Department of EconomicsUniversity of CologneAlbertus-Magnus-PlatzD-50923 KölnGermany

http://www.wiso.uni-koeln.de

U N I V E R S I T Y O F C O L O G N E

W O R K I N G P A P E R S E R I E S I N E C O N O M I C S

No. 70

PORK BARREL POLITICS, VOTER TURNOUT, ANDINEQUALITY: AN EXPERIMENTAL STUDY

JENS GROßERTHORSTEN GIERTZ

Porkbarrelpolitics,voterturnout,andinequality:

Anexperimentalstudy*

JensGroßer(FloridaStateUniversity)i

ThorstenGiertz(emeneo,Shanghai)ii

ABSTRACT

Weexperimentallystudyporkbarrelpolitics in two‐candidatemajoritarianelections.Candidates

form distinct supporter groups by favoring some voters in budget spending at the expense of

others.Wecomparevoluntaryandcompulsorycostlyvotingandfindthat,onaverage,theformer

mode induces more narrowly targeted favors and therefore more inequality among otherwise

identicalvoters.Whenthesamecandidatesactovermanyelections,suchaswithparties,theytend

tocultivatepolicypolarizationbyfrequentlyfavoringtheirexclusivesupportersagainandavoiding

thoseoftheopponent,andwithcompulsoryvotingwefindadditionalfrequentpolicyoverlapfora

separatesubsetofvoters.Ourfindingsareimportantforunderstandinghowaninclinationtowards

asustained“dividedsociety”canarisepurelyfromthepoliticalprocess,absentofanycoordination

devicessuchasideologicalpreferences.

Thisversion:January,2014

Keywords:Porkbarrelpolitics,voterturnout,inequality,ColonelBlottogames,laboratoryexperiments

iFloridaStateUniversity,DepartmentsofPoliticalScienceandEconomics&ExperimentalSocialScienceatFloridaState(xs/fs),531BellamyBuilding,Tallahassee,FL32306,U.S.A.iiemeneoconsulting,Shanghai,ThePeople’sRepublicofChina.e‐mail:jgrosser@fsu.edu;thorstengiertz@emeneo.com

* This is amuch improved version of “Candidates, voters, and endogenous group formation: A Colonel Blotto experiment“(2009).We thankWalterElberfeld,TomPalfrey, andArthurSchram forhelpful comments.Thepaperhasbenefitedgreatlyfrom comments of participants in seminars at the University of Amsterdam, University of Cologne, University of Hanover,Princeton University, and Florida State University, and at the 9th International Social Dilemma Conference in Chicago, thePublicChoiceSocietyandESAmeetings inSanAntonio, the InternationalESAmeetingsatHarvardUniversity, the1stEPCRMeetinginCanterbury,theGEWTagunginCologne,andtheSocialDilemmasConferenceatFloridaStateUniversity.

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1Introduction

Pork‐barrelspendingisacommonpracticeineverydaypolicymaking.1Inordertoboosttheirchances

in the election, candidates promise generous budget shares to subsets of the electorate, hoping to

receive their votes and political contributions in return. For example, they promise subsidies to

declining industries (e.g., theU.S. textileandcoal industries;DixitandLondregan1995)and financial

help for local infrastructure projects (e.g., building and improvements of roads and harbors). Such

tactical redistribution has the potential to create inequalities between voters (Myerson 1993), and

thereforetocounteracttheprogrammaticredistributionviataxesandthegeneralwelfaresystemthatis

rooted in the basic belief in equality (Dixit and Londregan 1996).2 So far, political scientists and

economistshavestudiedtacticalredistributionunderthepremiseofcompulsoryvoting,albeitvotingis

voluntary in most elections around the world.3 So how then can the voting mode affect tactical

redistribution?Throughthecostsofvoting!Ifsuchcostsareinvolved,thencompulsoryandvoluntary

votingcanaffectpork‐barrelingandthusinequalityverydifferently.Towit, inordertolurevoluntary

votes,a candidate’spromises to individualvotersmustnotonlyexceed theirpromises received from

the opponent, but also compensate for their voting costs. We therefore argue that under budgetary

constraints, compared to the compulsorymode, voluntary voting forces candidates to target budget

spendingmore narrowly (i.e., makemore generous promises to fewer voters) and thus yieldsmore

inequality among otherwise homogenous voters. In the present paper,we utilize game theory and a

laboratoryexperimentinordertostudythisrelationshipbetweenthevotingmodeandinequality.

Considerour two‐stagegameof electoral competition,orpolitygame. In the first stage, twoex‐

ante identical candidates independently and simultaneously announce binding policy offers. That is,

eachtargetsindividualsfromafinitenumberofex‐anteidenticalvoters(notincludingthecandidates)

1 For an annual overview of pork barrel projects in theUnited States, see for example Citizens Against GovernmentWaste(http://cagw.org/reporting/pig‐book).2Here,weseetacticalredistributionasallocationofshort‐term favorsandprogrammaticredistributionas long‐termpoliciesthatonlychangewithmajorideologicalshiftsintheelectorate(e.g.,DixitandLondregan1996).AccordingtoStokes(2009),aprogrammaticelectoralstrategyexecutesfavorsfollowingapublicdebate,whilethisdebateisabsentinanon‐programmaticstrategy.Inhertaxonomy,ourstudyisbestcategorizedas“distributivepolitics”(i.e.,favorsarematerial,non‐programmatic,biased,andnotbasedonquidproquoarrangements).3TheInternationalInstituteforDemocracyandElectoralAssistance(IDEA)providesalistofcountrieswithcompulsoryvoting:http://www.idea.int/vt/compulsory_voting.cfm.

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amongwhom,ifshewinstheupcomingelection,afixedbudgedisdividedevenly.Inthesecondstage,

majoritarianvotingtakesplace,withatie‐breakingcoinflip,wherethewinningcandidategetsabonus

(“spoilsofoffice”)andherpolicyoffer is implemented,and the losergoesawayempty‐handed.Thus,

candidates play a symmetric constant‐sum game. We focus on pure tactical redistribution, to wit,

candidatesneedonlyallocateafixedbudgetamongvoters(asinMyerson1993).4Forexample,theydo

not levy taxes or choose the budget level (Lizzeri 1999). And, we abstract away from exogenous

ideologicalpreferences(e.g.,CoxandMcCubbins1986;DixitandLondregan1996,1998)andeconomic

inefficienciesthatcanaccruefrompork‐barreling(e.g.,Baron1991;DixitandLondregan1995),albeit

efficiencyandinequalityaresomewhataffectedbythecostsofvoting.5Aswearethefirsttocompare

pork‐barrelingwithvoluntaryandcompulsoryvoting,usingpureredistributionseemsappropriate.

For the polity gamewith compulsory voting andmore than six voters, in any subgame perfect

equilibrium inweaklyundominated strategies, policy offersmustbe inmixed strategies and the two

candidateshaveequalchancesofwinning.Also,voterscastavoteforthecontenderwhopromisesthem

moremoneyor,iftheyareindifferent,voteforeithercontenderorblank(wefocusonequilibriawhere

eachoftheseactionsischosenwithprobabilityone‐third).If,tothecontrary,acandidateusesapure

strategythatfavorsaminorityofvoters,thentheopponentcanwinoutrightbytargetingtheremaining

majority.And,ifherpurestrategyfavorshalfoftheelectorateormore,thentheopponentcanwinwith

more than fifty percent chance by targeting all except one of these voters,which is a best response.

Thus,inanyequilibriumtheegalitarianoffercanonlyappearinastrictlymixedstrategyso,onaverage,

tacticalredistributioncreatesinequalityamongotherwisehomogenousvoters.Whilewithcompulsory

votingany strictlypositivepreference intensity (or, difference in receivedpromises)of a supporter is

sufficienttogarnerhervote,inthevoluntarymodetheintensitymustalsocompensateforthecostsof

4Incontrasttoourstudy,inMyerson(1993)thenumberofvotersisinfiniteandfavorsareiiddrawsfromthecandidates’offerdistributions,sothebudgetconstraintholdsonaverage.Further,inequilibrium,expostallvotershavedifferentoffersandareneverindifferentbetweenthecandidates,whileinourmodeltherearetypicallyindifferentvoters.Foranoverviewofmodelsoftacticalredistribution,seeforexamplePerssonandTabellini(2000).5Inthecompulsorymodethecostsofvotingaccruetoallvotersalike,whileinthevoluntarymodeonlythosewhochoosetoturnoutbearthecosts.Inthispaper,afixedbudgetmeansthatvoluntaryvotingisalwaysthemoreefficientmodeinthesenseof cost‐benefit analysis, unless everyone chooses to turn out in which case both modes are equally efficient. The greatestpossibleex‐postinequalityisbetweenvictor’ssupporterswhoabstainandvoterswhoreceivenopromisefromthevictorandturnout.Here,weconcentrateonredistributiveinequalitysolelycreatedviabudgetspending.

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voting. Therefore, we predict that pork‐barrel spending is on average more narrowly targeted and

hencecreatesmoreredistributiveinequalitywithvoluntarythancompulsoryvoting.

Inourstudy,differentvotergroupsemerge fromendogenouspolicymaking,and their sizesand

compositionsofpreferenceintensitiesarepubliclyannouncedbeforevoting.Withvoluntaryvoting,we

thencananalyzeourelectionsasparticipationgameswithexogenoussupportergroupsandcomplete

information about group sizes (Palfrey and Rosenthal 1983), which have also been studied in the

laboratory (e.g., Großer and Schram 2010; Schram and Sonnemans 1996).6 In any Nash equilibrium

(henceforthNE)ofthesegames,onlyvoterswithpreferenceintensityequaltoorlargerthantwicethe

votingcostshaveapositiveturnoutprobability,andthisprobabilityalsodependsonallothervoters’

preferenceintensities, theelectoratesize,andsupportergroupsizes. Infact,aminoritycandidatecan

havehigherchances in theelection thanheropponentdue tosmaller free‐rider incentives insmaller

groups,andthiseffectisstrengthenediftheminorityalsocontainsgreaterpreferenceintensitiesthan

themajority, which regularly occurs in our game (cf. Campbell 1999). In contrast, with compulsory

votingamajoritycandidatealwayshashigherchances.However,NEfailstopredictturnoutlevelsand

patterns in experimental participation games,which aremuch better explained by quantal response

equilibrium(QRE;McKelveyandPalfrey1995)thatallowsfornoisydecision‐making(e.g.,Goereeand

Holt2005;GroßerandSchram2010).Ourstudyprovidesfirstinsightsintohowcandidatesandvoters

dealwiththedifferentcomplexitiesofthetwovotingmodes.

