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European Politics and Society

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Scottish secession and voter turnout: simulatingthe effects of full voter turnout without Scottishparticipation in the union

Allan M. Wilford & Kevin Krivacsy

To cite this article: Allan M. Wilford & Kevin Krivacsy (2015): Scottish secession and voterturnout: simulating the effects of full voter turnout without Scottish participation in the union,European Politics and Society, DOI: 10.1080/07036337.2015.1109916

To link to this article: http://dx.doi.org/10.1080/07036337.2015.1109916

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Scottish secession and voter turnout: simulating the effects offull voter turnout without Scottish participation in the unionAllan M. Wilforda and Kevin Krivacsyb

aDepartment of Political Science, University of Tennessee, Knoxville, USA; bDepartment of Geography,University of Tennessee, Knoxville, USA

ABSTRACTThis paper examines how increases in voter turnout might allowLabour to remain competitive in future general elections ifScottish representation is removed from Parliament or Labourcontinues to remain uncompetitive in Scotland. The loss ofScottish representation would be deleterious to Labour’sprospects of gaining sizeable majorities again in Parliament.However, this prospect may be mitigated by an increase in voterturnout, as much has been made of the benefits that left partiescan accrue with across the board increases in voter turnout. Usingmethods of multiple imputation, our analysis shows that Labourcan modestly increase their vote share at full voter turnout, whilethe Conservatives consistently experience declining share. Resultsfrom this study also demonstrate that Labour losses could bemitigated by increasing voter turnout in the remainder of the UK.Using multinomial probit models for several elections, we are alsoable to see changes in the impacts of demographic attributes onvote choice. Combined, these results allow for an understandingof how Labour might mitigate the impact of losing Scottishrepresentation in Parliament.

KEYWORDSFull voter turnout; Scotland;voter turnout; resource-based theory; voterparticipation; UnitedKingdom General Election

Introduction

The recent referendum on Scottish secession from the UK afforded commentators theopportunity to speculate on some of the ramifications that a successful ‘yes’ vote wouldhave on the political landscape in the UK. While the vote was defeated and the possibilityof a second referendum is still far from certain, Labour’s poor showing in the 2015 GeneralElection effectively brought about the demise of Labour in Scotland. Could the loss ofScottish representation, while a body-blow to the Labour Party under current levels ofturnout, perhaps be mitigated by pursuing a strategy of increased voter turnout? Theresource-based theory of voter turnout suggests that Labour might gain seats in theremainder of the UK under increased levels of turnout (DeNardo, 1980; 1986). By simulat-ing full voter turnout in the UK, we can test these propositions in an empirical manner. Ourfirst hypothesis suggests that Labour is more likely to benefit from full voter turnout thanthe Conservatives in UK elections. Our second hypothesis concerns a hypothetical UKwithout Scottish representation, examining how prospective Labour Party loses may be

© 2015 Taylor & Francis

CONTACT Allan M. Wilford allanwilford@yahoo.co.uk

EUROPEAN POLITICS AND SOCIETY, 2015http://dx.doi.org/10.1080/07036337.2015.1109916

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mitigated by full voter turnout. To simulate full voter turnout, we will utilize methods ofmultiple imputation. The data sets that we will utilize will be the 2001, 2005 and 2010British Election Studies (BES).1

If Scotland does eventually secede from the UK in the near future, or by proxy thisoccurs through the Scottish Nationalists continued dominance of Scottish politics, the pol-itical landscape in the UK could be changed quite dramatically, with especially deleteriousconsequences for Labour’s chances of holding a large working majority. Yet, if theresource-based theory of voter turnout holds for the UK, prospective Labour lossescould be mitigated by promoting greater electoral participation across the remainder ofthe UK, and it is this hypothetical that we will explore further in this paper. This paper isorganized into several sections. Firstly, we will explore how the resource-based theoryof voter turnout applies in the UK context and identify what effects we might expect tofind in the UK with full voter turnout. The next section will detail our main hypothesisand will be followed by a section detailing our methodology used for estimating fullvoter turnout throughout the UK. Finally, there will be our results section that willdiscuss our findings alongside a concluding section that will highlight the main findingsof this paper.

Voter turnout

The 2014 vote on Scottish independence from the UK ultimately ended with defeat for theindependence movement and the survival of the 300-year-old political union. While thereferendum produced a decisive result, over 1.5 million Scots did vote to end the unionand a majority of citizens from Glasgow voted for independence. While many havesuggested that the question of independence for Scotland may now be put to rest for ageneration, it seems unlikely that this issue will be settled over the long term. Scottishnationalists may well become emboldened by the closeness of the campaign and encour-aged to re-visit this question sooner rather than later. In certain respects, the eventualresult did not matter, as the campaign has firmly put the question of further autonomyand possibly independence for Scotland at the forefront of British politics. Furthermore,the success of the Scottish Nationalist Party (SNP) in the 2015 General Election under-scored this changing dynamic, with Labour’s poor showing in Scotland effectively remov-ing Scottish representation from Westminster.

While a future referendum and subsequent vote for independence is far from certainand the SNP’s dominance of Scottish politics may not continue indefinitely, the removalof Scottish MPs from voting in Parliament would see the balance of power changed dra-matically as 59 Scottish seats will be permanently removed from the equation. Many ofthese seats have of course long been Labour strongholds, this allied to the fact that theConservatives have remained competitive in general elections often without a presencein Scotland, means that the political stakes for Labour are high. Save a further Labour rea-lignment to the right, the competitive balance in Parliament may well be permanentlyskewed in the favour of the Tories for the foreseeable future. While it is true thatLabour can still win a majority in Parliament without Scottish representation (as wouldhave happened in the 1997, 2001 and 2005 general elections), Labour may well find ithard to gain a sizeable majority in Parliament again on her current platform.

