Coordination and Communication in Multiparty Electionswith Costly Voting1

Bernhard Kittel2 Wolfgang Luhan3 Rebecca Morton4

November 28, 2008, Preliminary Draft; Do Not Cite

1This research was supported by2Zentrum für Methoden der Sozialwissenschaften, Institut für Sozialwissenschaften, Carl von Ossietzky

Universität Oldenburg, 26111 Oldenburg, +49-(0)441-798 4835, bernhard.kittel@uni-oldenburg.de3MSW - Center for Social Science Methodology, University of Oldenburg, A6-3-322, Ammerlaender

Heerstrasse. 114 - 118, 26129 Oldenburg, +49 441 798 4528, Wolfgang.Luhan@uni-oldenburg.de4Department of Politics, NYU, 19 West 4th Street, 2nd Floor, New York, NY 10012, re-

becca.morton@nyu.edu.

Abstract

We provide a preliminary report on experiments in process. In the experiments we investigatecostly voting in multiparty elections. Most previous formal and experimental research has eitherfocused on how voters coordinate in multiparty elections or the determinants of turnout in binarychoice elections. Theoretical and empirical research suggests that turnout in costly elections ispartly driven by social incentives as voters appear to choose such that the group of voters withsimilar preferences benets even at a cost to themselves. In multiparty elections, groups of voterswith similar preferences often have an incentive to coordinate on a strategic choice. In this paperwe contend that mechanisms that help groups voters coordinate in multiparty elections also helpinstill in voters the social incentives to participate when voting is costly. We investigate threetypes of mechanisms that may help voters coordinate in multiparty elections: party a¢ litation,communication within parties, and communication across parties. We nd signicant evidencethat communication of both types signicantly increases both strategic voting and participation.We also nd that all three mechanisms reduce wins by the candidate least favored by the majorityof voters.

Introduction

In his seminal work, Making Votes Count, Gary Cox (1997) emphasized the importance of

coordination in voting. When voters have more than two choices, typically labeled a multichoice

election, they often face a choice of whether to vote sincerely for their rst preference or to vote

strategically for a secondary choice that is more likely to win and prevent a worse choice from

winning. As Cox and Myerson and Weber (1993) demonstrated, voters in such situations face

strategic uncertaintyvoters with common preferences have a desire to coordinate on a common

strategy, either voting sincerely or strategically. Experiments by Forsythe, et al. (199x) and

Morton and Rietz (2008) explore how di¤erent aspects of elections such as polls, campaign

contributions, and majority requirements can be used by voters as coordination mechanisms to

resolve this uncertainty.1

However, the literature on strategic coordination in elections generally ignores the e¤ect

that costly voting can have on such coordination. That is, in Myerson and Weber and in

the experiments testing strategic voting, participation is costless and thus voters have little

incentive to abstain. A separate game theoretic and experimental literature has examined costly

voting in elections with only two choices.2 The focus of this literature is the extent that the

game theoretic model of voting explains participation in elections when voting is costly. This

experimental work in general nds that comparative static predictions of the game theoretic

model can explain voting patterns, but that voters in small electorates participate less than

predicted while those in large electorates participate more than predicted.

As Feddersen (2004) discusses, a number of researchers explain the rather robust result

1Rietz (1993) reviews these experiments.2The principal game theoretic research on turnout under complete information about voter choices can be found

in Ledyard (1984) and Palfrey and Rosenthal (1983, 1985). For examples of experimental studies of this gametheoretic work see Levine and Palfrey (2007), Du¤y and Tavits (2008), and Schram and Sonnemans (1996a,b).The original decision-theoretic rational choice model of voting was formulated by Downs (1957). In the gametheoretic models the probability of being pivotal is endogenous and related to the size of the electorate. To seethe importance of the endogeneity, consider that if everyone chose not to participate according to the rationalchoice decision-theoretic model, then the probability of any voters vote being pivotal is 1, since by voting thatindividual can decide the outcome.