Of central concern in pork barrel politics are the commitment problems involved. To wit, the

candidatescanneverbesurethattheirsupporterswillvoteforthem,andvotersinturncannottakeit

for granted that policy promises will be fulfilled (e.g., Alesina 1988; Corazzini et al., forthcoming)

albeitpromisesarebindinginourstudysovotersfacenopreferenceuncertainty.Also,politicalparties

havelong‐terminterestsinkeepingpromises,andthereforearemoretrustworthythanlegislatorswho

are tempted tobreakpartydiscipline in favorof their constituencies (GrossmanandHelpman2005).

Here,weexaminewhether,andifsohow,candidatesandindividualvotersarewillingandabletoform

6Inabasicparticipationgame,twovotergroupscompeteinamajoritarianelectionwhereeachvoterdecidesonwhetherornottoturnouttovoteatacost.Here,wedefineparticipationgamesmorebroadly,sinceinourstudyarelativelysmallnumberofelectionscanarisethatarespecialcasesofthesegames,suchasthevolunteer’sdilemmagame(Diekmann1985).

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long‐standingtacitpoliticalalliances(i.e.,viamutualpromisesandvotes)andhowsuchbondsimpact

pork‐barrelingandinequality.Inourexperiment,candidatesareeitherpartieswhoactineveryelection

orpoliticianswho change fromelection to election.7 Importantly, politicians cannot respond to voter

decisions in the current election,8 while parties can reciprocate these decisions in their next policy

offersalbeitwithdifficulties,asindividualvoterbehaviorcouldnotbetraced.Notethatlong‐standing

alliances are inconsistent with mixed strategy play and must rely on mutual reciprocity within the

respectivepairofapartyandvoter (e.g.,Axelrod1981;Krepsetal.1982).Butsince individualvoter

behaviorcouldnotbe traced,partiesmightrewardandpunishsubsetsofvoterscollectivelyvia their

budget promises. In practice, there are partisan voters and favors are often anchored in previous

policies. Therefore, in spite of the possibility that rivals can challenge each other’s alliances and the

absenceof coordinationdevices such as ideological preferences (e.g., Cox andMcCubbins1986;Dixit

andLondregan1996),weanticipatethatsomelong‐standingalliancesalsoariseinthelaboratory.

OurmodelbelongstotheclassofColonelBlottogames(e.g.,Borel1921;GrossandWagner1950;

Hart 2008; Owen 1968; Roberson 2006), where two antagonistic colonels independently and

simultaneously allocate their forces across various battlefields, and the number of battles won

determines the outcome of the war. These games find an immediate application in elections, where

candidates battle for votes or voting blocs (e.g., Brams and Davis 1974; Laslier and Picard 2002;

Myerson1993;SankoffandMellos1972;Snyder1989;Young1978).Theextentofinequalitycausedby

tacticalredistributiondependsonthespecificsoftheelectoralcompetition.Myerson(1993)showsfor

different electoral rules (i.e., rank‐scoring rules, approval voting, and single transferable votes) that

increasing thenumberof candidates raises their incentives to target smaller subsetsofvoters,which

yieldsmoreinequality.DixitandLondregan(1996)findthatcandidatesfavorthemorefamiliarallied

voters if these canbe targetedmoreeffectively,but they favor swingvoters ifboth typesareequally

receptive.InLizzeri(1999),candidatesaccumulatenationalbudgetdeficitssincetheadditionalmoney

7Notethatsomeelectioncampaignsemphasizeparties(e.g.,DutchNationalElections)andotherscenteronpoliticians(e.g.,U.S. Presidential Elections). Of course, outside of the laboratory politicians can to some extent coordinate policies acrosselections (e.g., using decisions of predecessors as clues) and parties sometimes disappear from the political arena. Forilluminatingtheeffectsofthelifespanofcandidatesonpolicymaking,itisconvenienttostudyourextremecases.8Inourexperiment,politiciansrandomlyrecurrednowandthenbutseemednottoreciprocatetheirearlierelectionresults.

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can be used for more effective targeting. With regard to economic efficiency, Dixit and Londregan

(1995)showthattacticalredistributioncanconservedecliningindustries(e.g.,theU.S.textileandcoal

industries) and thus prevent resources from shifting to more efficient uses. The reason is that

candidatescannotcrediblypromisefuturegainstothosewhoneedtoshift.And,inLizzeriandPersico

(2001) candidates can engage in both tactical redistribution and efficiency enhancing public goods

provision.Theyfindthatpublicgoodsareunderprovidedrelativetothesocialoptimumundervarious

electoral rules (i.e., winner‐take‐all, proportional representation, and the Electoral College), and

inequalityisgreaterthemoredesirablepublicgoodsare.Finally,LizzeriandPersico(2005)showthat

increasingthenumberofcandidateleadstogreaterinefficiency.Toourknowledge,wewerethefirstto

studytheColonelBlottogameexperimentally9aswellasexaminepork‐barrelingwithvoluntaryvoting.

Intheconclusions,weelaborateonexternalvaliditybylinkingourfindingstothoseofvariousrelated

empiricalstudiesthatdo,however,notutilizetheframeworkofaColonelBlottogame.

2Politygameandpredictions

In this section, we describe and analyze our game. Additional analysis is provided in our online

supportinginformation.10

Thepolitygame

Consider our two‐stage electoral competition game, or polity game, with two ex‐ante identical

candidates, labeled , ,andafinitenumberofex‐anteidenticalvoterswhoarenevercandidates,

labeled 1, … , . Inthefirststage(Policymaking), thecandidates independentlyandsimultaneously

announcebindingpolicyoffers.Towit, eachof them targets individual voters tobenefit frombudget

spending,with theonly constraint that at least one voter is selected.Thus, there are2 1possible

offersacandidatecanchoosefrom(4,095inourexperimentwithtwelvevoters).Ifsheprevailsinthe

election,thenafixedbudget 0, , willbedividedevenlybetweenher targetedvoters,

soeachreceivesbenefitsof ⁄ (non‐targetedvotersreceivezerobenefits).Andifsheloses,thenher

9 The recent, independent experiments of Avrahami and Kareev (2009) and Chowdhury, Kovenock, and Sheremeta (2013)studyasymmetricColonelBlottogames,thoughnotinthecontextofelections.10Thesupportinginformationisavailableathttps://sites.google.com/site/jwghome/research.

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offerwillbeinconsequential.Notethattargetingfewervotersincreaseseachselectedvoter’sbenefits,

which is a crucial relationship for our comparison of voting modes. In the second stage (Election),

majoritarianvotingtakesplacewhereacoinflipbreaksatie.Thewinningcandidategetsabonus, 1,

(“spoils of office”) and her offer is implemented, and the loser goes away empty‐handed, 0.We

assumethatallplayersareriskneutralandmaximizetheirexpectedownpayoffs.

Eachvoter’spreferenceintensity( ),ordifferenceinreceivedpromises,arisesfromendogenous

policymaking.Namely, shemaybe targeted by neither candidate so 0 and she is indifferent

betweenthetworivals; byonecandidateso 0andsheprefersthiscontender;or byboth

candidates,inwhichcasesheeitherprefersthecontenderwhopromiseshermoremoney( 0)oris

indifferent ifbothpromisethesameamount( 0).Notethatavarietyofdifferentcompositionsof

preferences intensities can emerge that define a supporter group for each candidate and a group of

indifferentvoterswithzerointensity.Thesegroupsvaryinsize,includingnonexistence,andpreference

intensities, with a maximal in‐group diversity of two different intensities in at most one supporter

group. The following two examples illustrate the formation of preferences and voter groups. A full

characterizationofallpossibleelectionsisintheonlinesupportinginformation.

Supposethat 5and 5inbothexamples.

Example1:

00010 0005001101 0 0

01111 0 5 ,

whereontheleft‐handside , , denotesthevectorofcandidate ’sselectionofvoters 1, … ,5

(1 if targeted and0otherwise) and gives the sumof the two rivals’ vectors.Andon the

right‐handside, denotesthevectorofcandidate ’sbudgetpromisestoeachvoter.Intheexample,

promises ⁄ 5toonevoter( 1)andtheremainingfourvotersarepromisednothing,and

promises ⁄ 5/3toeachof 3votersandtheother twovotersarepromisednothing.Also,

vector | | denotes the vector subtractionwhere the resulting absolute elements give the

preferenceintensityofeachvoter,respectively.Therearetwosupportergroups (consistingofvoter

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4)and (voters2,3,and5),and consistingof indifferentvoter1.Notethatthetwooffersdonot

overlap(i.e., 2, , )andeachsupportergroupcontainsonlyonepreferenceintensity.

Example2:

11100 00

00101 00 0

11201 0 ,

where 3and 2,andthetwopolicyoffersoverlapforvoter3.Further,therearetwosupporter

groups (consistingofvoters1and2)and (voters3and5),and consistingofindifferentvoter4.

This simple example already produces the maximum possible number of four distinct preference

intensities,thatis,5/3(5/6;5/2;0)forvoters1and2(voter3;voter5;voter4).