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Labour’s predicament may be alleviated by pursuing a strategy of increasing the levelsof voter turnout throughout the remainder of the UK. While all political parties are in thebusiness of increasing their own support, centre-left parties like Labour may have more togain than the Conservatives by seeing a general increase in voter turnout. The resource-based theory of voter turnout highlights how resource-poor individuals are less likely tovote in elections than more resource-rich individuals (Lazarsfeld et al., 1944; Wolfinger &Rosenstone, 1980, Blais et al., 1998). This theory of voting behaviour can then be directlyapplied to the behaviour and characteristics of individuals in particular parties to predictvoting levels of a party (Bernhagen & Marsh, 2006). Socio-economic factors can thereforenot only predict an individual’s’ expected party of choice, but also an individual’s’ propen-sity to cast a vote. That resource-rich individuals are more likely to vote in elections seemsa reasonable hypothesis to make considering their greater resources compared toresource-poor individuals. This behaviour is often explained by examining existing barriersto voting inherent in all democracies, barriers that are often too costly for many resource-poor individuals to overcome. Work from Lazarsfeld et al. (1944) found that sociologicalfactors influenced voting behaviour. In particular, social–economic status is a strong deter-minant of voting behaviour, a conclusion buttressed by decades of subsequent research(Wolfinger & Rosenstone, 1980). While many democratic systems are relatively easy tonavigate and cast a successful vote, such as the British system, others have significanthurdles to overcome before a vote can be cast, as in the US system (Blaise et al., 1998).This all combines to create barriers to voting for resource-poor individuals, individualsthat tend to vote for left and centre-left parties like Labour.

The assumption that many non-voters would favour left parties if they actually votedhas a modest record in extant literature. Early work examining this effect by DeNardo(1980) failed to find this expected effect in the US, instead finding that heavy turnout inCongressional races punished the majority party. Other studies of voting patterns in theUS during the first half of the twentieth century found that increased levels of turnoutactually helped Republicans (Tucker & Vedlitz, 1986; Nagel & McNulty, 2000). Later analysisby Erikson (1995) and Radcliff (1994) that focused on the second half of the twentiethcentury found that elections with high levels of turnout did benefit the Democrats asexpected. Citrin et al. (2003) utilized more novel methods to simulate full voter turnoutby comparing census data with exit-poll data in US Senate races. This approach again pro-duced only modest results, lending only a degree of support to the partisan theory. Analternative approach by Brunell and DiNardo (2004) utilized a semiparametric methodto simulate full turnout. However, echoing much of the work in the US context, this alsoshowed similarly modest support for the partisan theory.

Outside of the American context, Pacek and Radcliff (1995) uncovered a stronger posi-tive relationship between increases in turnout and support for left parties. The authorsshowed that left parties like the Democrats in the US would realize fewer gains athigher levels of turnout than say the Swedish Democrats, as lower status individualssupport the Swedish Democrats more uniformly than their counterparts in the US. In asimilar vein, Anderson and Beramendi (2012) expand upon the notion that not allparties on the left target low-income voters to the same extent. In societies with veryhigh levels of income inequality and a dearth of parties on the left, left parties havelittle incentive to target lower income voters. Lee and Hwang (2012) utilized methodsof multiple imputation on survey data to predict how non-voters might vote in elections

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in South Korea. The gains for left parties were enough to change election results in at leastone general election. The advantage that this approach holds over previous methods ishow the vote choice of peripheral voters can be predicted by comparing the socio-demo-graphic factors of non-voters to actual voters. Finally, Grofman, Guillermo, and Collet(1999) alongside Hansford and Gomez (2010) take a different approach to this question.They suggest that rather than being independent, there is in fact an endogenous relation-ship between turnout and voter choice. Individuals may not vote as they perhaps see fewmeaningful differences between the candidates and also may care little for the candidates:to assume increased turnout would benefit left parties is to mistake non-voters as similarto voters.

If the resource-based theory of voter turnout is correct, Labour should have much togain from an increase in voter turnout. However, the possibility exists that this theorydoes not hold for leftist parties at all times. Institutions such as strong unions coulddilute the effects that full voter turnout may have on left-wing parties, as participationrates may already be high for these individuals. It is also often suggested that countrieswith high levels of unionization are often associated with high levels of political efficacyand participation for left-leaning voters (Radcliff & Davis, 2000; Franklin, 2004). Theability of strong unions to mobilize left-leaning voters to ‘get out and vote’ may temperincreases for left-wing parties as voter turnout approaches 100 per cent. However, forthe UK, the dramatic decline in rates of unionization and relative power of unions com-pared to central government over the last quarter of a century should dampen any poten-tial increase in voter turnout that unions may have upon the electorate (Machin, 2002).

