2005 the citizen candidate model_an experimental analysis

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The Citizen Candidate Model: An Experimental AnalysisAuthor(s): John CadiganReviewed work(s):Source: Public Choice, Vol. 123, No. 1/2 (Apr., 2005), pp. 197-216Published by: Springer

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Public Choice (2005) 123: 197-216DOI: 11127-005-0262-4 C Springer2005

The Citizen Candidate Model: An Experimental Analysis

JOHN CADIGAN

Departmentof Public Administration,American University,4400 MassachusettsAvenue,NW

Washington,District of Columbia, U.S.A.20016; E-mail: [email protected]

Accepted 27 January2004

Abstract. Citizen candidate models representa significantadvance in the analysis of public

choice. They provide added realism to models of endogenous policy formation, relate thenumberof candidatesto the benefits and costs associatedwith electoralcompetitionandsupport

equilibriawithdifferentiatedcandidatepositions,even with a multidimensionalpolicy space.In

thispaper,experimentalmethodsare utilized to test two of the model's equilibriumpredictions.The results supportthe prediction that an increase in the net benefits to winning an election

increasesthe number of citizens enteringelectoral contests.When the net benefits to winningan election are low, the results supportthe predictionthat the only candidate has the median

preference.Further,the results suggest that when net benefits are high, two members of the

electoratewithpreferencesclose to andsymmetricabout he medianenter theelection, although

convergenceto this equilibriumtakestime. Because entryis costly, having multiplecandidates

lowersgroup payoffs

andmay

be seen as inefficient.

1. Introduction

Citizen candidate models representa significantadvance in the analysis of

publicchoice. A limitationof previousresearch nvolves the exogenous spec-ification of the number of candidatesorparties.Osborneand Slivinski (1996)and Besley and Coate (1997) developed an electoral frameworkwhere thenumberof candidates is an endogenousfeatureof equilibriumoutcomes. The

approachhighlights the importanceof non-policy-relatedbenefits and costsassociatedwith electoral competition,and their nfluenceon citizen decisionsto enterelectoral contests. In contrastto the predictionof candidateconver-

gence developed in the seminal work of Downs (1957), the citizen candidatemodel has equilibriawith differentiatedcandidates,and,as Besley and Coate

(1997) shows, equilibria to the model exist even when the policy space ismultidimensional.

Testingthe citizen candidate model using existing data may be difficult.The resultsdepend on the positioning of citizen ideal points, as well as other

parameters hatmay be difficult to estimate.The applicationof experimentalmethodsis particularly appropriatebecause the informationalrequirements,while difficult to satisfy in the naturally occurringworld, can be preciselycontrolledin the lab. This papercontributes o the citizen candidate literature

by developing an experimental methodologyused to test two of the model's

equilibriumpredictions. Investigatingthe citizen candidateframework n an







198

experimentalsettingalso helpsto identifywhat makespeople run n electionsand how this is related to efficiency.

The Osborne-Slivinskivariantof the citizen candidatemodel can be sum-marizedas follows:

1. Individuals have preferencesover a unidimensional policy space, char-acterized by a most preferredpoint. Utility from the policy variable is a

decreasing function of the distancebetween a citizen's idealpoint andtheactualpolicy implemented.Specifically, if a citizen's ideal point is x andthe policy implemented is w, utility takes the form -Ix- wI.

2. In the first stage of the policy determinationprocess, all citizens simulta-

neously decide whether to become a candidate for office (E), or not (N).Entrantsmustpay a cost C to runin the election, and receive a benefit B if

they win. If no citizen becomes a candidate,all citizens receive a "default"

payoff of -oo.3. Once the set of entrydecisions is made, an election is held, and a winner

of the electoral contest is determined.Votingis assumed to be "sincere" nthe sense that citizens vote for the candidate whose ideal point is closestto theirown.

4. The winner of the election implementshis or her own, commonlyknown,ideal point.

Implementationof the winner's favorite policy in the final stage is a dom-

inant strategy. Attemptsto commit to any other policy would not be cred-

ible. The default payoff of -oo is sufficient to guaranteeentry by at leastone citizen. In the presence of entry by at least one citizen, three payoffsare possible. If a citizen chooses N, and the winner has ideal point w, the

payoff is

-Ix - wl.

If a citizen becomes a candidateand loses the election, the payoff is

-C-Ix - wl.

If a citizen becomes a candidateandwins, the payoff is

B - C.

The basic approachusedby Osborneand Slivinski differs in some significantways from the Besley-Coate variantof the model. Specifically, Besley andCoate present a more generalframework,allowing for







199

1. A multidimensional ssue space2. A discretenumber of citizens

3. Utility functions that depend on the policy variable and identity of thepolicymaker

4. Differences in citizen skills with respectto policy implementation5. Votingbehavior that is sophisticated6. A defaultpolicy,xo, associated with thepossibilitythatno citizen becomes

a candidate.

Although the conditions associated with having more than two candi-

dates in equilibriumdiffer in the models, those associatedwith one andtwo-

candidateequilibriaare similar. Results from Osborneand Slivinski (1996)include

Proposition 1. (One-candidate equilibria underplurality rule). There is a

one-candidate equilibrium if and only if B < 2C. If C < B < 2C then the

candidate's ideal position is the median while if B < C, then it may be any

position within the distance (C - B)/2 of themedian.

Proposition2. (Two-candidateequilibriaunderpluralityrule).