Finally,wedistinguishbetweenelectionswithvoluntaryandcompulsoryvoting.Inthevoluntary

mode,eachvoterdecidesonwhethertopayacost 0andvoteforcandidateAorB,ortoabstainat

nocost.Bycontrast, inthecompulsorymodeeachvotermustpay andvote forcandidateAorB,or

voteblank(i.e.,voteforneithercandidate).11

Equilibrium

Weusebackwardinductioninordertoanalyzeinturnthepolitygamewithcompulsoryandvoluntary

voting,focusingonsubgameperfectequilibriuminweaklyundominatedstrategies.InthePolicymaking

stage, candidates play a symmetric constant‐sum normal form gamewhere each cell represents one

possibleelection(i.e.,pairofoffers)anditsentriesrepresenttherivals’probabilitiesofwinning.Then,a

purestrategy isa selectionof specificvoters (i.e., apolicyoffer)andamixed strategy isaprobability

distributionoverallpurestrategies. It ishelpful to sub‐dividemixedstrategies further.Specifically, a

pure [un]balanced number strategy is a selection of one specific number of voters, where all pure

strategies using this number are playedwith equal [at least twodifferent] probabilities, and amixed

[un]balancednumberstrategyisaprobabilitydistributionoverallpurebalancednumberstrategies[all

strategieswithstrictlypositiveprobabilityforatleastonepureunbalancednumberstrategy].

11Weassumeapenalty forabstaining thatexceedsc, so thisoption isstrictlydominatedbyvotingsincerelyandblank.Forexample,Australiausesthecompulsorymodeandvotershavetheoptiontocastablankvote.

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Proposition1(Politygamewithcompulsoryvotingand 6):12InthePolicymakingstage,inanyNE

inweakly undominated strategies each candidate has an equal chance ofwinning and always uses a

strictlymixedbalancednumber strategythus, inequality is createdonaveragethat cannot result in

4⁄ targeted votersor less. In theElection stage, inaNE inweaklyundominated strategiesof every

feasiblepair ofpolicy offers, eachnon‐indifferent voter votes sincerelyand each indifferent voter votes

blankorforcandidateAorBwithprobabilityone‐thirdforeach.

Proof:Seeouronlinesupportinginformation.

Thus,inequilibriumwithcompulsoryvoting,electionresultsareentirelydeterminedbythetwo

supportergroupsizes,andalsochanceifthereareindifferentvotersorties.Forindifferentvoters,any

voting strategy is optimal, which includes the random strategy used in Proposition 1 (various other

strategiesareanalyzedinGroßerandGiertz2014).Further,candidateshaveequalchancesastheycan

alwaysimitateeachother’sstrategy.Also,ifsomevotersaremorelikelyfavoredthanothers,thenthe

opponent can achieve a greater than fifty percent chance of winning by targeting or avoiding these

voters,socandidatesdonotusepurestrategiesorunbalancednumberstrategies inanyNE.And, the

opponent can exploit a pure balanced number strategy by a similar argument made earlier for the

intuition of mixed strategy equilibrium in the Policymaking stage, so only a strictly mixed balanced

numberstrategyisviableinNE.

Turning tovoluntaryvoting,mostof theemergingelectionsareparticipationgames á laPalfrey

andRosenthal(1983),andallothersarespecialcasesthereof(suchasthevolunteer’sdilemmagame,

Diekmann1985;moredetailsaboutthevariousgamesareprovidedbelowandintheonlinesupporting

information).Foreachpossibleelection,thewinningprobabilitiesofthecandidates(i.e.,therespective

cell’sentriesofthenormalformgame)arederivedfromthepredictedturnoutprobabilitiesandvotes,

soNEcanbesolved.

12Focusingonelectorateswithmorethansixvotersavoidsspecialcases inbothvotingmodes(seealsoProposition2).Forexample, if 2, then in both modes each possible offer pair is a NE. Or, if 6 and voting is compulsory, then thePolicymakingstagealsohaspurestrategyequilibria,whichneveroccurfor 6.Notethat 12inourexperiment.

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Proposition2 (Polity gamewithvoluntary voting and 6): In thePolicymaking stage, inanyNE

eachcandidatehasanequalchanceofwinningandneverusesanystrategythatpromisesvotersbenefitsof

⁄ 2 thus, inequality is always created if 2⁄ . Also, at least one NE in pure ormixed

balancednumberstrategiesexists.AndintheElectionstage,inaNEinweaklyundominatedstrategiesof

every feasiblepairofpolicyoffers,eachvoterwithpreference intensity 2 abstainsandeachvoter

with 2 turnsoutwithpositiveprobabilityandvotessincerely.

Proof:Seeouronlinesupportinginformation.

In the voluntarymode, in equilibrium election results depend on voters’ turnout probabilities,

whichinturndependonthevotingcosts,ownandallothervoters’preferenceintensities,andsizesof

relevantsupportergroups(i.e.,thatcontainonlyvoterswith 2 ,comparedtooriginalgroupsinthe

compulsorymodewhereallvoterscount).Arationalvoteronlyturnsoutifherexpectedbenefitsfrom

voting equals or exceeds the voting costs.13 Then, anticipating NE decisions in the election, each

candidatemustpromisehersupporters ⁄ 2 inordertoearnthechanceofreceivingtheirvotes.

Inaddition,wemakethefollowingtwoconjectures:

Conjecture1(Effectsofpreferenceintensityandgroupsizesonturnoutprobabilities):Ceterisparibus,

avoter’sturnoutprobabilityincreasesinherpreferenceintensityanddecreasesintheabsolutedifference

insupportergroupsizes.

Argument:Giventhelargevarietyofdifferentelections,sufficientlygeneralequilibriumpropertiesof

theeffectsofpreference intensityandsupportergroupsizesonvoterturnoutareverydifficult, ifnot

impossible, to obtain. Thus, our conjecture is based on findings from related studies. First, in many

experiments, higher incentives increase cooperation even if NE predicts no or opposite effects (e.g.,

PalfreyandPrisbrey1997).Forexample,inalaboratoryparticipationgameonreformswithexogenous

groups,CasonandMui(2005)findthatturnoutratesdecreaseinthevotingcosts.Hence,weanticipate

thatturnoutandpreference intensityarepositivelyassociated inourexperiment.Also, inGroßerand

13Avoteonlyraisestheindividual’sbenefitsifitispivotal(i.e.,forcesorbreaksatie,givenothers’votes).Thisincreaseequals

2⁄ (i.e.,theone‐halfstemsfromatie‐breakingcoinflip)sosheturnsoutwithpositiveprobablityifandonlyif /2 .

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Schram(2010)turnoutratesdecreaseintheabsolutedifferenceinexogenoussupportergroupsizes(as

in Levine and Palfrey 2007 where voting costs are private information), which is against the NE

predictionsbutinlinewithQRE(McKelveyandPalfrey1995)andgroupthinkmodels(e.g.,Feddersen

andSandroni2006).QREallows fordecision‐makingerrors that arise frombounded rationality (e.g.,

biasedperceptionsofcostsandbenefits)whereaparameter controlsthedegreeofnoise.14Forour

data,weexpect 0ofamagnitudesimilartothose inparticipationgameexperiments(e.g.,Goeree

andHolt2005;GroßerandSchram2010)andhencestrictlypositiveturnoutratesevenforvoterswith

2 whoabstaininNE.

Finally,usingbackwardinduction,Propositions1and2andConjecture1holdforeachrepetition

of the finitely played polity game, independent of whether candidates are parties who act in every

electionorpoliticianswhochangefromelectiontoelection.

Conjecture2(Inequalityandthevotingmode):Voluntaryvotingcreatesmoreredistributiveinequality

amongotherwise identicalvoters thancompulsoryvoting,while inequality is the samewithpartiesand

politicians.

Argument: In the voluntary mode, candidates’ promises must sufficiently compensate for the

supporters’votingcostsinordertoearnthechanceofreceivingtheirvotes(e.g.,inNEonlyvoterswith

2 turnoutwithpositiveprobability).Thecompensationmustbefinancedbyfavoringonaverage

fewervotersthanwithcompulsoryvoting,sovoluntaryvotingtendstocreatemoreinequality.Further,

in line with the conjecture, in NE candidates never target 4⁄ and 2⁄ voters with

compulsory and voluntary voting, respectively (Propositions 1 and 2). Finally, offers of parties and

politicians should not be different, as our predictions hold for each repetition of the finitely played

politygame.

14InQREplayersmakestochasticbestresponses,thatis,morelucrativedecisionsoccurmoreoftenthanlesslucrativeones.Inthe logit specificationofGoereeandHolt (2005), forexample, 0 in thenoise‐freeextreme (i.e.,QRE turns intoNE)and→ ∞intheotherextremewithpurenoise(i.e.,everyoneturnsoutwithprobabilityone‐half).Besidesturnoutpatterns,QRE

can also explain other important empirical phenomena, such as that majorities winmore often thanminorities where NEpredictstheopposite(GroßerandSchram2010).ButnotethatobservedcandidatechoicesofvotersareoftenclosertotheNEthanQREpredictions(e.g.,McKelveyandOrdeshook1990,albeitindifferentvotersareusuallynotexamined).

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3Proceduresandexperimentaldesign

Thecomputerexperiment15was runat theCREED laboratory,UniversityofAmsterdam. In total,184

studentsattendedtwelvesessionsoffourteentoeighteenparticipantsthatlastedabouttwohours(for

theread‐aloudinstructions,seeouronlinesupportinginformation).Earningswereexpressedintokens

andexchangedforcashforoneƒperfourtokensattheendoftheexperiment.Participantsearnedan

averageofƒ38.31(€17.38),includingaƒ10show‐upfee.