1

that voters participate more than predicted in large electorates as reecting the inuence of

groups. Morton (1987, 1991), Schram (198x), and Uhlaner (1989) point out that even with

costly voting, for a group of voters with common preferences, turnout rates can be sizeable.

They argue that groups can provide voters with selective incentives which might be social in

nature that may explain why turnout rates are higher than the game theoretic model would

predict. Feddersen and Sandroni (200x) provide a model of ethical voting where some voters

are motivated to participate because it maximizes the social welfare of the group. They contend

that as the electorate grows in size and the probability of being pivotal declines, then the voters

that participate are voters who have ethical preferences. Gailmard, Feddersen, and Sandroni

(2008) nd experimental support for the predictions of the ethical voting model.3

From a technical standpoint there are good reasons for separating out the two issues of

strategic voting in multicandidate or multiparty elections and the e¤ect of costly voting on

participation in the theoretical and experimental literature. Simpler models provide more

easily testable propositions that can be studied in the laboratory. Yet, doing so increases the

disconnect between observational elections with more than two candidates and costly voting

and the theoretical and experimental literature. Should we ignore the costly voting or should

we ignore the multiple choices when we attempt to draw conclusions for the game theoretic

literature for these elections?

Moreover, the desire to coordinate in multicandidate or multiparty elections may a¤ect voter

abstention decisions. That is, the need to coordinate as a group in multichoice elections may

also have an e¤ect on the ability of groups to inuence voter turnout decisions. Mechanisms that

facilitate coordination in multichoice elections may also be mechanisms that provide voters with

the individualistic selective utility from participating. If voters are more likely to participate

if they value group welfare or the social aspect of voting as a group, then coordinating in

multichoice elections may enhance the group driven utility they receive from participation.

3Empirical tests of group models of voting with observational data have been conducted by Filer, Kenny,and Morton (1993), Nalebu¤ and Schankar (1999), Coate and Conlin (200x). In general, the authors nd somesupport for the group modelspredictions.

2

In this paper we investigate this possibility. We consider experimentally multichoice elections

in which voters must choose whether to vote sincerely or strategically but also face a cost of

abstention. We consider also three mechanisms by which voters may attempt to coordinateparty

labels, free-form communication within a party, and free-form communication across parties.

In the next section we present our basic theoretical model. In section III we discuss our

experimental design and predictions. In section III we present our experimental results and

section IV concludes.

A Model of Costly Voting in Multichoice Elections

Basic Setup

As noted in the Introduction, there is little theoretical literature that models costly voting in

multichoice elections. Our experiments build on a variant of the model of Palfrey and Rosenthal

(1985) of turnout with privately known voting costs. In our experiments there are N voters who

are divided into four possible preference types which we label E;F;G; and H: Voters choose

between three parties, A;B; and C: Voters of type E have a preference for party A winning

and are indi¤erent between parties B and C: Voters of type E are therefore party A partisans.

Similarly, voters of type H have a preference for party B winning and are indi¤erence between

parties A and C and are therefore party B partisans. Voters of type F have a rst preference

for party A, a second preference for B; and a third preference for C and voers of type G have

a rst preference for party B, a second preference for party A, and a third preference for party

C: Voters of types F and G therefore may wish to vote strategically for the second preference if

their rst preference is less likely to win to prevent a win by party C.