The nature of the electoral system may also play a part in which types of party benefitmost from an increase in voter turnout. While we would expect left-wing parties to benefitacross most countries, in the single member first-past-the post electoral system in the UKminor parties of all hues may also benefit greatly from an increase in voter participation.Electoral systems that are broadly proportional representation (PR) are often seen as moreeffective at representing voters true preferences, and thus should see less disenfranchisedvoters and greater voter turnout as satisfaction with the system increases (Radcliff & Davis,2000). This is in stark contrast to a single member winner take-all form of representationthat is present in the UK, in which voters may feel disenfranchised and less likely to vote ifthey believe casting their vote is of little utility (Powell, 1986; Jackman, 1987). When wesimulate full voter turnout, we should also see a rise in support for smaller parties in asingle member system like the UK, an effect that may not be present in a PR system.Parties like the Liberal Democrats, the SNP and many other smaller parties should seean increase in their share much like Labour would under an increase in voter turnout.

The UK has seen a significant decline in turnout levels in recent elections. The 2001General Election is often seen as a watershed election, witnessing an unprecedenteddecline in voter turnout, falling 12 percentage points from 1997 to a historic low of just59.6% (Heath, 2007). Voter turnout in the 2010 General Election was just a little higherat 65.1% of eligible voters (Sanders et al., 2010). Therefore, a possibility does exist thatfull voter turnout may shift the political landscape significantly, as there is of coursemore than a third of votes potentially still uncast. By examining hypothetical full voterturnout in the UK, we can examine both the expected advantages that Labour couldgain from a UK both in its present form and if Scottish representation is removed. Further-more, the socio-economic factors associated with each party can also be analysed to

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identify which groups are more likely to vote for a particular party at full voter turnoutlevels. This analysis will identify which socio-economic groups are associated with eachparty and at what levels, as we examine both current voter turnout and full voter turnout.

Hypothesis

While the literature on voter turnout is far from settled, there is evidence showing thatresource-poor citizens are less likely to vote than resource-rich citizens (Lazarsfeld et al.,1944; Wolfinger & Rosenstone, 1980; Blaise et al., 1998). Political parties that appeal toresource-poor constituents may have a more difficult time getting these individuals tovote in elections. In the UK, resource-poor individuals have traditionally voted heavilyfor Labour, while more affluent members of society have voted for the Conservativesand to a lesser degree the smaller third party the Liberal Democrats (Denver, 2003). Forthe UK, any across the board increase in voter participation would likely help theLabour Party most keenly and the Conservatives to a lesser degree. We should alsoexpect that due to the nature of the political system used in the UK, smaller less politicallyviable parties should also benefit from full voter turnout. For these parties, ideology maybe less important than actual party size. As we simulate full voter turnout, disenfranchisedsupporters of small parties would expect to see an increase in these parties share of thevote as these votes are now captured. We should therefore see a ‘bump’ for all of theseparties. Therefore, our hypotheses for this paper are as follows:

Hypothesis 1: Ceteris paribus, the Labour Party is more likely to benefit from full voterturnout than the Conservative Party.

Hypothesis 2: Ceteris paribus, minor British political parties are more likely to benefitfrom full voter turnout than the Conservative Party.

Conventional wisdom suggests that the removal of Scottish representation from West-minster through secession, or the SNP’s continued dominance in Scotland, may provecostly for Labour’s prospects of forming a government (Hassan & Fraser, 2004). If theresource-based theory of voting is correct, and Labour losses can be mitigated to somedegree by full voter turnout, Labour may have much to gain from pursuing strategies ofincreasing voter turnout throughout the UK.

Methodology

In order to investigate the three stated hypotheses, it is necessary to employ differentmethodological approaches for each to gain an understanding regarding the effects ofthe removal of Scottish representation, demographics and voter turnout on the potentiallychanging political landscape in the UK.

The primary approach used in this research is to utilize a method of multiple imputationto simulate full voter turnout, when we have a data set where some data are missing atrandom as is the case with the BES.2 This data set and others often poses item non-response and survey non-response. While little can be done about survey non-response,there are many observations in this data set where the people surveyed did not vote ortheir vote choice was not recorded. However, all of the other ancillary information thatthe survey is concerned with is still collected. Thus, by using the methods of multiple

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imputation, we simulate the vote choice for these people along with values of missingdata for other variables using this information.

Then, multinomial probit models are conducted not only on actual voter turnout situ-ations (the original BES data set) but also on simulated full voter turnout (the data set afterconducting multiple imputation).3 We run several multinomial probit models on the UKand the UK without Scottish representation, along with other model specifications in anattempt to understand the relationship between our variables of interest and voting out-comes, and how this relationship may change across our study years and across differ-ences in the geographical area of the UK.

Running these multinomial probit models on the actual survey data as well as theassumed full voter turnout data allows for conclusions concerning the differences inimpacts of our independent variables with actual voter turnout survey data, comparedto estimated full voter turnout voting data along with changes in the impact of these vari-ables across years. Multinomial probit models are utilized in this study in order to relax theIIA assumption as we cannot state what would happen if one of the choices is removedfrom the choice of political parties.4 Perhaps people would not vote at all if one ormore choices were removed. The dependent variable of vote choice in these modelshas been recoded to have four possible outcomes: Labour (1), Conservative (2), LiberalDemocrats (3) and other (4). All of the multinomial probit models are estimated usingthe MNP package in R (Imai & Dyk, 2005). This package fits the Bayesian multinomialprobit models via Markov Chain Monte Carlo techniques and Gibbs sampling.