(2i) A two-candidateequilibriumexists if andonly if B > 2(C - Eh), whereEh

is the highest value of e such that no third candidatecan enter at the median

(/-) and win.

(2ii) In any two-candidateequilibrium,candidates' ideal positions areA - F

and tt + efor ebetween 0 and eh

(2iii) An equilibrium in which the candidates' positions are /t - e and It +

&exists if and only ifE > 0, E> C - B/2,C > I|i - sI (where s is the positionbetween the candidates such that a citizen enteringat s does not affect the

vote totalfor

the other twocandidates)

and eitherE

< hor 8 =eh

< 3C - B.

An importantcharacteristic of Proposition 2 is the multiplicity of equilib-ria.This featureis common to both the Osborne-SlivinskiandBesley-Coatemodels. In an experimental setting, this raises the issue of equilibriumse-

lection, andhow subjects' beliefs influenceentrydecisions. These topics are

addressed n detail later.

Generatingan experimental design that precisely replicates one of the

models is complicated. In the Osborne-Slivinski framework, it is difficult

to implement the continuum of ideal points, and enforce the default payoffof -oo. In the Besley-Coate framework,the general structureof the utilityfunction, differences in the skill associated with policy implementation and

the multidimensional policy space are difficult to replicate in a simple way. As

such, the experimental design developed below combines elements from both

models. The basic approach is to modify the Osborne-Slivinski framework







200

to allow for a discrete number of citizens and a finite default payoff. Theutilized design focuses on the characteristicsassociated with the one- and

two-candidateequilibria hat are common to both models.This researchis connected to a long history of experimentalstudies of ra-tional choice models of politics (good surveys arePalfrey (1991) and Kinder& Palfrey(1993)). Forexample,Down's predictionof candidateconvergencehas been studied in McKelvey andOrdeshook(1990, 1993), Williams (1991)and Plott (1991). Results from these studies of two-candidate elections are

generally supportiveof the theory, although convergence occurs over timeand may be slower if there is incomplete information about candidate orvoter preferences.Morton(1993) uses an experimentaldesign in which two

candidates have policy preferences and varies the information available tocandidates concerningvoter ideal points. She finds divergence in candidate

positions when thereis uncertaintyaboutvoter ideal points (which is consis-tent with theoreticalmodels developed by Wittman, 1977, 1983, 1991), butthe degree of divergenceis not as great as theory predicts.In contrast to the

design utilized in thispaper, hese studies rely on anexogenously determinednumber of candidatesor parties.Also, subject payoffs for the design beloware related to whethera subject enters and wins an election, as well as the

policy implemented.As such, candidates have both an electoral and policyrelated motivation.

Because the citizen candidateapproachfocuses on citizen entrydecisions,this research is also related to previous experimentalwork on binarychoice

participationgames.Forexample,marketentry games, wherepayoffs dependon the number of participants hoosing to enter,havebeen studiedby Kahne-man(1988), Ochs(1990) andSundali,Rapoportand Seale (1995). Theresultsfrom these experimentssuggest thatsubjects are able to coordinateentryde-cisions in a manner that is consistent with the expected profits from entry.

In contrast, however,Fischbacherand Thoni (1999) find over-entrywhen amonetaryprize is awardedto a randomly selected entrant,andCamererandLovallo (1999) find over-entrywhen payoffs depend on skill-based compe-tition among entrants.The results from these two papersare consistent withthose presentedlater.

The presence of multiple equilibriaconnects this researchwith the coor-dinationgames modeledin VanHuyck, Battalio andRankin(1997) and Van

Huyck, Battalio and Beil (1990), among others. These studies demonstratethe difficulties subjectsoftenhave in achieving coordination,andthatsubjects

may learnto coordinateover time. The majorityof experimentalresearchoncoordinationgames, as well as that on marketentry games, use a symmetricpayoff structure. The design utilized below leads to an interesting coordina-

tion game with asymmetric payoffs, and the results suggest coordination is

costly and (consistent with previous research) evolves over the course of the

experiment. The remainder of the paper is organized as follows. The next







201

section discusses the experimentaldesign, the following two sections presentthe results,andthe last section concludes.

2. Experimental Design

Subjectsfor the 10 experimentalsessions werepaidvolunteersrecruitedfrom

IntroductoryEconomics and Political Science classes at American Univer-

sity. Priorto volunteering, subjects were told thatthey would participate n

a decision-makingexercise andbe paid in cash an amountthatdependedon

the decisions of the experimentalparticipants. n addition,subjectswere paid$10 forkeeping theirexperiment appointment.All earningswere paid, in pri-vate, to subjectsat the end of theirexperimentalsession. Five of the sessionswere conductedusing a "highcost"parameterizationor the design, and fivesessions were conductedundera "low cost" parameterization.Each sessionhad five subjects, and lasted for about45 min. Averagesubjectearnings forthe high and low cost parameterizations includingthe $10 "show-up"fee)were $22.80 and $23.94, respectively.

At the beginningof the experimentalsession, subjectswere given instruc-tions (reproduced n theAppendix)thatcanbe summarizedas follows. At the

beginningof each of 10 rounds of the experiment,participantswere assignedto one of the ideal points depicted as follows:

15 30 50 70 95

Idealpoints were assigned so that in each roundone participantoccupiedeach ideal

point.For each round the medianideal

pointwas 50.