In the experiments we induce these preferences through voters payo¤s. Table 1 below

presents the payo¤s used in the experiment.4

4The payo¤s are given in experimental points which are then paid in euros at the end of the experiment atan exchange rate of 2.5 points per euro or each token was worth 40 euro cents. The subjects participated in 19periods and of these periods, 4 were randomly chosen for payment

3

Table 1: Subject Payo¤sWinning Party

Voter Type A B CE 155 75 75F 155 105 55G 105 155 55H 75 155 75

We assume that there are also M party C partisans who always participate and always vote

for party C: In the experiment these are votes cast by the computer. Hereafter when we refer to

voters we refer to subjects who made choices and not the votes cast by the computer. Denote

Ni as the number of voters who are of type i and denote N j as the number of voters whose rst

preference is party j: Therefore NA = NE +NF and NB = NG +HH : In our experiments we

vary the numbers of voters and consider two cases:

1. Equal Support where NA = NB

2. Unequal Support where NA > NB or NA > NB:

We also vary the size ofM from 0 to 1+N j where party j is the party with larger supporters

in case 2 or either paty in case 1: We varied these sizes in order to prevent super game e¤ects

across periods in a session.5 In Table A1 in Appendix A we present the distributions of voter

types used in a session with 22 subjects.6 If M = 0, then obviously there is no incentive for

voters of types F and G to vote strategically for their second choice, but as M increases the

incentives for strategic voting increase. M , each Ni, and the payo¤s to voters are common

knowledge.

Voters also have an option to abstain. Moreover, participating is costly to voters. We adopt

a voting cost distribution as in Levine and Palfrey (2007). That is, each voter pays a cost of

participating equal to c which is independently randomly drawn from 0 to 55.7 Each voters5This was particularly important in the treatments we describe below where subjects could communicate with

each other. In an early trial run of the experiment we found that when we held these distributions constant,subjects were able to coordinate on behavior across periods, and always voted for party A in the periods withcommunication. So our variation was necessary to prevent such coordination.

6 In some treatments we also gave the voters party a¢ liations, so the voter types in Appendix A are furtherdivided by these a¢ liations. We describe these treatments later in this section.

7 In the experiment only integer values were allowed.

4

cost of voting is private information to him or her and the distribution of voter costs is common

knowledge. As in Levine and Palfrey, we focus on quasi-symmetric equilibria where all voters

of the same type vote with the same probability. Dene p�ij as the equilibrium probability that

a voter of type i votes for party j: We assume that voters do not choose weakly dominated

strategies, so p�EB = p�HA = 0 and p

�iC = 0, all i:

Two Party Elections with Costly Voting

When M = 0 our experiments are comparable to Levine and Palfreys experiments since party

C receives zero votes in equilibrium with the exception that unlike Levine and Palfrey, voters

benets from their preferred party winning vary depending on their voter type.8 When M = 0,

a quasi-symmetric equilibrium is given by a set of cutpoints for each voter type c�i where the

cutpoint represents the cost at which a voter is indi¤erent between abstaining and voting for

their rst preference. Because M = 0; then p�FB = p�GA = 0: In equilibrium, these cutpoints

are given by the following equations:

c�i =

�155� 75

2

�PIV AB�i = 40PIV AB

�i ; i = E;H

c�i =

�155� 105

2

�PIV AB�i = 25PIV AB

�i ; i = F;G

where PIV AB�i is the probability that a vote by a voter of type i will be pivotal in the contest

between parties A and B, that is, make or break a tie given the equilibrium voting strategies of

other voters. These probabilities depend on the probabilies of voting and the number of voters

of each type as given by standard binomial formulas. The equilibrium probability of each voter

type participating is equal to the probability that his or her voting cost is less than their voter

type cutpoint. Thus, given that voting costs are uniformly distributed, p�iA =c�i55for i = E;F

and p�iB =c�i55for i = G;H:

8Levine and Palfrey also provide subjects with a bonus for abstaining rather than having them pay a cost ofparticipating.