The original survey data utilized from the University of Essex are assumed to be an accu-rate representation of actual voter turnout for each election.5 Using the Amelia R package(Honaker et al., 2013), we then impute missing values in the data set in order to create anew data set that is assumed to be an accurate representation of full voter turnout in theUK for the 2001, 2005 and 2010 general elections. This is done for each election year ofinterest. The Amelia package uses all the information in the data set to impute missingvalues for variables, thus providing better and more accurate results than simply droppingthe observations in the data that are only partially observed (i.e. listwise deletion method)as there would likely be bias in those missing observations. The actual values in the dataset remain the same of course. However, the missing values are filled in where separatecoefficients are produced and then combined by taking their mean.6

The Amelia package accomplishes this multiple imputation process using an iterativeexpectation–maximization algorithm for the maximum likelihood estimators for missingvalue imputation, in situations where data are missing at random or missing at completerandom (Honaker et al., 2013). In other words, this approach uses the existing data onmany different demographic attributes and survey answers to impute missing values forour variables including vote choice and vice versa. This method is a better approachthan listwise deletion and other methods of handling missing data for a variety ofreasons. For example, multiple imputation reduces bias and increases efficiency(Honaker et al., 2013). However, a precarious assumption when using the Ameliapackage is that it assumes that both the observed data and the unobserved data are multi-variate normal. The missing values are filled in with a sample of values from the predictivedistribution of missing data.7

In conclusion, there are twomain methods employed in this research study, that of mul-tinomial probit models and multiple imputation procedures for missing data. This research

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utilizes several multinomial probit models to understand the determinants of vote choicein different situations as well as multiple imputation techniques to understand the impactof full voter turnout compared to actual voter turnout in a variety of situations and timeperiods and across the major political parties. These techniques are also conducted withthe inclusion of Scotland and without the inclusion of Scotland to determine the effectsof full voter turnout on political parties in the case of a successful Scottish secession or con-tinued SNP dominance in Scotland. Thus, when combined, these results provide us with animportant understanding of the political dynamics in the UK and the impact that theremoval of Scottish representation may have on the political landscape in the UK.

Multiple imputation procedures are used to create data sets assuming full voter turnoutwhere the percentage of votes obtained by each political party are then calculated. Thesituations in which these vote percentages are calculated for different years and differentpolitical situations. Their implications for our hypotheses can be found in the next section.For example, we look at the difference between actual vote share and full voter turnout forthe major political parties across the full UK, the UK without Scottish representation andjust Scotland. These modelling approaches will allow the Labour Party to understandhow voter turnout from certain types of groups can enhance their chances of success ina kingdom without Scotland as well as further our understanding regarding generalvoting patterns in the UK.

Data analysis I

We begin our data analysis by examining some socio-demographic factors that are rel-evant to our hypothesis. In Tables 1 and 2, the first column represents coefficient estimates

Table 1. Multinomial probit model of party choice in UK elections (2001–2010).†

Conservative party Liberal democrats

Dep var. Actual turnout Full turnout Actual turnout Full turnoutParty choice Model 1.1 Model 1.2 Model 1.3 Model 1.4

Income 0.106*** 0.120*** 0.0270 0.068***(0.025) (0.006) (0.030) (0.009)

White British 0.276*** 0.330*** −0.029 0.168***(0.081) (0.025) (0.116) (0.026)

Union member −0.430*** −0.451*** −0.022 −0.170***(0.099) (0.021) (0.106) (0.026)

Married 0.070** 0.078*** −0.140** −0.066***(0.025) (0.013) (0.045) (0.013)

Male −0.066** −0.084*** −0.064 −0.046**(0.026) (0.014) (0.037) (0.015)

Democratic satisfaction −0.485** −0.481*** −0.571*** 0.461***(0.175) (0.029) (0.079) (0.045)

Age 0.083*** 0.081*** −0.085** −0.009(0.013) (0.006) (0.032) (0.006)

Constant −1.089** −0.818*** −0.323 −0.347***(0.415) (0.109) (0.243) (0.050)

N 15,068 142,545 15,068 142,545

Source: 2010, 2005 and 2001 British Election Studies (University of Essex).Notes: Missing values are imputed based on Amelia II program (Honaker et al., ‘Amelia II’).†The base category is ‘Labour Party’, two-tailed tests.***p ≤ 0.001.**p ≤ 0.01.*p ≤ 0.05

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from a MNP model using actual turnout from our data and the second column representsthe hypothetical full voter turnout model. Our baseline for both models is the Labour Partyand we can make use of the coefficient estimates to measure what factors affect voterchoice for both the Conservatives and the Liberal Democrats in a British general election.Minor parties are not discussed or highlighted in this section due to the very low numbersin the survey. Table 1 measures the relevant factors associated with voter choice and socio-demographic factors, and broadly illustrate how voter choice is affected differently under ahypothetical full voter turnout scenario. The data from the three elections (2001, 2005 and2010) are pooled. The parties’ share of votes, and perhaps even election outcomes, will beaffected in some degree by these changing voter preferences under a hypothetical fullvoter turnout general election in the UK.