Subjects,in

additionto being informed of their own ideal point, were told that in eachround one participantwould be located at each of the ideal points. Over thecourse of the experiment, assignmentof ideal pointswas manipulatedso thateach subject played each ideal point twice, once in the first five rounds andonce in the second five rounds(althoughthis was notrevealedto the subjects).Subjectswere endowed with "cashearnings"of $18, and informed thattheirfinal cash earningswould be influencedby two factors.

First, earnings were influenced by whether a participantnominated her

pointfor considerationby the group,andif so whetherherpointwas chosen asthe "winning point."In each round,each participantchose (simultaneously)whether to nominate her ideal point for considerationby the group. Thiswas done by writing YES (if they chose to nominate their point) or NO

(otherwise) on a piece of paper.Once each participantmade a decision, theset of nominatedpoints was announcedto the group.If a participantchose







202

to nominate herpoint,a fee ($3 or $1.50, dependingon the parameterizationused for the session) was deducted from her cash earnings. If a participant

nominatedthewinningpoint,she was awardeda benefit of $3.05. The winningpoint was determinedby the following process. The numberof votes for eachof the nominatedpoints was tallied, under the imposed condition that each

subjectvoted"sincerely"n the sense thathis orher vote was for the nominated

point closest to his or her own ideal point. If more thanone nominatedpointwas closest, the vote was determinedby a random draw.The sole decisionthe subjects made in each round was whether to nominate their ideal point.Subjects did not actuallycast a vote; the experimentercalculatedthe numberof votes for each nominatedpoint. Implementing sincere voting makes the

design consistent with the Osborne-Slivinski model, andfocuses the analysison nominatingdecisions. Once the votes were tallied, and the winning pointdetermined(ties were brokenby a randomdraw),the location of the winningpoint was announcedto the group.If no subjectchose to nominate her ideal

point, the winning point was determined by a random draw.In this case,no subject was chargedthe entry fee or received the benefit associated with

nominatingthe winning point. Although this implementationis at odds withthe Osborne-Slivinski model (which utilizes a default payoff of -oo), itis consistent with the Besley-Coate framework,and avoids the difficulties

associated with chargingsubjectsa large amount when no subjectbecomes acandidate.

Second, payoffs were influenced by the position of the winning point. In

particular,each participant'searningswere lowered by Ix- wl cents, wherex represents the participant's deal point, and w is the winning point. For

example, a subject assigned ideal point 15 would lose 15 cents if 30 was the

winning point, 35 cents if 50 was the winning point, 55 cents if 70 was the

winning point, and 80 cents if 95 was the winning point. At the end of each

round, subjectsrecordedtheir

assignedideal

point, nominatingdecision,the

position of the winningpointandadjustments o their cash earningson a sheet

provided by the experimenter.The values for B andC were chosen to replicatethe conditions associated

with one andtwo-candidateequilibriato the citizen candidatemodel. For the

high cost parameterization,he value for B ($3.05) was slightly largerthanthe value for C ($3.00), which leads to a one-candidateequilibrium.For thesecond (low cost) parameterization, chose to cut the value of C in half (to$1.50), while maintainingall other elements of thehighcost parameterization.

This simple changecreatesa muchricherstrategicenvironmentthatincludesa two-candidateequilibrium.Forbothparameterizations,apurestrategyNash

equilibriumexistswiththesubject assignedthe median ideal point(50) choos-

ing YES, andall otherschoosing NO. This equilibriumis "payoffdominant"in the sense that it maximizes group earnings. The implementation of 50







203

Table 1. Summary of experimentaldesigns

Parameters "High"cost "Low"cost

B $3.05 $3.05

C $3.00 $1.50

Equilibrium Single candidate Single candidate with ideal point 50

predictions with ideal point 50 Two candidateswith ideal points 30 and 70

Mixed strategy equilibriumwith entry by 30,50 and 70

Experimental A, B, C, D, E F, G, H, I, Jsessions

minimizes the losses associated with the policy relatedpayoffs and results

in a participant(at 50) capturingthe surplusassociated with winning ($.05or $1.55 depending on the parameterization).For the low cost parameteri-zation, there is a second pure strategyequilibriumhaving two candidatesat

30 and 70, as well as an equilibrium n mixed strategieswith positive entry

probabilitiesfor subjects assigned 30, 50 and 70. The existence of multiple

equilibriawhen B > 2C creates an interestingcoordinationgame, describedin detail later. Table 1 provides a summaryof the utilized parameterval-

ues, and lists the equilibriumpredictionsand sessions conductedunder each

design.

3. Results for High Cost Parameterization

Figure 1 displays the number of entrantsby ideal point for the sessions with

C = $3.00.The one-candidate pure strategy Nash equilibriumprediction (only the

subject with ideal point 50 enters in each round) is consistent with 86%

of the observed decisions. Of the 250 decisions made by subjects, only 35

were inconsistent with this prediction(entrywith ideal point 15, 30, 70 and

(.1

%I-

o

504030

20100

15 30 50 70 95

Ideal Point

Figure 1. Cumulativeentrydecisions: Design 1.