5

Multiparty Elections with Costly Voting

WhenM > 0, voters face a more complicated choice situation. There are four possible situations

where a voters choice may be pivotalthe election is a close race between A and B; the election

is a close race between A and C, the election is a close race between B and C, and the election

is a a close three-way race. By close race we mean either that the election is a tie and so the

voter, by casting his or her vote, can break the tie, or the election is one vote short of a tie and

the voter, by casting his or her vote, can force a tie. Following the notation used above for

PIV AB�i , PIV AC�i is the probability that a vote by a voter of type i will be pivotal in a close

race between A and C given the equilibrium voting strategies of other voters, and PIV BC�i is

the probability that a vote by a voter of type i will be pivotal in a close race between parties

B and C given the equilibrium voting strategies of other voters. For close three-way races we

devine the following pivot probabilities: PIV ABCT �i is the probability that a vote by a voter

of type i will force a three-way tie and PIV ABCW �i is the probability that a vote by a voter of

type i will break a three-way tie.9

For voters of types E and H, the equilibrium voting cost cutpoints are determined as follows

since they either vote for their rst preference or abstain:

c�E =

�155� 75

2

�(PIV AB�E + PIV AC

�E)

+

�2 (155)� 150

6

�PIV ABCT �E +

�2 (155)� 150

3

�PIV ABCW �E

= 40(PIV AB�E + PIV AC�E) + 80

�PIV ABCT �E + 2PIV ABCW

�E

3

�c�H =

�155� 75

2

�(PIV AB�H + PIV BC

�H)

+

�2 (155)� 150

6

�PIV ABCT �H +

�2 (155)� 150

3

�PIV ABCW �H

= 40 (PIV AB�H + PIV BC�H) + 80

�PIV ABCT �H + 2PIV ABCW

�H

3

�9We need to distinguish between these two situations in the case of three way ties because the di¤erence in

utility varies depending on the situation. In contrast, in the situations in the case of two-way ties, the di¤erencein utility is the same whether a voters vote breaks a tie or makes a tie.

6

For voters of types F and G the equilibrium strategies are more complicated since these

voters choose whether to vote and, if they participate, whether to vote sincerely or strategically.

Assuming that these voters nd it optimal to vote sincerely, then the equilibrium voting cost

cutpoints can be similarly determined as for voters of types E and H:

c�F (sincere) =�155� 105

2

�PIV AB�F +

�155� 55

2

�PIV AC�F )

+

�2 (155)� 105� 55

6

�PIV ABCT �F +

�2 (155)� 105� 55

3

�PIV ABCW �F

= 25PIV AB�F + 50PIV AC�F + 25PIV ABCT

�F + 50PIV ABCW

�F

c�G (sincere) =�155� 105

2

�PIV AB�G +

�155� 55

2

�PIV BC�G

+

�2 (155)� 105� 55

6

�PIV ABCT �G +

�2 (155)� 105� 55

3

�PIV ABCW �G

= 25PIV AB�G + 50PIV BC�G + 25PIV ABCT

�G + 50PIV ABCW

�G

If these voters nd it optimal to vote strategically, then the equilibrium voting cost cutpoints

are determined as follows:

c�F (strategic) =�105� 155

2

�PIV AB�F +

�105� 55

2

�PIV BC�F )

+

�2 (105)� 155� 55

6

�PIV ABCT �F +

�2 (105)� 155� 55

3

�PIV ABCW �F

= �25PIV AB�F + 50PIV BC�F

c�G (strategic) =�105� 155

2

�PIV AB�G +

�105� 55

2

�PIV AC�G

+

�2 (105)� 155� 55

6

�PIV ABCT �G +

�2 (105)� 155� 55

6

�PIV ABCW �G

= �25PIV AB�G + 50PIV AC�G

If they participate, voters of types F and G will choose as follows assuming that when

indi¤erent, voters vote sincerely (i = F;G):

7

If c�i (sincere) � c�i (strategic) vote sincerelyIf c�i (sincere) < c

�i (strategic) vote strategically

Substituting in for these critical cost values we have that if they participate, type F voters

vote sincerely if the following is true and vote strategically otherwise:

50PIV AB�F + 50PIV AC�F + 25PIV ABCT

�F + 50PIV ABCW

�F � 50PIV BC�F

And if they participate, type G voters vote sincerely if the following is true and vote strate-

gically otherwise:

50PIV AB�G + 50PIV BC�G + 25PIV ABCT

�G + 50PIV ABCW

�G � 50PIV AC�G

We focus on three possible quasi-symmetric equilibria, one in which if voters participate,

all voters vote sincerely, one in which if voters participate, voters of types E; F; and H vote

sincerely and voters of type G vote strategically, and one in which if voters participate, voters

of types E;G; and H vote sincerely and voters of type F vote strategically. The calculations

are available from the authors.