All of our coefficients in Model 1.1 are in the expected direction for Conservative voterswith the variables income, white British, and age all positive and significant. This reinforcesconventional wisdom on Conservative voters that, compared to Labour voters, Conserva-tive voters are more likely to have high-income levels, be less ethnically diverse and older.8

The coefficient for democratic satisfaction is negative and significant, perhaps highlightingConservative voters dissatisfaction with the current democratic process and the Conserva-tives recent spell out of power. In interpreting these results, it is apparent that the Conser-vatives core constituents are quite similar at full voter turnout as they are at current levelsof turnout, and coefficients continue to point in the same direction and hardly differbetween Models 1.1 and 1.2. For the Liberal Democrats, we find fewer socio-demographicdifferences between the parties at actual voter turnout, suggesting that their supportersare not all that dissimilar. Interestingly, Model 1.4 highlights how at full turnout, the

Table 2. Multinomial probit model of party choice in hypothetical UK elections without Scotland(2001–2010).†

Conservative party Liberal democrats

Dep var. Actual turnout Full turnout Actual turnout Full turnoutParty choice Model 2.1 Model 2.2 Model 2.3 Model 2.4

Income 0.115*** 0.125*** 0.026 0.077***(0.028) (0.006) (0.035) (0.006)

White British 0.861* 0.361*** 0.048 0.188***(0.349) (0.025) (0.076) (0.025)

Union member −0.698*** −0.468*** −0.074 −0.199***(0.120) (0.021) (0.104) (0.027)

Married 0.282* 0.090*** −0.018 −0.046*(0.133) (0.012) (0.029) (0.019)

Male 0.012 −0.080*** −0.022 −0.047***(0.092) (0.013) (0.033) (0.011)

Democratic satisfaction −0.791*** −0.559*** −0.190 −0.538***(0.145) (0.016) (0.257) (0.031)

Age 0.071* 0.080*** −0.003 −0.005(0.032) (0.006) (0.008) (0.010)

Constant −2.591* −0.645*** 0.020 −0.150**(1.188) (0.078) (0.051) (0.050)

N 13,505 126,445 13,505 126,445

Source: 2010, 2005 and 2001 British Election Studies (University of Essex).Notes: Missing values are imputed based on Amelia II program (Honaker et al., ‘Amelia II’).†The base category is ‘Labour Party’, two-tailed tests.***p ≤ 0.001.**p ≤ 0.01.*p ≤ 0.05.

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Liberal Democrats attract more diverse supporters, for example, the democratic satisfactioncoefficient changes direction quite dramatically suggesting that more apathetic voters arelikely to vote for the Liberal Democrats at full turnout than Labour.9

Our results in Table 2 provide us with estimates for our hypothetical model of a Britishgeneral election without Scottish representation. Again, the baseline for all these MNPmodels is the Labour Party and we have highlighted both the Conservative and LiberalDemocrat results. Much like in our previous analysis, relevant factors associated withvoter choice and socio-demographic factors broadly illustrate how voter choice isimpacted differently under a hypothetical full voter turnout scenario. All our coefficientsin Model 2.1 are in the expected direction for Conservative voters once again much likein our first model. For the Liberal Democrats, there are once again fewer differencesbetween their supporters and Labour voters, again highlighting how both parties havequite similar demographics.

Data analysis II

We now turn to the effect that full voter turnout has on political parties’ share of thepopular vote in the UK. Here, our dependent variable is the difference (+/−) in voteshare between actual and simulated full voter turnout for Labour, Conservatives, LiberalDemocrats, SNP and the remainder of the minor political parties. The three electionsthat we have data for (2001, 2005 and 2010) are all included. Table 3 provides OLS esti-mates with robust standard errors. Model 3.1 examines the UK as a whole and showssupport for our hypothesis that full voter turnout increases the vote share for Labour.Our control variables include an interaction term that highlights the diminishing returns

Table 3. Influences on party shares of election votes (2001–2010).‡

Model 3.1 Model 3.2 Model 3.3Dep. var. Estimates Estimates Estimates

Vote change (SE) (SE) (SE)Full Just Scot Non-Scot

Labour party 16.577*** 17.542** 23.611**(4.981) (6.303) (7.436)

Actual turnout −0.268 −0.345 −0.446(0.228) (0.473) (0.427)

Minor party 8.066** −0.337 5.047(2.862) (1.761) (3.341)

Seats 0.019 −0.009 0.015(0.016) (0.009) (0.013)

Labour*seats −0.048** −0.059** −0.077**(0.019) (0.021) (0.024)

Unemployment 0.012 −0.283 0.022(0.400) (0.826) (0.711)

Constant 9.347 25.610 23.056(14.456) (24.909) (22.608)

N 15 15 15R2 0.68 0.76 0.65F-test 10.65*** 3.56** 2.82**

Source: 2010, 2005 and 2001 British Election Studies (University of Essex).‡OLS estimates with robust standard errors; two-tailed tests.***p ≤ 0.01.**p ≤ 0.05.*p ≤ 0.10

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possible for the Labour Party with full voter turnout the larger their share of seats in thegovernment. The inclusion of the interaction term effectively means that the coefficientfor the effect of Labour is significant when seats equal zero. As this is substantially mean-ingless, the effect is also calculated with seats at its mean of 130. At its mean, the effectcontinues to be significant with the coefficient for Labour changing to 10.327. In sum,the Labour Party coefficient is positive and significant, suggesting that in the timeperiod examined, Labour would benefit from full voter turnout with an increase in theirshare of the popular vote. Minor parties also see a predicted increase in vote change.This finding makes much sense in the context of the single member electoral systemfound in the UK that could dissuade supporters of smaller parties from voting. Model3.3 reflects the UK without Scotland, and the results support our second hypothesesthat Labour can in part mitigate the loss of Scotland with full voter turnout. Again, ourcoefficient for Labour is significant and positive. When calculated at its mean, the effectcontinues to be significant with the coefficient for Labour changing to 13.639. Model3.2 is included for completeness and represents just Scottish respondents. While onceagain the coefficient for Labour is positive and significant in Model 3.2, this model maybe of limited use due to the uncertainty of the makeup of any future Scottish electoralsystem after a possible secession from the UK.