Ineachsession,apolityconsistedoftwocandidatesandtwelvevoters.Eachparticipantwaseither

acandidateorvoterthroughoutthesession,andwasinformedaboutherorhisroleatthestartofthe

experiment.Westudytwotreatmentvariables inabetween‐subjectsdesign,varyingthevotingmode

(CompulsoryversusVoluntary)andlifespanofcandidates(PartiesversusPoliticians).Withcompulsory

voting,eachvoterautomaticallypaidonetokenandhadtovoteblankorvoteforcandidateAorB.With

voluntary voting, each voter decided on whether to spend one token in order to vote for either

candidate,ortoabstainatnocost.Forthecandidates’lifespan,inPartiestwoparticipantsfromapoolof

fourteenwererandomlyappointed“CandidateA”and“CandidateB,”respectively,onceandforallatthe

start of the session, and the remaining twelveparticipantswere voters throughout. InPoliticians, six

participantsfromapoolofeighteenwererandomlyappointedpotentialcandidatesonceandforallat

thestartofthesession,andtheremainingtwelveparticipantswerealwaysvoters.Beforeeachelection,

allsixpotentialcandidateschosetheiroffers,andthereaftertwopoliticianswererandomlyappointed

actual “Candidate A” and “Candidate B.”16 This procedure not only provides us with more offer

observations, but also averts implicit coordination across elections via the A‐ and B‐labels, so

interactionsofpoliticiansareroughlyone‐shotencounters.

Eachsessionconsistedof51periodswithtwodecisionstageseach.Inthefirststage,candidates

independentlyandsimultaneouslymadetheirpolicyoffersbytargetingindividualvoters(i.e.,clickon

buttons thatwere arranged in a circle on the screen,where eachbutton represented the samevoter

throughoutthesession).Inthesecondstage,thetwo(actual)offerswereannouncedandmajoritarian

15WeusedRatImage(AbbinkandSadrieh1995)toprogramtheexperiment.16Weused the samepredetermined random sequence of actual candidates in allPoliticians sessions,where each potentialcandidatewasanactualcandidatefifteen,seventeen,ornineteentimes(seeouronlinesupportinginformation).

12

votingwithrandomtie‐breakingtookplace.Thereafter,abudgetofeighteentokenswasdividedevenly

between the winner’s targeted voters (non‐targeted voters received zero tokens), while the loser’s

policy offerwas inconsequential. In order to avoidnegative earningsdue to the costs of voting, each

voter received one extra token independent of her or his decision. Also, the bonus for the winning

(losing)candidatewastwenty(zero)tokens.Further,voterswerepaidforeachperiod,andcandidates

inParties(Politicians)werepaidforseventeenperiodsrandomlyselectedattheendofthesession(i.e.,

eachperiodinwhichtheywereactualcandidates;seefootnote16).

When making their decisions, candidates knew if in the previous period a specific voter was

targetedbyAorBorbothcandidates(i.e.,thiswasvisibleonthevoterbuttonsonthescreen),butnot

herorhisdecision.And,whenvotersmadetheirdecisionstheyknewtheirownreceivedpromisesand

thosemadetoallothervoters,butcouldnottraceothers’promisesfrompreviousperiods.Finally,all

participants were informed about the procedures outlined here and in the instructions.17 Table 1

summarizesourtreatmentsandparameters:

Table1:Summaryoftreatmentsandparameters

Note: denotes thenumberofvoters targetedby thewinner.All treatmentshad51decisionperiodsandtwelvevoters.Wehavefourindependentobservations(i.e.,politiesorsessions)pertreatment.

Forourexperimentalparameters 12, 18,and 1weemployedGAMBIT(McKelveyet

al.2013) to compute symmetricNE in strictlymixedbalancednumber strategiesof thePolicymaking

stage,whichisshowninTable2.

17Theinstructionsusedmoreneutrallabelsforrolesanddecisionsthanthepaper(seeouronlinesupportinginformation).

Treatment

Candidatepayoffsforwinning(losing)

Voterpayoffs Numberofactual

(potential)candidates

Benefits if (not)targetedbywinner

Costsofparticipation(abstention)

Compulsoryvoting‐Parties 20(0) 1 18/ (1) 1(‐) 2(2)

Voluntaryvoting‐Parties 20(0) 1 18/ (1) 1(0) 2(2)

Voluntaryvoting‐Politicians 20(0) 1 18/ (1) 1(0) 2(6)

13

Table2:NEpredictionofthenumberoftargetedvoterswithcompulsoryvoting

Numberofvoterstargeted 1 2 3 4 5 6 7 8 9 10 11 12

ProbabilityusedinNE 0 0 0 0 .291 .344 0 .044 .079 .070 .098 .074

Note:Candidatestargetonaverage7.24outoftwelvevoters(60.4%).

BecauseofthecomplexityoftheElectionstagewithvoluntaryvoting,wecannotprovidesubgame

perfect equilibrium predictions for this mode for our experimental parameters (albeit NE can be

computedforeachpossibleelection,andtheequilibriumconditionsareinthesupportinginformation).

4Experimentalresults

Inthissection,wepresentandanalyzeourexperimentalresults,startingwithaggregatecandidateand

voter behavior. Thereafter, we study whether turnout and vote decisions are affected by the own

preference intensity, absolute difference in supporter group sizes, and repeated favoritism by a

candidate.Finally,weexaminesimplepolicydynamicsandlong‐standingalliancesbetweencandidates

and voters. For our nonparametric statistical analysis we treat the polity, or session, as the unit of

independentobservation.Additionalprobit regressionsof candidate andvoterbehaviorare runwith

randomeffectsattheindividuallevel.

Figure1:Averagefractionofvoterstargetedpercandidate

14

Aggregatebehavior

We examine aggregate candidate and voter behavior, in turn. Figure 1 shows for each treatment

observedfractionsofvoterstargetedpercandidate,averagedoverblocksoftenperiods(eleveninthe

lastblock).InPoliticians,thepolicyoffersofallpotentialcandidatesareincluded.18

Asseeninthefigure,thereisconsiderableredistributiveinequalityinalltreatments,thatis,the

averagefractionsofvoterstargetedpercandidatearemuchsmallerthanone(i.e.,theegalitarianoffer).

Further,thefractionissmallerinVoluntaryvoting‐PartiesthanCompulsoryvoting‐Partiesineachblock

ofperiods (overall,0.42versus0.56). In the firstblock thegap is about0.10points, and increases to

about 0.15 points in the remaining blocks. Also,with voluntary voting the average fraction of voters

targeted per candidate is smaller in Parties than Politicians in each block (overall, 0.42 versus 0.48,

albeitthisdifferenceisnotstatisticallysignificant).Thefractionsaresimilarinthefirsttwoblocks(0.42

versus0.44and0.44versus0.48),butgreatergapsof0.06to0.11pointsoccurintheremainingblocks.

Experimental result 1: There is substantial redistributive inequality in all treatments. On average,

partiescreategreater inequality in thevoluntary thancompulsorymode,and inequality is the same for

partiesandpoliticianswithvoluntaryvoting.

Support: One‐tailedWilcoxon‐Mann‐Whitney tests reject thenull hypothesis of nodifference in average fractions of voters

targetedpercandidateinfavorofsmallerfractionsinVoluntaryvoting‐PartiesthanCompulsoryvoting‐Parties( 0.029),but

not forVoluntaryvoting‐PartiesversusVoluntaryvoting‐Politicians ( 0.171).Theexactsameresultsalsohold for the last

three blocks of periods only. For comparison, average fractions are smaller inVoluntary voting‐Politicians thanCompulsory

voting‐Parties( 0.100),butnodifferenceisfoundifonlythelastthreeblocksareconsidered( 0.171).

Confronting this resultwith our NE, in the compulsorymode (see Table 2 for predictions) the

averagefractionofvoterstargetedpercandidateiswith0.56closetothe0.60inNE.Also,outof408

policy offers, 3, 4, 5, 25, and77 offers targeted one, two, three, four, and seven voters, respectively,

comparedtothezeropredicted.InNEwithvoluntaryvoting,eachcandidatetargetsatmost 2⁄ 9

voters (Proposition2). InVoluntary voting‐Parties, 3, 1, and 13 out of 408policy offers targeted ten,

eleven, and twelve voters, and in Voluntary voting‐Politicians, for the two actual (six potential)

18AveragepolicyoffersinPoliticiansarenotdifferentbetweenthesixpotentialandtwoactualcandidates(two‐tailedWilcoxonsignedrankstest, 0.313).

15

candidatesthesenumbersare3,2,and18outof408(19,5,and49outof1224).Thus,inalltreatments,

offers that never occur inNE are indeed rarely observed (with the only exception of seven targeted

votersinthecompulsorymode).Finally,consistentwithConjecture2,averageinequalityisgreaterwith

voluntarythancompulsoryvotingand,inthevoluntarymode,thesameforpartiesandpoliticians.

Figure2:Averagevotingrates

Next,weturntoaggregatevoterbehavior.Figure2showsforeachtreatmentobservedratesofvoting

for a candidate per electorate (lines without markers) and per targeted voters (lines with markers),

averaged over blocks of ten periods (eleven in the last block). The rates are computed as the total

numberofvotesforthetwocandidates,dividedbytheelectoratesizerespectivelythenumberofvoters

whoreceiveatleastonepromise.Inthecompulsory(voluntary)mode,thevotingratedecreaseswith

eachblankvote (abstention).Therefore,whenvoting is compulsory the rateperelectorate is smaller

thanoneifthereisatleastoneblankvote,andtheratepertargetedvotersislargerthanoneifthereare

moreA‐andB‐votesofnon‐targetedvotersthanblankvotesoftargetedvoters.Notethatoutsideofthe

laboratoryonlyturnoutratesperelectorateandperregisteredvotersarereported.

16

Theobservedvoluntaryvoting(or,turnout)ratesperelectorateareaboutthesameinPartiesand

Politicians in the first twoblocksofperiods(0.38versus0.38and0.37versus0.36,respectively)and

0.04to0.06pointshigherinParties intheremainingblocks.Incomparison,thelevelsanddifferences

aregreaterforratespertargetedvoters(0.61versus0.57and0.56versus0.56inthefirsttwoblocks,

andgapsof0.12to0.13pointsintheremainingblocks),sinceindifferentvoterswithnopromiseswho

abstainarenotconsidered.19

Experimentalresult2:Voterturnoutratesaresimilarwithpartiesandpoliticians.