204

Table 2. Binomial test for randomplay and EPW (p-values in

parentheses)

Observedentry Hypothesized value: HypothesizedIdealpoint proportion Randomplay value: EPW

15 0.02 0.5 (.000) 0.188 (.001)

30 0.18 0.5 (.000) 0.437 (.000)

50 0.86 0.5 (.000) 0.75 (.039)

70 0.3 0.5 (.007) 0.437 (.067)

95 0.06 0.5 (.000) 0.125 (.227)

95 or failure to enter with ideal point 50). However, there was significantentry by subjectswith idealpoints 30 and 70. Previousexperimentalresearchon binarychoice participationgames where a monetary prize is awardedtoan entranteither randomly (see Fischbacher and Thoni, 1999) or through"skill-based"competition among entrants(see Camererand Lovallo, 1999)reportsexcess entryrelative to the Nash prediction.While entry by subjectswithidealpoints30 and70 is notconsistent with theNashprediction,excessive

entry may be a feature of experimentalplay of binary choice entry games.This suggests thatsubjects may be using strategiesthat are not mutual best

responses. Two alternativehypotheses about subject play are tested. First, itis clear from the datathatsubjectdecisions were not consistent with random

play. Table 2 presents the results of a Binomial test of the null hypothesisthatsubjectsentered withprobability1/2.Foreach ideal point, this hypothesiscan be rejectedat the .05 level of significance. A second alternative s that a

subject'spropensityto enter is a function of the number of ways in whichthe

entrydecisions of othersubjectsallowthatsubject'sidealpointto win. Table2also contains the resultsof aBinomial test of the null hypothesisthatsubject'senteredwith theirprobabilityof winning (EPW) under the assumptionthatotherplayers in the middle (30, 50 and 70) would enter withprobability1/2,and that other subjects with ideal points on the outside (15 and 95), wouldnot enter. Specifically, randomentry by participantsassigned to 30, 50 and

70, coupled with non-entryby the participantat 95, results in a win for the

subject at 15 (should he or she enter) with probability .1875. This reflectsthe probabilitythat each of the middle players stays out of the race (which

occurswithprobability1/8) andtheprobabilitythat 50 and70 enter,while 30stays out (also occurringwith probability1/8). This second case results in atie between 15 and70, which implies 15 wins with probability1/2.Underthisalternativebehavioralassumption,the entry probabilities for subjects withideal point 30, 50, 70 and95 are .4375, .75, .4375 and .125, respectively.Thenull hypothesis of EPW can be rejectedfor ideal points 15, 30 and 50 at the







205

5% level of significance. However,EPW cannotbe rejected at the 5% levelfor ideal points 70 (p-value, .067), and95 (p-value, .227).'

Theory predicts that in each round,a subject's entrydecision will dependon his or her expectations regarding he entrydecisions of the othersubjects.As there were five separate experimentalsessions, it may be the case that ex-

pectationsandentrydecisions variedby session.2 Table3 presentsthe resultsof two logistic regressions used to assess the extentof "session"effects. The

dependentvariablewas a dummy takingthevalue 1if a subjectentered,and0

otherwise. The independentvariablesincludeddummies for ideal point (oneeachfor30, 50, 70 and95), experimental ession (oneeach forexperimentsA,

B, C andD, the firstthroughfourthexperiments or this design) andwhether

the subject'sdecision was a "Best Reply."This variable takes the value 1 ifthe subject's entry decision was a best response to the patternof entrydeci-sions thatprevailed in the preceding period,and 0 otherwise. Includingthisvariable lowers the sample size from 250 to 225, because one observation

(entrydecision in period 1) is lost for each of the five participants n each ofthe five sessions. The baseline case for each regressionmodel was a subjectwith ideal point 15 who participated n the fifthexperimentalsession.

For Model 1, the coefficients on the session variablesare not statistically

significant. However, while the coefficients on 30 and 70 are positive and

significant(which is consistent with Figure 1), the coefficients on best replyand idealpoint 50 are not significant,and the coefficient on best replyhas the

Table 3. Logistic regressionoutput

Model 1 Model 2

B Sig. B Sig.

Thirty 2.21069 .0459Fifty 13.24222 .5121

Seventy 3.151735 .0037

Ninety-five 1.17495 .3224

A -1.13759 .1409 -1.63565 .00885

B -0.25805 .7122 -0.95016 .10285

C 0.832418 .1824 0.79765 .10681

D -1.00287 .1652 -0.72673 .20352

Best reply -7.04438 .7269 2.804316 2.10E-10

Constant -3.68646 .0008 -1.36413 .00032

%Correcta 87.6 78.2

Nagelkerke R2 0.631 0.333

N 225 225

aPercentcorrect based on a cut value of .5.







206

wrong sign. These are classic signs of multicollinearity.Essentially,in mostroundsof most sessions, the best response to the patternof decisions in the

previous round had the subjectwith ideal point 50 enter, and subjectswithother ideal points stay out. As such, the best reply variable is similar to the

dummyvariable for ideal point50, and induces collinearity.Intuitively, deal

pointis important o the extentthat t determines a subject'sbest reply.Model2 dropsthe idealpoint dummyvariables(this reducesboththeNagelkerkeR2

andthepercentof correctpredictions).In thiscase, the coefficient on bestreplyis significant and in the expected direction. Also, the coefficient on sessionA is significant.3The significanceof the best reply variablesuggests that the

assumptions underlyingthe Nash prediction may be more appropriate han

the other behavioralassumptionsdescribed earlier (randomplay or EPW).Further,the experimentalresults can be used to assess the efficiency of

this institution in terms of the share of the potential surplus capturedbyparticipants.The maximumearnings orsubjectsin eachroundoccurredwhen

only 50 entered.Thechangeincashearningsin this case would be -$1.15 perround.Thus, over 10 rounds,the minimum amount subjectscould lose was

$11.50. In connectionwith their endowments of $18, this implies maximum

groupearningsfor eachexperimentwere $78.50. As there werefive sessions,the maximum level forsubjectearnings

(ma,,x)

underthis designwas $392.50.