Figure 1 illustrates the data from Table 3 and highlights how as a party increases in size,a party’s opportunity to accrue further votes as vote share approaches 100 per centdecreases. Each data point represents a political party from the three elections examinedwith smaller parties seeing an increase in their vote share at full voter turnout. While theeffect is modest with smaller parties seeing only a percentage or two increase in votershare at full voter turnout, this broadly supports the notion that the UK’s first-past-thepost electoral system does seem to dissuade some voters of smaller parties to go outand vote in general elections. Although it is certainly true that left-wing parties such asLabour in the UK can increase their share of votes at full voter turnout much like our

Figure 1. Party size and changes in voter share with full turnout (2001–2010 General Elections).

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hypothesis suggests, smaller parties are also beneficiaries with full voter turnout. For right-wing parties like the Conservatives, Figure 1 highlights the diminishing returns availablefor large right-wing parties as voter participation increases. This finding confirms DeNar-do’s (1980, 1986) assertion of the diminishing returns possible for leftist parties with fullvoter turnout the larger the share of vote these parties already enjoy.

Table 4 provides a more detailed breakdown of the party data highlighted in Figure 1.Our figures for ‘Sample Turnout’ in Table 4 do not reflect the actual General Electionresults, rather this represents the pooled share of the vote from the BES surveys for2001–2010. While the BES surveys are close to the actual general election results, theyare not fully representative of the actual election results. With this in mind, we chose tocompare simulated full voter turnout with the original data from the BES survey, so thatwe are effectively ‘comparing apples with apples’. The percentage increase/decreasebetween the survey and the simulation can then be inferred to be an accurate represen-tation of the effect of full voter turnout. As we can see Labour experiences increase in votershare at full voter turnout levels in both our model of the UK as a whole and the UKwithout Scotland, again supporting our main hypothesis. The Conservative Party is pro-jected to decrease its share of the vote for all models. Yet, these results are quitemodest, with both main parties only gaining/losing a percentage point or two at fullvoter turnout. Somewhat surprisingly, however, the Liberal Democrats do not seeexpected gains at full voter turnout levels in two of our models, instead, realizingdouble-digit losses. Perhaps, this finding suggests that many Liberal Democrats arealready driven to cast their vote regardless of the competitiveness of their candidate. Itmay also be true that the Liberal Democrats’ poor showing may also be due to the simu-lation not being able to differentiate between strategic and sincere voting patterns forLiberal democrat voters. Further enquiry may be fruitful here. Finally, we see largeincreases in voter share for the remainder of the minor parties and the SNP in allmodels. While the differences are modest for the two largest parties, the SNP realizesan impressive 65 per cent increase in vote share at full voter turnout, mirroring the close-ness of much polling during the referendum campaign and the SNP’s success at the 2015General Election.

While Table 4 examined differences in voting for our sample data, Table 5 provides uswith a calculation of actual projected shares of the popular vote in the last three generalelections in the UK, with the projection reflecting the effects that full voter turnout mayhave. Table 5 reflects the actual share of the vote from each election with theincreases/decreases from our earlier analysis, to gain some understanding of the real-world effect of full voter turnout. The effect that full voter turnout would have on aBritish General Election can be calculated by examining previous elections and analysingwhat effect full voter turnout may have had in a hypothetical election. Here, we see thatthe Labour Party reduces the gap between themselves and the Conservatives in all threegeneral elections when voter participation reaches 100 per cent. The increase in vote sharefor Labour coupled with the decrease for the Conservatives sees modest gains for Labourin these elections. In our hypothetical elections without Scotland, these results highlightthe gains that Labour could enjoy at full voter turnout. The only contrary finding here con-cerns the 2001 General Election; however, Labour’s share of the vote in this election wasespecially high perhaps highlighting the diminishing rates of return for parties with anexisting large share of the vote.

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Table 4. Sample vote share (BES survey) versus projected vote share (simulated full turnout).Pooled sample full UK Pooled sample UK no Scotland Pooled sample just Scotland

Sample turnout Full turnout Diff. (%) Sample turnout Full turnout Diff. (%) Sample turnout Full turnout Diff. (%)

Conservatives 32.7 32.3 −1.2 34.7 34.3 −1.2 15.8 13.1 −20.6Labour 30.9 31.4 +1.6 30.0 30.9 +2.9 38.5 37.1 −3.8Lib dems 25.8 22.4 −15.2 26.4 23.9 −10.5 20.5 22.2 +7.7SNP 2.3 3.8 +65.2 21.8 27.6 +21.0Other 8.2 10.1 +23.2 8.8 10.7 +17.8 3.4 5.0 +32.0

Source: 2010, 2005 and 2001 British Election Studies (University of Essex).

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Data analysis III

General elections in the UK are of course not decided on the popular vote. Therefore, wewill next identify what a hypothetical British general election with and without Scottishrepresentation would look like by simulating full voter turnout and applying our resultsto marginal seats in the 2010 general election. To calculate which seats may come intoplay at full voter turnout, we simply used the difference between actual and full turnoutfor each party from Table 4 to determine which seats may change hands. The percentagedifference between actual turnout and full turnout is applied to a party candidate’s shareof the vote in each marginal seat. New estimates of each parties’ share of the vote underfull voter turnout is then calculated, which allows us to determine if any of these marginalseats would produce a new winner.