Support: One‐tailedWilcoxon‐Mann‐Whitney tests cannot reject the null hypothesis of no difference in turnout rates per

electorateandpertargetedvotersbetweenPartiesandPoliticians( 0.557and 0.343),andthisalsoholdsforthelast

threeblocksofperiodsonly( 0.243and 0.171).

In Compulsory voting‐Parties, the average voting rate per electorate is smaller than one in all

blocksofperiods.Also,theaverageratepertargetedvotersisgreaterthanoneinallblocks,indicating

thatsome indifferentvoterswithnopromisesneverthelessvoted forAorB,which isconsistentwith

our prediction that these voters vote randomly (Proposition 2;more about this below). This rate is

highest in the first block and lowest in the last block (1.19 and 1.04, respectively), and it is greater

(smaller)thanoneinthree(one)outoffourpolities.

Voterbehavior

In the following, we study turnout and vote decisions by taking into account the specific electoral

composition (i.e., group sizes and pattern of preference intensities).We first categorize and present

observed fractions of the various elections, and thereafter investigate whether non‐indifferent and

indifferent voters vote sincerely and randomly, respectively (Propositions 1 and 2). Finally, we use

probitregressionsinordertoexaminewhethervoter’sdecisionsareaffectedbytheirownpreference

intensity,theabsolutedifferenceinsupportergroupsizes,andrepeatedfavoritismbyacandidate.

Electoralcompositions

Foranoverviewofthevariouselectoralcompositionsinourexperiment,wecategorizeelectionsusing

relevantsupportergroupsthatconsistmerelyofvoterswith 2(notethatouranalysisbelowalso

19Recallthattheturnoutratepertargetedvotersincludesindividualswith ∈ 0,2 ,whoabstaininNE(Proposition2).

17

usesoriginal supporter groups).Moreover, a game is calledstandard if every supporter in a relevant

grouphasthesamepreferenceintensity,albeit candifferacrossgroups,andmodifiedifonerelevant

groupcontainstwodifferent 2(which,inthevoluntaryvoting,requiresanadditionalequilibrium

condition). In Voluntary voting‐Politicians (‐Parties) we find 75.5% (81.4%) standard participation

games,5.9%(3.9%)modifiedparticipationgames,11.3%(11.3%)standardvolunteer’sdilemmagames,

0%(0%)modifiedvolunteer’sdilemmagames,and7.3%(3.4%)gameswithuniversalabstention.And,

inCompulsoryvoting‐Partiesthesenumbersare71.1%,2.0%,12.7%,0%,and14.2%.Thus,overall,most

electionsarecategorizedasstandard“participationgames.”

Sincerevoting

Withcompulsoryvoting,77.7%ofallobservedvoterdecisionsweremadewith 0,ofwhich89.2%

(7.0%;3.8%)weresincere(insincere;blank)votes.And,63.6%(36.4%)oftheremaining22.3%votes

with 0were for a candidate (blank).Moreover,with voluntary voting66.2% (69%) of all voter

decisions inPoliticians (Parties)weremadewith 0, ofwhich 49.9% (43.3%)were abstentions,

48.8% (54.8%) sincere votes, and 1.3% (1.9%) insincere votes. Of the remaining 33.8% (31.0%)

decisionswith 0,92.9%(92.8%)wereabstentionsand7.1%(7.2%)werevotesforacandidate.20

Experimental result 3: In the compulsory mode, non‐indifferent voters mostly vote sincerely and

indifferentvotersvoteforacandidateabouttwo‐thirdsofthetime.Inthevoluntarymode,non‐indifferent

voterswhochoosetoturnoutvotesincerely,andindifferentvoterssometimesturnouttovoteforAorB.

TheresultmainlysupportsPropositions1and2thatnon‐indifferentvotersvotesincerelyinboth

votingmodes,andthatindifferentvotersvoterandomlyinthecompulsorymode(i.e.,voteblankorfor

A orBwithprobability one‐third for each).Although relatively small innumbers, the findingof non‐

indifferent insincere voting, especially in the compulsory mode, and indifferent voluntary voting is

againstNEbutinlinewithQRE.Becauseinsincerevotingisquiterareandourfocusisonvotingfora

candidateversusvotingblankorabstaining,ourfollowinganalysissimplyassumesthatnon‐indifferent

voterswhogotothepollsvotesincerely.

20Note that49 (25;22)outof204election results inCompulsoryvoting‐Parties (Voluntaryvoting‐Parties;Voluntaryvoting‐Politicians)changeifdecisionsofindifferentvotersareexcluded.

18

Votingdecisions

Figure3depictsobservedaveragevotingratesforacandidatepertreatmentperdifferentcategoriesof

preferenceintensities.Inalltreatments,theintensitymarkedlyaffectsthedecisionto(turnoutto)vote

foracandidate.Ascanbeseen,verysimilarpatternsofvoluntary turnoutratesare found in the two

respectivetreatments,wheretheratesgenerallyincreaseinthe ‐category.Amaindifferencebetween

Voluntary voting‐Politicians and ‐Parties is that the biggest jump in turnout rates occurs in different

categories(0.35in ∈ 2,3 versus0.28in ∈ 3,4 ,respectively).Bycontrast,inCompulsoryvoting‐

Partiesthevotingrateforacandidateis0.64forindifferentvoters, 0,andveryclosetooneforall

categorieswith 0(0.96overall).Atlarge,ourfindingsareinlinewithPropositions1and2.

Figure3:Votingratesandpreferenceintensities

Next, we further examine voter decisions by running, for each treatment separately, probit

regressions with random effects at the individual level. Specifically, our panel models estimate the

effectsofthepreferenceintensity,absolutedifferenceinsupportergroupsizes,repeatedfavoritismbya

candidate,andinequalityconcernsontheindividualdecisionto(turnoutto)voteforacandidate.Our

dependentdummyvariable, ,equalsoneifvoter jvotedforAorB inperiodt,andzerootherwise.

Further,weutilizethefollowingindependentvariables.Tobegin, measuresj’spreferenceintensity

intokensinperiodt.Forthecompulsory(voluntary)mode,thedummyvariable ( )equals

19

oneif 0( 2)tokensandzerootherwise,whichallowsustoexamineajumpinvotingrates

for this intensity rangeversus 0 ( 2) tokens,aspredicted inProposition1 (2).Also, for the

voluntarymode,theinteractionvariable measurestheeffectofpreferenceintensitiesofat

leasttwotokensontheturnoutprobability.Moreover,∆ ,∆ ,∆ ,and∆ measurethe

absolutedifferenceinsupportergroupsizesinperiod ,wheresuperscript“”(“”)indicatesthat isin

theminority(majority)groupandsuperscript“O”(“R”)referstooriginal(relevant)groupsconsistingof

voterswith 0( 2).We interact the∆ ‐variableswith thedummyvariables in the

compulsory mode, and , (equal to one if ∈ 0,2 and zero otherwise) and in the

voluntarymode,sowecantestwhethervoterswith intensities intheserangesresponddifferentlyto

supportergroupsizedifferences.Further, | |measurestheabsolutedifferenceinthe

candidates’ numbers of targeted voters in period t, which is utilized to examinewhether indifferent

voters inthecompulsorymodedecidebasedon inequalityconcerns(recall thattheirearningsdonot

dependontheelectionresult;seealsoFeddersen,Gailmard,andSandroni2009).And, isadummy

variableequaltooneif isasupporterofthesamecandidateinperiods 1andt,andzerootherwise,

sowecantestwhetherjrespondstorepeated(stronger)favoritismbyacandidate.Finally,thevariable

Period(t)measuresatimetrendand and areerrorterms,wherethelattertermisarandomeffect

usedtocorrectforthepanelstructureinourdata.Table3givestheresultsofourprobitestimations.21

Wefirstfocusonvoluntaryvoting,whereourestimatesareverysimilaracrosstreatments.Towit,

forstatisticallysignificantcoefficientsthesignsandsignificancelevelsare,withoneexception,identical

in Politicians and Parties. Specifically, the coefficients of the dummy variable are large and

positive,supportingourNEpredictionthatpreferenceintensitiesofat leasttwotokensareimportant

forinducingturnout(seeProposition2).Also, ∈ 0,2 andmuchlessso 2positivelyaffectthe

turnoutprobability (i.e., thecoefficientsof are0.78and0.57,andarereducedby thecoefficients

0.62and 0.40of ,respectively).Notethattheeffectof ∈ 0,2 isnotpredictedbyNE

(see Proposition 2) but consistent with QRE. Further, the absolute difference in relevant supporter

group sizes, ∆ , negatively affects the turnout probability of voters with 2, and somewhat

21Theresultsaresimilarifweonlyconsiderthevastmajorityofelectionscategorizedasstandard“participationgames.”

20

strongersoinminoritiesthanmajorities( 0.23versus 0.12inPoliticiansand 0.46versus 0.34in

Parties, respectively). These relationships are also reported for exogenous supporter groups (Großer

andSchram2010).Finally,theprobabilityofturnoutisunaffectedby∆ forvoterswith ∈ 0,2

who abstain in NE, the period, and repeated favoritism by a candidate (i.e., the coefficients of the

respectivevariablesarestatisticallyinsignificant).

Table3:Randomeffectsprobitregressionsofvotingforacandidate

ConstantandIndependentvariables

Coefficients

Voluntaryvoting‐Politicians

Voluntaryvoting‐Parties

Compulsoryvoting‐Parties

Constant ‐1.72(10.73)*** ‐1.72(13.04)*** 0.15(0.88)

1.69(6.35)***

1.97(11.76)*** 2.18(10.06)***

0.78(8.70)*** 0.57(4.86)*** 0.16(1.93)*

‐0.62(6.36)*** ‐0.40(3.07)**

∆ ‐0.07(1.19)

∆ ‐0.05(1.03)

∆ , ‐0.05(0.50) 0.28(1.29)

∆ , ‐0.06(1.52) 0.02(0.31)

∆ ‐0.23(3.91)*** ‐0.46(7.43)***

∆ ‐0.12(3.75)*** ‐0.34(8.39)***

0.13(2.76)**

‐0.06(1.09)

Period(t) ‐0.00(0.76) ‐0.00(0.67) 0.00(1.13)

‐0.12(1.57) ‐0.06(0.73) ‐0.02(0.12)Note:The independentdummyvariable isavoter’sdecisiononvoting foracandidate( 1)orabstaining

respectivelyvotingblank( 0).Absolutez‐valuesareinparentheses,and*(**;***)indicatessignificanceat

the5%(1%;0.1%)‐level.

