082) (1 minus 2 times 044) [

058 minus018

minus018 059] minus 119868

2 (108) (1 minus 2 times 035) [

058 minus018

minus018 059] minus 119868]

= [[

minus089 minus004


minus062 minus012

minus012 minus062]]

(A6)







[120573US1198712008 120573



US2008119871rep 120588

US2080119880rep ] = [026 035]



[119888US1198712008 119888

US1198802008 ] = [2 (073) (1 minus 2 times 035) (163)

2 (097) (1 minus 2 times 026) (163)]

= [071 152]

[119862US2008119871rep 119862

US2008119880rep ]

= [2 (073) (1 minus 2 times 035) [

080 minus013

minus013 083] minus 119868

2 (097) (1 minus 2 times 026) [

080 minus013

minus013 083] minus 119868]

= [[

minus065 minus006


minus026 minus012

minus012 minus023]]

(A7)



US2008119871rep = (minus075





are [120573UK1198712005 120573



UK2005119871lib 120588

UK2005119880lib ] =



from (A3) are

[119888UK1198712005 119888

UK1198802005 ] = [2 (013) (1 minus 2 times 032) (561)

2 (017) (1 minus 2 times 018) (561)]

= [051 125]

[119862UK2005119871lib 119862

UK2005119880lib ]

= [2 (013) (1 minus 2 times 032) [

165 000

000 396] minus 119868

2 (017) (1 minus 2 times 018) [

165 000

000 396] minus 119868]

= [[

minus085 000

000 minus064] [

minus063 000

000 minus012]]

(A8)



UK2005lib


UK2005119880lib =



are [120573UK1198712010 120573



UK2010119871lab 120588

UK2010119880lab ] =



[1198882010119871UK 119888

2010119880UK ] = [2 (081) (1 minus 2 times 032) (146)

2 (090) (1 minus 2 times 029) (146)]

= [086 110]

[119862UK2010119871lib 119862

UK2010119880lib ]

= [2 (081) (1 minus 2 times 032) [

060 007

007 086] minus 119868

2 (090) (1 minus 2 times 029) [

060 007

007 086] minus 119868]

= [[

minus065 004

004 minus049] [

minus055 005

005 minus035]]

(A9)








I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References



















































I1996 = 1207 are [120573

I1198711996 120573

I1198801996] =


I1996119871TW 120588

I1996119880TW ] = [0006 0034] implying



[119888I1198711996 119888

I1198801996] = [2 (1076) (1 minus 2 times 0034) (1732)

2 (1338) (1 minus 2 times 0006) (1732)]

= [3474 4579]

[119862I1996119871TW 119862

I1996119880TW ]

= [2 (1076) (1 minus 2 times 0034) [

100 0591

0591 0732] minus 119868

2 (1338) (1 minus 2 times 0006) [

100 0591

0591 0732] minus 119868]

= [[

1006 1185

1185 0468] [

1644 1563

1563 0935]]

(A10)




119879119882 = (minus048 195) 119862I1996119880TW =




0375 are [120573T1198711999 120573

T1198801999] = [0375 plusmn 196 times 0088] =


[120588T1999119871FP 120588


T1999 in



[119888T1198711999 119888

T1198801999] = [2 (0203) (1 minus 2 times 0145) (234)

2 (0547) (1 minus 2 times 0046) (234)]

= [0675 2234]

[119862T1999119871FP 119862

T1999119880FP ]

= [2 (0203) (1 minus 2 times 0145) [

120 078

078 114] minus 119868

2 (0547) (1 minus 2 times 0046) [

120 078

078 114] minus 119868]

= [[

minus0654 0225

0225 minus0671] [

0192 0775

0775 0132]]

(A11)










152 are [120573T1198712002 120573

T1198802002] = [152 plusmn 196 times 012] = [1285 1755]


T2002119871ANAP 120588

T2002119880ANAP ] =



(A3) are

[119888T1198712002 119888

T1198802002] = [2 (1285) (1 minus 2 times 0133) (233)

2 (1755) (1 minus 2 times 0038) (233)]

= [4338 7438]

[119862T2002119871ANAP 119862

T2002119880ANAP ]

= [2 (1285) (1 minus 2 times 0133) [

118 074

074 115] minus 119868

2 (1755) (1 minus 2 times 0038) [

118 074

074 115] minus 119868]

= [[

minus0660 0213

0213 minus0669] [

0172 0735

0735 0142]]

(A12)




ANAP = (minus0878







P1997 = 1739 are [120573

P1198711997 120573

P1198801997] =


P1997UPR in (60) are [120588

P1198711997 120588

P1198801997] = [0002 0022] so that



[119888P1198711997 119888

P1198801997] = [2 (1512) (1 minus 2 times 0022) (2)

2 (1966) (1 minus 2 times 0002) (2)]

= [5782 7833]


[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References
















































[119862P1198711997 119862

P1198801997]

= [2 (1512) (1 minus 2 times 0022) [

1 0

0 1] minus 119868

2 (1966) (1 minus 2 times 0002) [

1 0

0 1] minus 119868]

= [[

1891 0000

0000 1891] [

2916 0000

0000 2916]]

(A13)




P1997119871UPR =






2008 = 078 are [120573G1198712008 120573

G1198802008] =


G2001198718N 120588

G2008119880N ] = [003 007] So



[119888G1198712008 119888

G1198802008] = [2 (066) (1 minus 2 times 007) (173)

2 (089) (1 minus 2 times 003) (173)]

= [199 289]

[119862G2008119871N 119862

G2008119880N ]

= [2 (066) (1 minus 2 times 007) [

082 003

003 091] minus 119868

2 (089) (1 minus 2 times 003) [

082 003

003 091] minus 119868]

= [[

minus006 003

003 005] [

037 005

005 052]]

(A14)






N = (0355 0535)]




2007 = 0181 are [120573R1198712007 120573

R1198802007] =


R2007LSR 120588

R2007119880SR ] = [004 012] So



[119888R1198712007 119888

R1198802007] = [2 (015) (1 minus 2 times 012) (59)

2 (015) (1 minus 2 times 004) (59)]

= [135 228]

[119862R2007119871SR 119862

R2007119880SR ]

= [2 (015) (1 minus 2 times 012) [

295 013

013 295] minus 119868

2 (02) (1 minus 2 times 004) [

295 013

013 295] minus 119868]

= [[

minus033 003

003 minus033] [

014 005

005 014]]

(A15)








2010 = 134 are [120573A1198712010 120573

A1198802010] =


A2010AXCP-MP = 021 in (75) are [120588

A2010119871AXCP-MP 120588

A2010119880AXCP-MP] =



are

[119888A1198712010 119888

A1198802010] = [2 (077) (1 minus 2 times 047) (093)

2 (191) (1 minus 2 times 008) (093)]

= [0085 2984]

[119862A2010119871AXCP-MP 119862

A2010119880AXCP-MP]



= [0037 1428]

(A16)








Acknowledgment


References




















































Acknowledgment


References





























































Documents

The convergence coefficient across political systems