For the 2010 General Election, proper undersimulated full voter turnout Labour picks upan extra 7 seats (5 from the Conservatives and 2 from the Liberal Democrats). The 0.7 percent increase in vote share that Labour enjoys from full voter turnout does not then trans-late into any substantial changes in the 2010 result. The Conservative majority is merelyreduced from a 48-seat majority over Labour to a more modest 36 seats. Yet, thischange is not as insignificant as it seems. It is not inconceivable that a minority govern-ment consisting of Labour and the Liberal Democrats might have come into play afterthe election, as together both parties were only 10 seats shy of a working majority. Alter-natively, if we examine the arrangement that did occur, we find that under full voterturnout the Conservative–Liberal Democrat coalition does weakens a little, going from ahealthy 363 seat majority (out of 650) to a little more perilous 356 majority.

When we examine our simulated full voter turnout of the UK without Scotland from the2010 election, we find similar results. Without Scotland, the number of seats would bereduced from the original 650 to 591, meaning that a party now only requires a 296-seat majority to govern. If we calculate the number of seats for the Conservativeswithout Scotland included for the election, we find that the 305 Tory seats (306 minus 1solitary Scottish seat) now provide for a small majority in the remainder of the Union,and a government could theoretically be formed by the Conservatives without a coalitionpartner. If we simulate full-voter turnout, we once again find that the Conservatives lose 5seats outright to Labour to put them at an even more perilous 300 seat majority, makingthe formation of a one-party government perhaps unthinkable. Furthermore, three moremarginal seats Stockton South, Lancaster and Fleetwood, and Broxtowe are now virtual

Table 5. Actual vote share versus projected vote share at full voter turnout.

No. ElectionLabourparty

Conservativeparty

Actualdifference

Projecteddifference

Labourgains

1 2010 General Election 29.0 36.1 −7.1 −5.7 +1.42 2010 Hypothetical no

Scotland27.8 37.8 −10.0 −8.5 +1.5

3 2005 General Election 35.2 32.4 2.8 6.7 +3.94 2005 Hypothetical no

Scotland34.8 33.9 0.9 4.3 +3.4

5 2001 General Election 40.7 31.7 9.0 11.0 +2.06 2001 Hypothetical no

Scotland40.4 33.2 7.2 −0.2 −7.0

Source: 2010, 2005 and 2001 British Election Studies (University of Essex).

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dead heats between Labour and the Conservatives, prospectively weakening the Conser-vatives hand further.

Conclusion

The resource-based theory of voter turnout holds for our analysis vis-a-vis different politi-cal parties in the UK, yet this effect is modest making little meaningful difference to elec-tion outcomes. Our results show that as voter turnout increases to 100 per cent, Labourbenefits more than the Conservatives. Across all of our models, the Conservatives consist-ently loses ground to Labour, suggesting that large right-wing parties have the most tolose with increased voting levels. However, Labour does not always accrue extra voterswith increased turnout. Most noticeably Labour fails to achieve these gains whensupport for Labour is already high. The potential gains that a left-wing party can makewhen moving to full voter turnout levels diminish the larger the share of the existingvote that it already has. In the context of the UK, if support for Labour is already veryhigh, Labour may not see any noticeable increase in levels of support at full voter turnout.

Our analysis of the UK minus Scottish representation is also instructive. Levels ofsupport again increase for Labour at full-voter turnout, as does the expected decline forthe Conservatives. But once more, the effects are modest. Interestingly, we also noticevery high increases in support for the Scottish Nationalists at full turnout, echoing the clo-seness of much polling during the referendum campaign and the 2015 General Electionresults in Scotland. Following much of the literature, this paper illustrates how full-voterturnout generally benefits left parties, yet these increases do not seem substantialenough to change the outcome of elections in any meaningful way. However, as our analy-sis of the UK without Scottish representation illustrates, full voter turnout may have alarger effect around the margins as prospective majorities are reduced. The reduction inthe gap between Labour and the Conservatives predicted by all of our models perhapspoint to a greater chance of reduced majorities and a greater possibility of coalitiongovernments under full voter turnout.

Clearly, the electoral dynamics are changing rapidly in the UK. While the dramaticchanges in Scotland have served as inspiration for the analysis, demographic changesin Northern Ireland resulting in the potential weakening of the Unionist vote may alsoserve to change political calculations at Westminster. While the loss of a potential coalitionpartner would be a blow to the Conservatives, the effective loss of Scottish representationfor Labour has already dramatically changed the political landscape in the UK. The benefitsfor Labour of increased voter turnout, while not as dramatic as many originally theorized,may go at least some way for Labour to remain competitive in future elections.

Notes

1. Data for this paper were obtained from the British election Survey at the University of Essex</www.essex.ac.uk/bes>.

2. The BES survey is weighted to reflect the electorate at the time of a general election, and so anymissing data should come from a random sample. While it is possible that there is some systema-tic bias in this missing data, the socio-demographic characteristics modelled in the multiple impu-tation (sex, age, ethnicity, marital status, union membership and democratic satisfaction) seemunlikely to suffer from bias as these are simply demographic characteristics and not reflective

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of a particular party affiliation. In other words, a respondent’s propensity to refuse or simply leaveblank a question on the survey should not be associated with their vote.