With compulsory voting, the estimatesmostly support our NE predictions (see Proposition 1).

Compared to indifferent voters, there is a statistically significant, largepositive effect on voting for a

candidate for non‐indifferent voters, but also an unpredicted significant, small positive effect of the

preferenceintensity(capturedbythecoefficients1.69of and0.16of ,respectively).And, in

linewithNE, neitherminority normajority voters respond to∆ . Finally, indifferent butnotnon‐

21

indifferent votersdo indeed somewhat resort to inequality concerns (i.e., the coefficient of is

statisticallysignificantandpositive,andthatof isinsignificant).

Experimental result 4: With voluntary voting, turnout levels jump up drastically for preference

intensitiesofat least two tokens.Further, the turnoutrate increases in thepreference intensityand, for

voters with 2 tokens in both the minority and majority, in the absolute difference in relevant

supportergroupsizes.Withcompulsoryvoting,non‐indifferentvotersalmostalwaysvoteforacandidate,

while indifferent voters do so two‐thirds of the time and somewhatmore likely for the candidatewho

allocatesthebudgetmoreequally.

Candidatebehavior

Inthefollowing,weanalyzecandidatebehaviorinmoredetail.Wefirstlookattheirwinningrates,and

thereafterexamine simplepolicydynamics (i.e., changes inoffers fromoneelection to thenext), also

usingprobitestimationswithrandomeffectsatthecandidatelevel.

Winningrates

For the more successful candidates per polity, the winning rates are 0.53, 0.55, 0.61, and 0.65 in

Compulsoryvoting‐Parties,0.53,0.55,0.55,and0.63inVoluntaryvoting‐Parties,and0.51,0.55,0.57,and

0.63inVoluntaryvoting‐Politicians.Notethatthelowestpossiblerateis0.51 26/51periods.

Experimentalresult5:Inone‐thirdofthepolitiesthecandidates’winningratesareunequal.

Support: In four out of twelve (3 4) polities one candidate wins statistically significantly more often than the rival(s).

Binomial tests reject the null hypothesis of equalwinning rates for these polities (one per treatment 0.05 plus one in

Compulsoryvoting‐Parties, 0.10)butnotforallotherpolities( 0.10).Ofthetwentyfour(4 6)potentialcandidatesin

Politicians, thirteen win more and eleven win fewer than half of their actual candidacies, which is significant for four

respectivelythreeofthem( 0.10).

Weconjecturethatdeviationsfromthepredictedequalchancesofcandidates(seePropositions1and

2)areduetothecomplexityofpolicymaking.

22

Voterstatesandtransitions

Next, we study whether candidates choose their policy offers depending on offers in the previous

period.Therearefourpossible“voterstates,”asdefinedbythepromisesavoterreceives.Namely,sheis

targetedby Neithercandidateor OnlyAor OnlyBor Bothcandidates.Figure4depicts

thesevoterstatespertreatmentas“circles.”Further,eachvotereitherremainsinthesamestatefrom

oneperiod to thenext,orentersanother state as representedby “arrows”directed to thenewstate.

Therefore, each circle has three outgoing and three incoming arrows. For periods 1 to 50, observed

average fractions of voters in each state are given in the figure next to the respective state’s label

(predictionsareinbrackets),andobservedaveragefractionsofremaininginandtransitingtoanother

state are given atand visualized by the size ofthe respective circles and arrows (predictions are

explained in the text, anda full overview is available on request from theauthors).Note that a state

fractionisequaltothesumofitsthreefractionsofoutgoingtransitionsplusthefractionofremainingin

thatstate.Forexample,inVoluntaryvoting‐Politicians(toppanelofFigure4)theobservedaveragestate

fractionofOnlyAis0.244 0.069 0.060 0.054 0.061.

Figure4:Voterstatesandtransitionsbetweenelections

Voluntaryvoting‐Politicians

Voluntaryvoting‐Parties

.068 .051

.061 .050

Neither .275 (.269) Only B .244 (.250)

Only A .244 (.250) Both .237 (.232)

.061 .055

.069 .069

.068 .054

.076 .058

.060

.078

.060

.062

23

Compulsoryvoting‐Parties

Wenowexaminewhethercandidatestarget individualvotersrandomly(seePropositions1and

2),usingBinomialtestsandprobitregressionsinturn.FortheBinomialtests,wesimplyusepereach

treatment as our predicted target probability, labeled , the observed average number of voters

targetedinanoffer(i.e.,inthegiventreatment, isaveragedoverallcandidatesand51periods).22So,

we have 0.48 (0.42; 0.56) in Voluntary voting‐Politicians (Voluntary voting‐Parties; Compulsory

voting‐Parties).Assumingthateachcandidate’sdecisionsonwhetherornottotargetindividualvoters

areindependentfromeachotherandheropponent’sdecisions,wethenpredictthateachvoterenters

22 Note that does not capture any variation in target probabilities across candidates and periods. To some extent, suchdifferencesareaccountedforinourprobitregressions,below(seeTable4).Also,withprobability 1 acandidatedoesnottargetanyvoter,but inourgameat lastonemustbetargeted.However, thisprobability isverysmall( 1 0.420.0014)soouranalysisisvirtuallynotaffected.Finally,theresultsaresimilarforvariousalternativesto .

.098 .134

.170 .031

Neither .309 (.336) Only B .248 (.244)

Only A .295 (.244) Both .148 (.177)

.053

.021

.095 .031

.064

.069

.020

.014

.084 .040

.056

.020

.115 .136

.034 .110

Both .298 (.313)

Only B .278 (.246)

Only A .243 (.246)

Neither .181 (.194)

.061 5.6%

.049

.037 .060

.072 .056 . 057

.031 .067

.036

.038

.041

24

stateNeither,OnlyA,OnlyB,andBothwithprobability 1 , 1 , 1 ,and ,respectively.

And,thepredictedprobabilityofeachoutgoingtransitioniscomputedastheproductoftherespective

probabilitiesofthedepartureanddestinationstates.Therearesixteensuchprobabilitiespertreatment,

fourforeachvoterstate.Forexample,inVoluntaryvoting‐Parties(middlepanelofFigure4)wepredict

that each voter entersNeither with probability 0.336 and her respective transition probabilities are

0.113 0.336 0.336 for NeitherNeither, 0.082 0.336 0.244 for NeitherOnly A, 0.082

0.336 0.244forNeitherOnlyB,and0.059 0.336 0.177forNeitherBoth,with0.113 0.082

0.082 0.059 0.336.

Confronting our predictionswith the data usingBinomial tests,23 inVoluntaryvoting‐Politicians

(toppanelofFigure4)noneof theobservedstate fractions is statistically significantlydifferent from

ourrandombenchmark,andonlyfouroutofsixteenfractionsofoutgoingtransitionsandremainingina

statearesignificantlydifferent(3 0.1and 0.01).Further,inVoluntaryvoting‐Parties(middle

panel) these numbers are three ( 0.01, 0.001, and 0.0001) and thirteen ( 0.1,

2 0.01, and 8 0.0001), and in Compulsory voting‐Parties (bottom panel) they are one

( 0.001)andfourteen(2 0.1, 0.001,and11 0.0001).Therefore,andalsovisible in

Figure 4, politicians target votersmostly randomlywhile parties deviatemarkedly fromour random

benchmark,andweexaminenextwhethertheydososystematically.

Focusing first onParties,with voluntary voting the fractions of voters remaining inOnlyAand

OnlyBarefargreaterthanpredicted,whilethetransitionfractionsofOnlyAOnlyBandOnlyBOnlyA

are much smaller (all 0.0001). Thus, in the voluntary mode parties tend to cultivate polarized

groupsbyrepeatedlyfavoringtheirexclusivesupportersandavoidingthoseoftherival.And,asseenin

themiddlepanelofFigure4,policypolarization is assisted in that voterswhoarenewly included in

(excludedfrom)offersareusuallydrawnfrom(releasedto)Neither,andthosewhohappenedtobein

BothareusuallyreleasedbybothpartiessotheyenterNeither.Moreover,inthecompulsorymodethe

fractionsofvotersremaininginOnlyAandOnlyBarealsofargreaterthanintherandombenchmark,

23InrunningourBinomialtests,forvoterstatesweuse 2,400observations(4sessions12voters50periods)andfortransitionsweuse observations(i.e.,theactualnumberofobservationsperstatefromwheretherespectivetransitiondeparts),where rangesfrom354to741.

25

however, the sameholds for remaining inBoth (all 0.0001) so in addition to policy polarization

parties bump into each other’s offers for some voters. And, as with voluntary voting, the transition

fractions of Only AOnly B and Only BOnly A are much smaller than predicted ( 0.001 and

0.0001).Allinall,policyoffersinthetwoPartiestreatmentsareconsiderablypredictable,whichis

inconsistentwithmixedstrategyplayofcandidates(seePropositions1and2)andhintstosometacit

agreementsbetweenpartiestowardsfocusingtheirbattleforvotesonasubsetofvoters.