Actual earnings (Hact) were $319.90 (meaning that relative to the best casescenario, they lost an additional$72.60). Thus, subjects captured81.5% ofthepossible surplus.This measure s somewhatmisleading,however,because

it does not control for what subjects could be expected to earn relative toother behavioralspecifications.Forexample, randomentry by all participantswould resultin expected perround osses of $6.00. This implies thataggregateexpected surplusunderrandomplay (Hrand)would be $150. The followingindex can be used to assess the efficiency of subject decisions relative to

randomplay:

E = (Hact -Hrand)/(Hmax

-Frand)

Note that E = 1 if Iact= H-max, 0 if lact

=Irand and is negative if

Hact <Irand. Using thismeasure,for the high cost parameterization,E = .70.

Under the alternativeassumptionthat players enter accordingto the proba-bility they can win, expected surplus (Hepw) s 237.121. SubstitutingHepwfor Hrand in the formulaabove results in E = .533. As such,

subjectsin the

experiment were able to capturea greater share of the surplusthan wouldbe expected under either of the other behavioral specifications.However,thedecrease in E associatedwithchangingthe baseline case showsthatthe clear-est determinantof surpluslost is related to entry costs (which are lower, in

expectation,under EPW thanrandomplay). To highlight this point, note that







207

the largest"policy"-relatedoss for thegroupoccurswhen 95 is implemented.Totalpolicy-related osses in this case are2.15, while the loss associated with

one excess entrant s 3.00.

4. Results for Low Cost Parameterization

For the low cost parameterization, he value of C was changed to $1.50. This

simple change complicates the decision environment,because it introduces atwo-candidateequilibriumand at least one equilibriumn mixed strategies(inadditionto thepayoff dominantequilibriumn which50 is the only entrant).Asecondequilibriumnpure strategieshasonly subjectswith idealpoints30 and

70 become candidates. In this case theoutcome of the election dependson thevote of 50, which is determinedby a randomdraw. nexpectation,thepayofftocandidatesassociated with the B and C parameterss 1/2*3.05 - 1.50 = .025.For the candidates,entry also increases the policy-related payoff because itmakespossibletheimplementationof the candidate's deal point. Entryby anyothersubjectwould result in a loss, andmay lower the policy-relatedportionof payoffs for the entrant. In a sense, the existence of multiple equilibria(acommon feature of citizen candidate models) creates a coordination gamebetween players with ideal points 30, 50 and70. For50, entry is a best replyif one of the subjects at 30 or 70 fails to enter. For either 30 or 70, entry isa best reply if 50 stays out, or if 50 enters and the subject on the oppositeside of 50 also enters. While 30 and70 preferthe two-candidateoutcome, 50

prefersthe single-candidateequilibrium.Theasymmetryof subjectpositionsandpayoffs is a novel feature associatedwith this coordinationgame.

Further,heexistence of two pure strategyequilibriagives rise to anequilib-rium in mixed strategies.The following entry probabilitiesconstitutea mixed

strategyNashequilibriumo thegame:P15 = P95= 0, P30 = P70 = .73439,and

P50=

.6315,where

pxis the

probabilityhat a

subjectwith ideal

pointx

enters.Dynamic pressuresaroundthe mixed strategyprobabilitiespush sub-

ject play towards one of the pure strategyequilibria.For example, holdingP50 constant,an increase in p70 (relativeto the mixedstrategyprobability) n-creases theexpected payoff to entryfor the subjectwithideal point 30. This isbecause an increase in P70 makes the two-candidateequilibriumpayoff more

likely and lowers the payoff to staying out for the subjectat 30 (she is more

likely to get -.40 (the payoff when 70 wins) than -.28 (the payoff when 50

wins)). Also, a decrease in P50(holdingP70 constant) ncreases the expected

payoff to entryfor a subjectwith idealpoint30, because it increases the prob-ability that he or she wins the election outright(which occurs when neither

50 nor 70 enter).Similardynamicpressuresapplyto subjectswith ideal point70. When 30 enters with probabilityabove the mixedstrategyor when 50 en-ters with probability ess than the mixed strategyequilibrium,70 should entermore often. For subjects with ideal point50, an increase in the probabilityof







208

3

en a

50

40

30

20100

15 30 50 70 95

Ideal Point

Figure2. Cumulativeentry decisions: Design 2

entry for either 30 or 70, relativeto the mixed strategy probabilities,lowerstheexpected payoffsto entry,because it makes it morelikely that50 is "brack-

eted"by candidates,and loses. Tosummarize,if 30 or 70 startout above theirequilibrium probabilities,50 should enter less. This makes 30 and 70 evenmore likely to enter,andpushes the play towards the two-candidateequilib-rium.Alternatively, f 30 and 70 startbelow theirequilibriumprobabilities,50should enter moreoften,which reinforces the direction of movement towardsthe one-candidateequilibrium.In other words, both pure strategyequilibriahave unambiguousbasins of attractionaway from the mixed strategyequilib-rium.As such, if subjectsbegintheexperimentalsession withdifferentbeliefsabout how other

subjectswill

play, dynamic pressures maylead them to one

of the pure strategyequilibriaover the course of the experiment.Figure 2 displays the number of entrantsby ideal point the low cost pa-

rameterization.Similar to the results from the high cost parameterization, ubjects with

idealpoint 15 or95 rarelyentered.Forthe low cost parameterization, owever,

subjectswith idealpoint30 and70 enteredmuch morefrequently,andsubjectswith ideal point 50 entered less often. Entry by subjects with each of the

middle ideal points suggestsexperimentalplay was not consistentwith one of

thepure strategyequilibria in whicheither 50 or both 30 and 70 do notenter).Table 4 presents the results of binomial tests of the hypotheses that subjectplay was random,consistent with EPW, and that subjectsenteredaccordingto the mixed strategyprobabilities.