3. There has been substantial discussion on the appropriate modelling approaches when investi-gating voter behaviour. Dow and Endersby (2004) provide a discussion about the differencesbetween multinomial probit models and multinomial logit models and conclude that the MNLis preferred for models of voter behaviour. The MNL model is often criticized because of theIIA restriction. Dow and Endersby (2004) conclude that this is not a concern for most studiesand suggest that the MNL often performs better. However, the relative merits of any statisticalmodel primarily depend on the method that best represents the underlying choice processthat generates the observed data. Dow and Endersby (2004) also state that the estimated MNPand MNL coefficients and standard errors, probabilities and marginal effects will often be indis-tinguishable. Regardless, other papers (Quinn &Martin, 1998; Quinn et al., 1999) demonstrate thatthe MNP model is best in a voter choice model in the Netherlands while the MNL model is best ina voter choice model in Denmark highlighting howmodel choice is application dependent. Multi-nomial probit models on voter choice using Markov Chain Monte Carlo algorithms for Bayesiananalysis of the multinomial probit model have also remained in the literature (Imai & van Dyk,2005). These results suggest that whether to apply a MNL or MNP model depends crucially onthe data (Quinn et al., 1999). Thus, the authors feel confident that the approach stated is appro-priate for this paper though a more complete model comparison may be interesting in the future.

4. The assumption of independence of irrelevant alternatives (IIA) states that the presence orabsence of irrelevant alternatives does not affect the odds of one preferring one course ofaction over another.

5. The BES survey employs several measures to help assure that the survey is an accurate sample foreach election including. The BES employs stratified samples of 200 Parliamentary Constituencies,random sample of two electoral wards selected with probability proportionate to size within eachsampled constituency, a systematic random sample of addresses within each ward and only oneindividual randomly sampled from each dwelling.

6. For a detailed analysis of the Amelia package, see Honaker and King (2010) companion piece inthe American journal of Political Science.

7. In order to discuss how we conducted multiple imputation more formally, assume we have a dataset, named S, with two parts. That is, an observed part of the data (So) and an unobserved part ofthe data (Su). The assumption that Amelia makes when imputing missing values is that S ∼ Nk(µ,∑) with mean vector µ and covariance matrix ∑, that is, multivariate normal. We also make theassumption when using Amelia that these data are missing at random in that the pattern of miss-ingness depends on So, but not on Su. Thus, the missingness at random assumption is that p(M|D)= p(M|So) where M is a matrix of missingness. If missingness is not dependent on the data at all,we say that the data are missing completely at random (Honaker et al., 2013). When using Ameliafor multiple imputation, we are interested in the parameters for the complete data set includingobserved and unobserved, θ = (µ,∑). Therefore, the likelihood of the observed data and the miss-ingness matrix M can be written as p(So,M|θ) or rather p(So,M|θ) = p(M|So)p(So|θ). Given that inter-est is only in inference on the complete data parameters, the likelihood function is L(θ|So) = p(So|θ) and the posterior is p(θ|So) ∝ p(So|θ) = ∫p(S|θ)sSu. The Amelia package then incorporates anExpected–Maximization-Bootstrap algorithm in order to take draws from this posterior. Witheach draw, Amelia bootstraps the data in order to simulate estimation uncertainty and thenthe expectation–maximization algorithm is run to find the mode of the posterior (Honakeret al., 2013). With these draws of the posterior, imputations are made from values of Su fromits distribution conditional on So and the draws of θ. Therefore, this is a linear regression par-ameter calculated directly from θ.

8. Descriptive statistics from the BES data set are included in the Appendix and confirm the charac-terizations of the various parties alluded to above.

9. Democratic satisfaction reflects an individual’s satisfaction with the workings of the democraticprocess and how dissatisfied an individual is in general with the way that democracy works.We might then expect Liberal Democrat supporters to have low levels of democratic satisfactioncompared to Labour supporters due to their dissatisfaction with the United Kingdom’s single

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member electoral system. The coefficients change of direction at full turnout may suggest that,by and large, the most dissatisfied voters in the country currently vote for the Liberal Democrats.This finding somewhat contradicts the assumption that those individuals with low levels ofdemocratic satisfaction are the same individuals that tend to be non-voters.

Acknowledgements

Many thanks to Wonjae Hwang, Kyung Joon Han and Ian Down for their valuable input.

Disclosure statement

No potential conflict of interest was reported by the authors.

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Appendix. Descriptive statistics

Labour Conservative Liberal dems Other parties

Mean Std dev Mean Std dev Mean Std dev Mean Std dev

Life satisfaction 0.73 0.54 0.68 0.47 0.66 0.47 0.67 0.47Income 3.37 1.79 3.68 1.86 3.64 1.78 3.36 1.74Married 0.55 0.50 0.64 0.48 0.52 0.50 0.61 0.49Union membership 0.29 0.45 0.16 0.36 0.23 0.42 0.24 0.42Ethnicity 0.95 0.21 0.98 0.15 0.96 0.20 0.98 0.14Sex 0.50 0.50 0.49 0.50 0.49 0.49 0.56 0.50Age category 4.20 1.40 4.51 1.39 4.08 1.46 4.45 1.37Democratic satisfaction 0.70 0.46 0.41 0.49 0.41 0.49 0.38 0.49

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