Table4:Randomeffectsprobitregressionsofcandidatebehavior

ConstantandIndependentvariables

Coefficients

Voluntaryvoting‐Politicians

Voluntaryvoting‐Parties

Compulsoryvoting‐Parties

Constant ‐0.20(3.13)** 0.28(4.44)*** 0.39(6.22)***

Period(t) 0.01(4.36)*** 0.00(0.52) 0.00(1.41)

‐0.12(1.56) 0.20(2.78)** ‐0.09(1.23)

, 0.15(2.01)* ‐0.38(5.59)*** ‐0.34(4.27)***

, ‐0.02(0.32) ‐1.13(15.16)*** ‐0.67(9.24)***

, ‐0.01(0.16) ‐0.54(6.39)*** ‐0.01(0.20)

, 0.05(0.46) ‐0.30(3.08)** 0.11(0.95)

, 0.13(1.29) ‐0.58(5.15)*** ‐0.12(1.14)

, 0.13(1.23) ‐0.13(1.13) ‐0.09(0.90)Note:Theindependentdummyvariableisacandidate’schoicewhethertotargetaspecificvoter(=1),or

not(=0).Absolutez‐valuesareinparentheses.*(**;***)indicatessignificanceatthe5%(1%;0.1%)‐level.

Next,weanalyze candidatebehavior inmoredetailby runningprobit regressionswith random

effects at the candidate level. Specifically, we studywhether the probabilitieswithwhich voters are

targeted depend on previous voter states and are different afterwinning and losing. Our dependent

dummy variable indicates whether or not (one or zero) candidate targets voter in period t. Our

independent variables are the Period (t), measuring a time trend, and the following seven dummy

variables (equal to one if true, and zerootherwise): indicateswhether won in theprevious

period; , , , (i.e.,Other refers to candidate ), and , indicate ’s

voterstateinthepreviousperiod,respectively,sotheconstantrepresentsthestatewheresheorhewas

26

targeted only by candidate ; and, finally, three variables that interact with each voter state

variable,respectively.OurestimationsareshowninTable4.

InVoluntaryvoting‐Politicians, ourestimatesaremostlyconsistentwithmixedstrategyNEplay

(seeTable2) in thatpolicyoffersaremade independentofpreviousvoterstatesandelectionresults

(i.e., six of the seven dummy variables are small and insignificant). Albeit relatively small, the two

statisticallysignificantexceptionsarethenegativeconstantandpositivecoefficientof , .24By

contrast, inVoluntaryvoting‐Partiescandidatesstronglyrespondtopreviousvoterstatesandelection

results(i.e., thecoefficientsofthesevendummyvariablesareusuallygreaterthanforpoliticians,and

sixare significant). Specifically, exclusive supporters in 1aremore likely favoredagain, andeven

moresoafterwinning(i.e.,theconstantandcoefficientof arepositiveandsignificant,andthe

coefficientsofallotherdummyvariablesarenegative).Note that theseestimatesbackupourearlier

finding that parties tend to cultivate policy polarizationin particular, the negative coefficients of

, , , , and , stand out the most, which accentuates the

parties’ active avoidance of the rival’s targeted voters. Moreover, in Compulsory voting‐Parties the

constantisstatisticallysignificantandpositiveandthecoefficientsof , and ,

are significant and negative,whereas all other coefficients are insignificant. Also these estimates are

consistentwithourearlierpolicypolarizationfinding,andcomparingthecoefficientsof , inthe

two Parties treatments emphasizes the important difference caused by the voting mode: in the

compulsorymode theestimate isminisculewhile in thevoluntarymode it is largeandnegative (i.e.,

0.014n.s.versus 0.540***)hence,partiesseek(avoid)policyoverlapwithcompulsory(voluntary)

voting.Also,interestingly,partiesdonotrespondtoelectionresultswhenvotingiscompulsory(i.e.,all

coefficients of variables involving are insignificant). Thus, in contrast to voluntary voting,

partiesdonothold their targetedvotersresponsible forwinningor losing,which is intuitivebecause

the supporters’ compulsory votes are almost always sincere, so there is virtually no room for

24 One possible reason why politicians target voters in , somewhat more often than other voters are fairnessconcerns(i.e.,sothatthistimethesevotershaveachancetoearnmoney).Recallthatinthistreatmentsomeindifferentvotershadfairnessconcernstoo,asindicatedbythe ‐coefficientinTable3.

27

reciprocatingtheirdecisions.Inotherwords,partiesknowthattheybearmostoftheresponsibilityfor

electionsresultsundercompulsoryvoting.

Finally, we find no period effects on the probabilities with which candidates target individual

votersinParties(i.e.,bothcoefficientsarestatisticallyinsignificant)andasignificant,tinypositiveeffect

inPoliticians.Weconjecturethatthesefindingsareduetothedifferentfeedbackpartiesandpoliticians

receiveabouttheirownpolicyoffers.Towit,politiciansareactualcandidatesonlyone‐thirdofthetime,

whilepartiesexperiencetheconsequencesoftheirdecisionsineveryperiod.

Experimentalresult6: Parties choose their policy offers based on voters’ previous states. In both

votingmodes,theytendtocultivatepolicypolarizationbyrepeatedlytargetingtheirexclusivesupporters

again and avoiding those of the opponent, and in the voluntarymode this behavior is boosted after a

victory.Withcompulsoryvoting,theyalsoseekpolicyoverlapforaseparatesubsetofvoters.

Politicalalliances

Weconcludeourexperimental results sectionbypresentingaparticularly illustratingexampleof the

formationoflong‐standingtacitalliancesbetweenpartiesandindividualvoters(i.e.,continuousmutual

promisesandvotes).Recallthatsuchalliancesareinconsistentwithmixedstrategyplayofcandidates

sincetheanticipationofbondscanusuallybeexploitedbytherival.Alsorecallthatinourexperiment

individualvoterdecisionswerenotrevealed,soinordertosustainalliancespartieshadtoreciprocate

basedontheirsubjectivebeliefsaboutthesedecisions.Inshort,itseemsthatlastingalliancesbetween

partiesandvotersaredifficulttoachieve.

Figure5depictsforonepolity(Session6,Voluntaryvoting‐Parties)thedecisionsofeachpartyand

voterineveryperiod.PolicyoffersofpartyA(B)areshownontheleft‐hand(right‐hand)side,andon

bothsideseachvoterisrepresentedbyacolumnandeachperiodbyarow.Ablack(gray)cellindicates

thatinthisperiodvoter wastargetedbyparty , anddid(not)voteforthisparty.And,an“M”

(white)cellindicatesthatinthisperiod wasnottargetedby anddid(not)votefori.Theexampleis

self‐explanatory,sowerefrainfromdefiningalliancesbyanexactdurationofmutualfavors.

28

Figure5:TacitpoliticalalliancesinSession6,Voluntaryvoting‐Parties

PolicyofferA PolicyofferB

Note: PartyA‘s (B’s) offers are shownon the left‐hand (right‐hand) side.On each side, each voter isrepresentedbyacolumnandeachperiodbyarow.Ablack(gray)cell indicatesthat wastargetedby

, anddid(not)voteforthispartyandan“M”(white)cellindicatesthat wasnottargetedby anddid(not)votefor .

Ascanbeseen,partyApersistentlytargetsvoters2,8,and9fromperiod22onwardsandvoter

10isaddedstartinginperiod29,andthesefavorsarereturnedbyavotein74.3%ofthecases.Voter8

often abstains, so alliances only form betweenA and voters 2, 9, and 10. By contrast, for period 21

onwards, partyB targets voters less persistently andon averagemore of them thanA (5.11 vs. 3.77

votersperperiod),yielding45.2%ofreturnedfavors.RepeatedmutualfavorsareshortforB(atmost

fiveperiods)sonoalliancesarefoundforthisparty.Notethatbothpoliciesareclearlypolarizedfrom

period22onwards (withonly twooverlaps inperiod48). Surprisingly, althoughBwinsonlynineof

these thirty elections, she or he does not attempt to increase the own chances via bumping intoA’s