Table 4. Binomial tests or randomplay, EPW and mixedstrategy(p-values inparentheses)

Observedentry Hypothesizedvalue: Hypothesized Hypothesizedvalue:

Idealpoint proportion Randomplay value: EPW Mixed strategy

15 0.06 0.5 (.000) 0.188 (.020)30 0.88 0.5 (.000) 0.437 (.000) 0.734 (.007)

50 0.56 0.5 (.322) 0.75 (.005) 0.632 (.362)

70 0.88 0.5 (.000) 0.437 (.000) 0.734 (.007)

95 0.08 0.5 (.000) 0.125 (.469)







209

The hypothesis of randomplay can be rejectedfor each ideal point otherthan 50 (subjects assigned 50 entered 56% of the time), and the EPW

hypothesis can be rejected for ideal points other than 95. The mixed strat-egy hypothesis,while consistent with the entrydecisionsof subjects assignedideal point 50, can be rejected for subjects with ideal point 30 and 70.4 Incontrast with the results from the high cost parameterizationwhich supportthe one-candidateequilibriumprediction),aggregatesubjectdecisions for thelow cost parameterizationare not consistent with theequilibriumpredictionsdescribed earlier. This may not be surprising,given the coordinationprob-lems associated with the decision environment; ubjectsprobablyhad differ-ent expectationsabout each other's play at the beginningof the experimental

sessions.Fortunately,examining changes in subject play overthe course of the ex-

perimentprovidesmore insight into subjectbehavior.Specifically, it suggeststhat subjectbeliefs aboutplay startedin the basin of attraction for the two-candidateequilibrium,and convergedto the two-candidateequilibriumovertime. Table5 presentsthe entry decisions groupedoverthe first and last fiverounds of the experimentfor each ideal point, as well as two statistical testsused to see whethersubjectbehavior was different nthe last five rounds thanin the firstfive.

The results of both the t-test and the Wilcoxon test suggest that play bysubjects with ideal points 30, 50 and 70 changed over the course of the ex-

periment. Subjects with ideal points 30 and 70 enteredmore often duringthe

last five rounds, while subjects with ideal point 50 entered less frequently.The intuitionbehind this result is straightforward.Overthe first five rounds,

subjects with ideal point 30 or 70 entered about76% of the time (which is

higher than their mixed strategy probabilities).As such, 50 had about a 43%

chanceof winningshouldhe orshe enter.Since theexpected payoff toentering

(about -.3)was less thanthe

expected payoffassociatedwith

stayingout of

the election (-.2), it is not surprisingthat50 entered ess frequentlyover the

remainderof the experiment.That is the direction his or herbeliefs/expected

payoffs were pushing him or her. Similarpressures (resulting in an increasein entry) prevailedfor subjects with ideal points 30 and 70. Because subjects

assigned ideal points 30 or 70 enteredfrequentlyduringthe firstfive rounds,

Table 5. Subject entrydecisions 1stfive roundsvs. lastfive rounds low C

15 30 50 70 95

1stfive rounds 2 19 18 20 1

Last five rounds 1 25 10 24 3

Pairedsample t-test (p-values) .327 .011 .008 .042 .327

Wilcoxon signed rankstest (p-values) .317 .014 .011 .046 .317







210

Table6. Logistic regressionoutputfor low cost parameterization

Model 1

B Sig.

Thirty 0.808809 1.99E-06

Fifty 0.701036 5.33E-05

Seventy 0.839951 2.36E-06

Ninety-five 0.824117 0.425727

F 0.657156 0.727674

G 0.666764 0.965438

H 0.659823 0.797999

I 0.655421 0.797247

Best reply 0.528879 0.000395

Constant 0.775033 8.62E-05

% Correcta 87.1

NagelkerkeR2 0.668

N 225

apercentcorrectbased on a cut value of .5.

they were able to coordinatetheir entry decisions over the final rounds (forwhich entry occurred49 times in 50 opportunities).This patternof play is

consistent with the basins of attractionargumentdescribedearlier,and does

not appearto have varied with experimental session. A logistic regression

using entry as the dependentvariable and maintainingthe independentvari-

ables discussed under the high cost parameterizationwas utilized to assess

the extent of session effects. The results arepresentedin Table 6.

The ideal pointcoefficients,as well as the best

reply coefficient,have the

expected signs andsignificanceresults. The session coefficients are not statis-

tically significant, suggesting experimentalsession did not play a significantrole in subjectdecision making.5

Interms of theefficiencyindex,the maximumearningsforsubjectsin each

roundoccurredwhenonly 50 entered.The changein cashearnings n this case

is $.35 per round.Thus over 10 rounds, subjects could win a maximum of

$3.50. In connection with the endowments of $18, this implies maximum

group earnings for each session were $93.50. As there were five sessions,

the maximum level for subjectearningsunderthis design was $467.50. Sub-jects actuallyearned$348.60 (meaningthatrelative to the best case scenario,

they lost $118.90). This implies subjectscaptured74.5% of the availablesur-

plus. Using the efficiency index described in the high cost parameterization,and under the baselineof randomplay, the value for E was .102. Under the

assumptionthatsubjectsenteraccording to theirprobabilityof winning, the







211

value for E is -.282. Thus, while subjectsfaredmarginallybetter thantheywould have underrandomplay, they did worse than would be expected un-

der entryaccording to the probabilityof winning. This reinforces the notionthat the main determinant of subject earnings was the value of entry costs.

