16. Social Welfare

7/25/2019 16. Social Welfare

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Welfare, EquitySocial Choice, Welfare Criteria

Social Choice

Diferent economic states preerred by diferent individuals

How can individual preerences be aggregated into social preerence over all possible economic

states?

Welfare

Economics dened:

o

Social ordering over states o te world !diferent allocations o resources"o Social ordering permits to compare and ran#

Welfare Ordering and Utility Orderings

$tility unctions or individuals assume to be Complete!all bundles can be compared % Transitive

Transitivity

& consumer li#es bundle ' !(a) *a" better tan bundle + !(b) *b" % li#ed bundle + better tan ,

consumer li#es bundle ' better tan bundle ,

Preferences that are Not Transitive

'lbert-s preerences

o Has bundle ') ofer im bundle , in e.cange or ' / 01

o 2en ofer bundle + in e.cange or , / 01o 3ow ofer ' in e.cange or + / 01

albert as bundle e started wit and 04 poorer

ndividual vs! "roup

5ationality in consumer coice implies preerence orderings are transitive or an individual

& aggregate diferent individual preerence ordering !all transitive"

o End up wit a social ordering tat is nottransitive

Pu#lic Choice and Condorcet Parado$

2ransitivity propertyrelation greater tan id . 6 y and y 6 7 . 6 7 don-t old wen

aggregatingpreerences

Grouppreerences can violate transitivity even i all individualsin group ave transitive preerence

o %Condorcet Parado$&

$ ' Stay out!os SE 'sian) not our problem" y ' (imited !involvement" ) ' total *ar!invade"

+ggregating Preferences a-ority .ulee.8 4 voters +ill) +erta and +ob

o +ill peace activist:

9reers . to y) y to 7

o +erta believes $S souldn-t lose

9reers y to 7) 7 to .

o +ob

9reers 7) . to y

'll tree ave individually transitivepreerences a;ority vote results

( beats y * beats 7 / #eats $

o 3o socially best alternative

o a;ority voting does not always aggregate transitive individual

preerences into a transitive social preerence

Single0Pea1ed Preferences and Transitive Social Orderings

& states can be orderedlogically according to some reasonable criterion)

can grap te preerences to see i all are single pea#ed


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o 'mount o resources committed to SE 'sia war

o +ill and +erta ave preerences tat are single pea#ed) +ob

as =

>en ordered along a.is o uantity o military resources to SE

'sia@o 2o#s preerences are 3A2 singleBpea#ed NOT rational

Cives rise to ,ondorcet 9arado. 9S5

Social Ardering 3A2 2ransitive

anipulating preferences

ost voting scemes are manipula#le

Ane individual can cast an untrutul vote to improve te social outcomeor imsel

o %strategic voting&

consider +orda ,ount !ran#Border voting"

3esira#le 4oting .ule Properties18 i all individuals- preerences are complete) reFe.ive and transitive so sould be te social

preerence created by voting rule=8 i all individuals ran# . beore y ten so sould voting rule 5pareto648 social preerence between . and y sould depend on individuals- preerences between . and y

5independence of irrelevant alternatives"

7enneth +rro*8s mpossi#ility Theorem9te only voting rule wit all o properties 1)= and 4 is

dictorial

&mplicationnondictorial voting rule reuires giving up at least one o properties 1)= or 4

Social Welfare :unctions

Civing up wic one o te GDesirable voting rule properties-?

& we can compare diferent states o te world !distributions o resources"o ust believe tat utilities can be compared across diferent individuals

ust believe tat we can some ow aggregateutilities

Social *elfare functiondescribe te result o tis aggregation process

o 2ells us ow well of societyis and as individual utilities as arguments

Compara#ility;

>at #ind o comparability do we believe in?

o 'nswer will tell us wat orms o social welare unction we can use

= #inds:

o unit comparability

o level comparability

Unit Compara#ility

comparability o unitso utility

o principle wic underlies te standard utilitariansocial welare unction

to use utilitarian unction need to #now tat a unit o utility !owever measured" same or 2om a

it is or Ioe

add up utilities

o i everyone-s utility counts eually in unction:

ob;ective nd an allocation tat ma.imi7es sum o utilities

o add up all utili7es ten divide by J o people weigted average were all weigts are te

same

general utilitarian social welare unction:


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a-s add up to oneo orm allows possibility tat

!= utility units o 2-s are to 1 o Ioes"o i we li#e Ioe more tan we li#e 2om can put twice as muc weigt on Ioe-s utility as on

2omesa5?a5Tom6

(evel Compara#ility

;udge absolutelevels o utility !conclude ary is absolutely appierKbetter of tan Sue"

o unitso measure do not matter) as long as te levelscan be compared

ob;ective

raisingo te utility o tose wose utility is small 5awls teory o ;ustice etical standard based around worst of member o society

o any redistributiontat doesn-t increase te utility o te least-well-ofis useless

o social welare is improves &< welare o tepoorestperson is raised

5awlsian Social >elare


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a$imi)ing Social Welfare

ob;ective: reac igest easible isoBwelare contour

set o candidates or social welare ma.: only tose utilityBpairs tat are 9aretoB

optimal

Social Optima A EBciency

any socially optimal allocation must be Pareto-optimal

if not9

o ten somebody-s utility can be increased witout reducing anyone else-s utility

!$tility possibilities"e.8 social suboptimality ineMciency

+llocations that are NOT Pareto0Optimal

one tat is one not on te contract curve

maps to combination o utilities tat is &3S&DE !rater tan A3" te utilities

possibilities rontier!diagrammapping o productively eMcient vs8 productively ineMcient allocation o


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B Contradictiono 5$D

#,$>#6is not afordable or agent '

tis proves: if every agents endowment is identical, then trading in competitive market results in a

fair allocation

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16. Social Welfare