VotersRound 1 2 3 4 5 6 7 8 9 10 11 12

1 2 0 0 0 0 0 0 0 0 0 0 0

2 3 2 2 3 0 0 0 0 0 0 3 2

3 0 3 2 2 2 2 2 2 0 0 0 0

4 3 0 0 0 0 0 0 0 0 2 2 2

5 0 2 2 2 2 2 2 0 0 0 0 0

6 0 3 2 2 3 0 0 0 0 0 0 0

7 0 2 3 2 2 0 0 0 0 0 0 0

8 3 0 0 0 0 0 0 0 0 0 2 3

9 3 0 0 0 0 0 0 0 0 0 2 3

10 3 3 3 0 0 0 0 0 0 0 2 2

11 3 3 2 2 0 0 0 0 0 0 3 2

12 3 0 0 0 0 2 2 2 0 0 2 2

13 0 0 2 2 2 3 3 0 0 0 0 0

14 0 0 3 3 3 2 2 0 0 0 0 0

15 0 0 2 2 3 2 3 0 0 0 0 0

16 0 0 3 3 2 2 2 0 0 0 0 0

17 0 0 3 3 2 2 2 0 0 0 0 0

18 0 0 2 3 2 3 0 0 0 0 0 0

19 0 0 2 3 2 2 0 0 0 0 0 0

20 0 2 0 0 0 0 2 3 2 0 0 0

21 0 3 2 2 0 0 0 0 0 0 0 0

22 0 3 0 0 0 0 0 3 3 0 0 0

23 0 3 M 0 0 0 0 3 3 0 0 0

24 0 3 0 0 0 0 0 3 3 0 0 0

25 0 3 0 0 0 0 0 3 3 0 0 0

26 0 3 0 0 0 0 0 3 3 0 0 0

27 0 3 0 0 0 0 0 3 3 0 0 0

28 0 3 0 0 0 0 0 3 2 0 0 0

29 0 3 0 0 0 0 0 2 2 3 0 0

30 0 3 0 0 0 0 0 2 3 3 0 0

31 0 3 0 0 0 0 0 3 3 3 0 0

32 0 3 0 0 0 0 0 2 3 3 0 0

33 0 3 0 0 0 0 0 2 3 3 0 0

34 0 3 0 0 0 0 0 2 3 3 0 0

35 0 3 0 0 0 0 0 3 3 3 0 0

36 0 3 0 0 0 0 0 3 2 2 0 0

37 0 2 0 0 0 0 0 2 2 3 0 0

38 0 3 0 0 0 0 0 3 3 3 0 0

39 0 3 0 0 0 0 0 2 3 3 0 0

40 0 3 0 0 0 0 0 2 2 2 0 0

41 0 3 0 0 0 0 0 2 3 3 0 0

42 0 3 0 0 0 0 0 3 3 2 0 0

43 0 3 0 0 0 0 0 3 3 3 0 0

44 0 3 0 0 0 0 0 2 3 3 0 0

45 0 3 0 0 0 0 0 2 3 3 0 0

46 0 3 0 0 0 0 0 2 3 3 0 0

47 0 3 0 0 0 0 0 2 3 3 0 0

48 0 2 0 0 0 0 0 2 3 3 0 0

49 0 3 0 0 0 0 0 2 3 3 0 0

50 0 3 0 0 0 0 0 2 3 3 0 0

51 0 3 0 0 0 0 0 2 2 2 0 0

VotersRound 1 2 3 4 5 6 7 8 9 10 11 12

1 2 2 3 2 3 2 2 0 0 0 0 0

2 0 2 2 2 3 3 3 3 0 0 0 0

3 0 0 2 2 2 2 2 2 3 0 0 0

4 0 0 3 2 2 2 2 3 3 0 0 0

5 0 0 2 2 2 2 2 3 2 0 0 0

6 0 0 2 2 2 3 3 0 0 0 0 0

7 0 0 0 2 2 2 3 3 0 0 0 0

8 0 0 0 2 2 2 3 0 0 0 0 0

9 0 0 M 2 3 2 2 3 3 3 0 0

10 0 0 0 0 0 3 3 3 3 2 0 0

11 0 0 0 2 3 3 3 3 0 0 0 0

12 0 0 0 0 0 0 2 2 3 2 2 0

13 0 2 2 2 2 0 0 3 3 2 0 0

14 3 0 0 0 0 0 0 0 0 2 2 2

15 2 0 0 0 0 0 0 3 3 3 2 2

16 0 0 0 0 0 0 0 3 3 2 2 0

17 0 0 0 0 0 0 0 3 3 2 3 2

18 3 0 0 0 0 0 0 0 0 0 2 2

19 3 0 0 0 0 0 0 3 3 3 3 2

20 2 0 M 0 0 0 2 2 3 2 2 2

21 2 0 0 2 2 0 0 0 0 2 3 2

22 2 0 0 0 2 0 0 0 2 2 2 2

23 3 0 0 0 0 0 0 0 0 2 2 2

24 2 0 2 3 3 2 0 0 0 0 0 2

25 0 0 3 3 3 0 0 0 0 0 0 0

26 0 0 2 3 2 3 0 0 0 0 0 0

27 3 0 3 2 3 0 0 0 0 0 0 2

28 3 0 3 2 3 0 0 0 0 0 0 2

29 2 0 2 2 3 2 2 0 0 0 0 2

30 3 0 3 3 3 0 0 0 0 0 0 2

31 2 0 3 2 3 0 0 0 0 0 0 2

32 3 0 3 2 2 0 0 0 0 0 0 2

33 0 0 0 0 0 3 3 0 0 0 2 2

34 0 0 M 0 2 3 3 0 0 0 2 3

35 0 0 0 0 3 3 3 0 0 0 2 0

36 0 0 M 3 2 3 3 0 0 0 3 3

37 2 0 2 2 3 3 0 0 0 0 0 2

38 0 0 0 0 3 2 2 0 0 0 3 3

39 0 0 0 3 3 2 2 0 0 0 3 2

40 2 0 2 3 2 2 0 0 0 0 2 2

41 3 0 3 2 2 3 0 0 0 0 0 2

42 0 0 2 3 0 3 2 0 0 0 2 2

43 3 0 3 3 2 0 0 0 0 0 0 2

44 3 0 3 2 2 3 0 0 0 0 0 2

45 3 0 2 3 2 0 0 0 0 0 0 2

46 0 0 0 0 0 3 2 0 0 0 2 2

47 0 0 0 0 0 3 2 0 0 0 2 2

48 0 3 0 0 0 0 0 0 2 0 0 0

49 2 0 0 3 3 3 2 0 0 0 0 2

50 3 0 0 2 3 3 2 0 0 0 0 3

51 2 0 2 0 3 2 2 0 0 0 3 2

29

alliancesormakingofferstofewervoters.25Generally,votersstopvotingforacandidateassoonasan

offergetstoosmall,whichisinlinewithourfindingthatvotersrespondmainlytomonetaryincentives

butnottofavoritismperse,andthattheyhaveastronger“bargaining”positionthancandidateasthey

decideafterobservingtheirpolicyoffers.Thisexample,andothersthatareavailablefromtheauthors

onrequest,yield:

Experimental result 7: Some long‐standing political alliances arise between parties and individual

voters.Thesebondsare rational in the sense that votersonly casta vote for thepartyas longas their

preferenceintensitiesdonotgettoosmall.

5Conclusions

Althoughpork‐barrel spending isubiquitous ineverydaypolicymaking,manyof its consequencesare

stillnotunderstood.Here,weprovidenovelinsightsonhowvoluntaryversuscompulsorycostlyvoting

can affect tactical redistribution and thus inequality. Our experimental results show that, for a fixed

budget,candidatesmakeonaveragegreaterpromisestofewervoterswithvoluntarythancompulsory

voting,because in the formermodesupportersmustbecompensated for thevotingcosts inorder to

earn the chance of receiving their votes. Thus, among otherwise homogenous voters, redistributive

inequality is on average greater with voluntary voting. Further, the voters’ decisions are generally

similartothosereportedinexperimentsusingexogenousgroupswithbothcompulsory(e.g.,McKelvey

andOrdeshook1990)andvoluntaryvoting(e.g.,GroßerandSchram2010;LevineandPalfrey2007).

That is, they vote sincerely most of the time and voluntary turnout rates are positively related to

preferenceintensityand,forsufficientlyhighintensities,negativelyrelatedtotheabsolutedifferencein

relevantsupportergroupsizes.

Our paper also adds to studies of electoral competition by comparing elections that center on

politicians and parties, respectively. Specifically, parties can coordinate their policies across several

legislativeperiodswhilepoliticianscannot,whichweimplementintheexperimentasfinitelyrepeated

25ForanexampleofhowB coulddefeatA, suppose thatB targets fivevotersandbumps intoall foursupportersofA.ThisyieldsfourA‐supporterswith 0.9tokensandoneB‐supporterwith 3.6tokens.Theoretically,inNEallA‐supportersabstainsince 2tokens,andBwinsoutrightasherorhisonlysupportersurelyturnsouttovotesincerely.

30

versusnearlyone‐shotcandidateencounters.Wefindthatthisdistinctionmattersa lot.Towit,while

politicians’ promises to voters are virtually unpredictable across elections, parties tend to cultivate

policy polarizationby repeatedly favoring again their exclusive supporters and avoiding those of the

opponent, so that some long‐standing tacit alliances form between parties and individual voters. In

addition,partieswithcompulsoryvotingbattleforthevotesofaseparatedsubsetofvoters,something

whichisnotobservedinthevoluntarymode.

Morebroadly,thepresentpaperlinksgreatlytoavarietyof importanttheoreticalandempirical

studies in the electoral competition literature,which accentuates its external validity. First,we show

that a lasting divided society can emerge via pork barrel politics in spite of the absence of apparent

“coordinationdevices”thatmoreeffectivelyfacilitatelong‐standingalliancesbetweenpartiesandtheir

supporters.Forexample,wedonotuse ideologicalpreferencesofvoterssuchas inmodelsofspatial

competition (e.g., Dixit and Londregan 1996; Downs 1957; Hotelling 1929), other characteristics of

voters(e.g.,educationandreligion),costsrelatedtopolicychanges,oropportunitiestomonitorvoter

behavior(e.g.,Nichter2008;Stokes2005).Inthisregard,ourexperimentnotonlyprovidesinsightson

short‐term favors, but also on a more fundamental distributive process that contributes to shaping

society in the long run. Second, observational evidence suggests that voters do indeed respond to

political favors inways consistentwithour theoretical andexperimental findings for thepolitygame

withvoluntaryvoting.Chen(2013)findsthatgovernmentdeliveryofdistributiveaidraisesturnoutfor

the incumbent party and decreases turnout for the opposition. In our terminology, the aid increases

preference intensities of incumbent supporters and decreases those of opponent supporters (and

potentially turns them into incumbent supporters). As a consequence, because voters’ preference

intensities andpositively associatedwith their probability of going to the polls, turnout rises for the

incumbentpartyandfallsfortheopposition.NotethatinChen(2013)thedistributiveaidoperateson

anexistingdivideintheelectorate(i.e.,theDemocraticandRepublicandivideintheU.S.),whileinour

experimentpolarization isendogenous.Third, there isobservationalevidencethatcompulsoryvoting

leads to less redistributive inequality than voluntary voting. In particular, Fowler (2013) shows that

Australia’sadaptionofthecompulsorymodemarkedlyincreasedturnoutandpensionspendingatthe

31

national level, and hence yielded a public policy that considers the preferences of larger numbers of

citizens.Moreover,higherlevelsofvoterparticipationareassociatedwithmoreequaldistributionsof

income (e.g., Lijphart 1997; Mueller and Stratmann 2003). Finally, voluntary turnout patterns with

respecttopreferenceintensitiesanddifferencesinsupportergroupsizesinourandotherexperimental

studies(e.g.,GroßerandSchram2010;LevineandPalfrey2007)areverysimilartothoseobservedin

the field (for surveys, seeBlais 2000andMatsusaka andPalda1993).Thus, in strong support of the

externalvalidityofthispaper,manyofourfindingsareconsistentwiththoseofotherempirical,more

partial studies. In linking thevarious important studiesonelectoral competition,webelieve that our

studycanhelptoobtainamorecoherentpictureofthegeneralpoliticalprocess.

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