Lowering the cost of entry resulted in more subjects becoming candidates,which more thanoffset the lower cost associated with each entrant.Althoughearningsfor the groupwould have been higherif theycoordinatedon the one-candidate equilibrium, the payoff-maximizing outcome did not serve as afocal pointfor individual decision making.Instead,frequententry by subjectsassignedideal points 30 and 70 in earlyroundsof theexperimenthighlightedthe strategic considerations. In each round, individualpayoffs were higher

for subjects assigned ideal points 30 and 70 when both entered,bracketingthe median candidate and having a chance to win the election. In this case,

successfully resolving the coordinationproblem in the latter rounds of the

experiment actually served to reducegroup payoffs.

5. Conclusion

The citizen candidateapproachprovidesadded realismto models of endoge-nouspolicy formation,andrepresentsasignificantadvanceover the traditional

median voter model. The predictionof candidatedivergenceunderhigh netbenefits is supported by casual observation of many electoral contests. Un-

fortunately,a more rigorous examination of the model using existing datais complicated by its precise informationalrequirements,but it remains an

importantmodel to test. This paper utilizes experimentalmethods to testtwo equilibriumpredictions of the citizen candidatemodel. To my knowl-

edge, this is the first set of such experiments.While the experimentaldesignis a simple modification of the Osborne-Slivinski framework, t capturesthe

relevant eatures of one- and two-candidateequilibria

hatare commonto both

Osborne and Slivinski (1996) and Besley and Coate (1997). The followingconclusions are supportedby the research.

Equilibriumpredictions from the citizen candidate model suggest thatan increase in the net benefit associated with winning an electoral contestshould increase the number of candidates. This predictionis supported bythe data.For the high cost parameterization, ntrywas observed28.4%of the

time, while the percentage of entrantsfor the low cost parameterizationwas49.2%. The point predictionsassociated with the high cost parameterization

are generally supported. The pure strategy Nash equilibrium prediction,which has only the median citizen become a candidate, is consisted with

86% of observed subject decisions. While subjects with other ideal points,particularly those at 30 and 70, entered more often than the theoretical

prediction,this "over-entry"s consistent with otherexperimentalstudies of

binarychoice participationgames.







212

One aspect of the citizen candidateapproach,studied under the low cost

parameterization,nvolves the multiplicity of equilibria when the net ben-

efits to winning are large. The parameterizationutilized for these sessionsgenerated wo equilibria n purestrategies(one of which haddivergentcandi-datepositions) and at least one mixed strategy equilibrium.Importantly, he

pure strategy equilibriahad clear basins of attractionaway from the mixed

strategyequilibrium.Subjectplay under this parameterizationsuggests con-

vergenceto the two-candidateequilibriumover the course of the experiment.Convergenceto equilibriumover time is a featureof many experimentalpa-pers, including several on coordination games. In this case, subjects withideal points 30 and 70 entered above their mixed strategy probabilitiesearly

in the experimentalsession, which may have focused expectations on thetwo-candidateequilibrium.Over the finalfive rounds of the experiments, hisresultedin greaterentryby subjectsat 30 and 70, and less by subjects withthemedian idealpoint.Thispatternof entrydecisions does not appear o havevariedby session, and can be seen to supportthe two-candidateequilibriumprediction.

One implicationof the experimentalresults involves the efficiency asso-ciated with this institutionin terms of the surplus captured by subjects.Forthe high cost parameterization, ubjects did better than would be expectedunder random play or EPW. However, for the low cost parameterization,subjects fared only marginallybetter than they would have been expectedunder random play, and actually did worse than would be expected underEPW. Although policy implications from the experiments may be limitedbecause they rely on the use of a very controlled setting, the results sug-gest that having a large number of candidates may be inefficient from aneconomic perspective. Intuitively,when campaigningis expensive, increasedchoice amongstcandidatescomes at a cost. Inmy view, futureresearchshould

be devoted to the relaxation of the sincere voting assumption (which im-plies futuredesigns should supportmore thantwo candidatesin equilibrium,because sincere voting with two candidates is sophisticated). It would alsobe interesting to vary the relative weights attached to the policy and non-

policy-relatedbenefits associatedwith electoral competition (perhapsby us-

ing differentparametersorthepolicy-relatedpayoffs). However,resultsfromthe experimentreportedearlier can be viewed as generally supportiveof theone- and two-candidateequilibrium predictions from the citizen candidate

approach.

Acknowledgements

The author thanks James Walker, Arlington Williams, Robert Feinberg,Kurtis Swope and an anonymous referee for their thoughtful comments anddiscussion.







213

Notes

1. Over the course of each session, each subjectplayed each ideal point twice, and as such

contributed wo entry decisions to the calculation of each entryproportion.This may callinto question the assumption of independentobservationsrequiredfor a Binomial test.