Experimental Design and Predictions

Our experiments were conducted at the University of Oldenburg with undergraduate students

over a computer network using the software program zTree [see Fischbacher (200x)]. The

experimental program is available from the authors. Appendix B contains the instructions used

in the experiment in sessions with Sequence 1, to be described below.

As discussed in the Introduction, our goal in this experiment is to investigate whether at-

tempts by voters to coordinate in multiparty elections a¤ects their tendency to participate in

elections when voting is costly. To evaluate this prediction we conduct four di¤erent treatments:

8

1. Baseline Treatment Voters were simply told their voter types, the distribution of types,

and the number of computer votes.

2. Party Label Treatment Voters were assigned not only a type but also a party a¢ liation.

The a iations were assigned such that E and H voters were always assigned to parties A

and B, respectively, but F and G voters were assigned to both parties A and B:

3. Within Party Communication Treatment Voters were assigned parties as in the Party

Label Treatment and were also allowed to engage in free-form communication within their

parties before voting.

4. Across Party Communication Treatment Voters were assigned parties as in the Party

Label Treatment and were also allowed to engage in free-form communication with all the

other voters.

In the two communication treatments, the communication could last as long as 10 minutes.

Subjects were not able to communicate any information that might identify them to other

subjects in the experiment.

Our prediction is that communication and party labels can facilitate coordination of voters

and that we would nd more strategic voting in the treatments with party labels and commu-

nication than in the baseline treatment. We also expect that if these coordination mechanisms

enhance votersvalue for participating as a group, that we will see less abstention by all vot-

ers in the party label and communication treatments than in the baseline treatment. Finally,

we expect that communication will have a stronger e¤ect on voters than party labels without

communication with the strongest e¤ect in the Within Party Communication Treatment. These

predictions are summarized below:

Prediction 1 Voter types F and G will engage in more strategic voting in the Party Label,

Within Party Communication, and Across Party Communication Treatments than in the Base-

line Treatment. Strategic voting will be higher in the two treatments with communication than in

9

the Party Label Treatment, with the greatest strategic voting in the Within Party Communication

Treatment.

Prediction 2 Given the cost of voting, all voters will be more likely to participate in the Party

Label, Within Party Communication, and Across Party Communication Treatments than in the

Baseline Treatment. Participation to be higher in the two treatments with communication than

in the Party Label Treatment, with the greatest participation in the Within Party Communication

Treatment.

Prediction 3 From predictions 1 and 2, party C will win fewer elections in the Party Label,

Within Party Communication, and Across Party Communication Treatments than in the Base-

line Treatment. Party C will win the fewer elections in the two treatments with communication

than in the Party Label Treatment, with the fewest in the Within Party Communication Treat-

ment.

We used a within and between subjects design to evaluate these predictions. Specically,

we conducted two types of sessions, sessions with Sequence 1 and sessions with Sequence 2.

In sequence 1, subjects rst participated in 5 periods using the Control Treatment, 7 periods

using the Party Label Treatment, and then 7 periods using the Within Party Communication

Treatment. In sequence 2, we replaced the Within Party Communication Treatment with the

Across Party Communication Treatment.