Looking at the results from the last five rounds,over which each subject contributes a

single entrydecision per ideal point, generatessimilar results.2. Because subjects engaged in multiple rounds of the experiment, it is also importantto

consider whether learning played a role in subject decisions. Using a paired samples t-

test, or a non-parametricWilcoxon test, the null hypothesis of no difference between

subject play in the first and last five rounds of the experimentcannot be rejectedat the5% level of significance for any of the ideal points. This suggests that for the high cost

parameterization, ubject learningdid not significantlyaffect experimentalplay.The roleof

learnings addressed in more detailunderthe results for the low cost

parameterization.3. Includingvariables for period effects does not substantivelyaffect the regressionresults.If subjectbehavior converges to the equilibriumpredictionover time, it is importanttointeractperiod with ideal point,because the effect should differby ideal point.Intuitively,thiseffect is pickedup by the bestresponsevariable. ncludingperiodeffects and nteraction

terms,however,lowers thedegreesof freedomassociated with theregressionresults.Other,morecomplex, specifications of the bestreplyvariable arepossible. Forexample, subjectsmay consider the patternof entrydecisions thatprevailednotonly in theprecedingperiod,but in other earlierperiods as well. Modelingthe best reply variable as the percentageof

previous periods in which entry is a best reply (a modified version of "fictitious"play)does not substanfively affect the regressionresults. Finally, each subject made 10 entrydecisions, which raises the issue of independence.The inclusion of dummy variablesforeach of the 25 subjects (to controlfor subject specificeffects) does not qualitativelyaffect

anyof the model estimates. The signs of theestimated coefficients andsignificanceresultsremainas reported n Table4, and no dummyvariableon subject s statisticallysignificant.

4. Lookingat decisions over last five roundsresults in similarconclusions. Thehypothesisofrandomplay can be rejected for ideal points 15, 30, 70 and95, butnot for 50. Results for

the test of EPW are the same as those in the table. Interestingly,however, the hypothesisthatsubjectplay is consistent with the mixedstrategyprobabilitiescan be rejectedfor each

of theideal points over the last five rounds.Thisreinforces the notion thatsubjectplay was

moving towards the two-candidateequilibriumover the course of the experiment.

5. As wasthecase for thehigh cost parameterization,ncludingperiodeffects does notchangethequalitativeresults. Adding a periodvariable, nteractedwith each ideal point,generatescoefficient estimates that are marginally significant (p-values around .1), and have the

expected signs (the interaction variablecoefficients arepositive for ideal points30 and70,and negative for ideal point 50). Includinga more complex variantof the best responsevariable or dummy variables for each subjectdoes not substantivelyaffect the results. No

specification generated session coefficients that were statistically significant.

Appendix: Instructions (High Cost Parameterization)

You are about to participate n an economics experimentthat involves makingdecisions. If you read the following instructionscarefully and make gooddecisions, you may earn a considerable amountof money. This money willbe paid to you privatelyat the end of the experiment.

In this experiment, one of five competing alternatives will be chosen bymajorityrule. The alternativesare representedby points on the blackboard.







214

At the beginning of each of 10 rounds, you will be assigned one of thesealternativesas your "idealpoint."You will choose whether to nominate this

point for consideration of the group, according to a process describedlater,at the beginning of each of the 10 rounds.Once all participantshave chosenwhether to nominate their idealpoints, a point will be selected accordingtoa process described later.Your deal point is the alternativethat,if chosen bythe group,maximizes your earnings.Yourearningswill be influencedby two factors:

1. The distance between the winningalternativeand your ideal point.2. Whetheryou choose to nominateyouridealpoint, and whether t is selected

as the winner.

Youbegin theexperimentwith "cashearnings"of $18 (thisdoesnot includethe $10 "show up" fee). At the end of each round, your cash earnings are

updatedas follows:

1. The distance between youridealpoint and the point selected by the groupis SUBTRACTED fromyour earnings.

2. Ifyou

nominateyour

idealpoint,

$3.00 is SUBTRACTED fromyourearnings.

3. If you nominate the winning point, $3.05 is ADDED to yourearnings.4. If no participantnominateshis/her ideal point, the winning point will be

determinedby a randomdrawamong the set of ideal points. In this case,$3.05 will not be added to the participantwhose ideal point is the winner.

Upon completion of the tenthround, you will be paid, in cash, an amount

equalto your cash earnings.

The distributionof ideal pointsfor the five participants n each round willbe as follows: This meansthat,for each round,one participant's dealpoint is

I----------------------------------------------------I -------I------ ---------I

15 30 50 70 95

15, one participant's s 30, one participant's s 50, one participant'ss 70 andone participant's s 95.

In each round, the winning point will be determined by the followingprocess:

1. Each participant simultaneously chooses whether to nominate his/herideal point, by writingYES (if you want to nominate your ideal point) orNO (otherwise) on a piece of paper.Any participant nominatinghis/her







215

ideal point will be charged $3.00. The participantwho nominates the

winningpoint earns$3.05. If no participantnominates his/her ideal point,

the winning point will be determinedby a randomdrawamong the set ofideal points.2. Once the set of nominatedpoints is determined, he winning point will be

determinedby majorityrule.Participants, owever,will notactuallychoosethepointforwhich theyvote. Eachparticipant's otewill be forthe alterna-tive that s closest to his/her idealpoint.If morethanone alternative s clos-est to aparticipant'sdeal point,the vote is castrandomlybetween theclos-est points.The winning alternative s the one thatreceives the most votes.If morethan one alternative ies for thehighestnumberof votes, thewinner

is determinedrandomly among thepointsthattie for the highest vote total.

This process will be repeatedfor a totalof 10 rounds.

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2005 the citizen candidate model_an experimental analysis

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