In sessions 1 and 2 we recruited 22 subjects, in session 3 we recruited 20 subjects, and in

session 4 we recruited 24 subjects. In each period subjects were divided into voting groups.10

The number of groups per period varied from 1 supergroup to 4 separate groups. As noted in

the previous section we also varied across periods the number of computer votes, as well as the

distributions of voter types. Tables A1 and A2 in Appendix A summarizes the distributions

by period and group for the two sessions with 22 subjects. We used these variations to reduce

10Due to a computer error, the data was improperly recorded for ve periods in session 3. We do not use thedata for those periods. Our results are robust to excluding session 3 altogether.

10

supergame e¤ects, particularly in the periods with communication. The design, although it

make the experiment more complex for subjects, appeared to also motivate subjects somewhat

in that a number of subjects reported that they found the experiment interesting and engaging.

Results

Individual Behavior

First we investigate the evidence in support of Predictions 1 and 2 for individual behavior.

Table 2 below summarizes the aggregate individual choices of the subjects by voter type and

treatment. The rst half of the table summarizes the behavior of voters of types F and G. We

divide the choices into whether these voters abstained, voted sincerely for their rst preference,

strategically for their second preference, or voted for party C, which was their third preference.

Our predictions are that these voters will be more likely to vote strategically in the Party Label

and the two communication treatments and that overall participation will also be higher in the

Party Label and the two communication treatments. We nd signicant evidence in support

of some of these predictions. Specically, we nd that strategic voting is lowest in the Baseline

Treatment and is highest in the Within Party Communication Treatment. We also nd that

participation is highest in the Across Party Communication Treatment. However, participation

is lowest in the Party Label treatment. Finally, we nd that although some subjects vote for

party C, even though that party yields the lowest payo¤ for them, this tendency occurs mainly

in the Baseline Treatment which takes place in the rst ve periods of the experiment.

11

Table 2: Percentage Voter Choices by Voter Type and TreatmentF and G Voters

Treatment Abstain Sincere Strategic Voted C ObservationsBaseline 53.57 31.43 12.50 2.50 280

Party Label 58.05 26.83 14.15 0.98 410Party Chat 42.79 31.84 24.88 0.50 201All Chat 37.28 42.54 20.18 0.00 228

E and H VotersTreatment Abstain Sincere Other Voted C ObservationsBaseline 49.17 45.83 3.33 1.67 120

Party Label 53.61 44.58 1.81 0 166Party Chat 49.32 42.47 8.22 0 73All Chat 40.43 52.13 7.45 0 94

The second half of the table summarizes the behavior of voters of types E and H: The

column labeled Other summarizes the cases where voters of these types voted for a party that

was not their rst preference but not party C; while the columns Abstain, Sincere, and Voted C,

respectively represent the remaining cases. As noted above, these voters should either abstain

or vote sincerely, since they are indi¤erent over which two parties are their second choice. We

nd that this is indeed the case; these voters primarily either abstain or vote sincerely. We do

nd some signicant di¤erences in behavior across treatments, one as predicted. Specically, we

nd that in the All Chat treatment these voters participate signicantly more than in the other

treatments. Furthermore, we nd in the two chat treatments these voters are signicantly more

likely to vote for one of the parties that is not their rst choice but not party C even though

doing so is not rational for them and at this point in the experiments the subjects should be well

aware of the e¤ects of such votes. This suggests that in the communication treatments, these

voters are inuenced by communications from the supporters of these parties to vote against

their own interests.

Overall these results suggest that the communication treatments do increase strategic voting

and participation of voters. However, the above table does not take into account two factors

that might a¤ect behavior and conate these results. Specically, the results above may simply

be a consequence of the fact that voting costs varied across periods. In the treatments with more

participation and strategic behavior, voting costs may be on average lower than in the other

12

treatments. To estimate treatment e¤ects controlling for voting costs, we estimate multinomial

logits of voter choices by voter type. To control for subject specic e¤ects, we cluster the

observations by subject. These estimations are presented in Table 3 below. In the estimation

we also include a measure of the value of strategic voting. That is, since we varied across groups

and periods the size of the computer votes and the size of the voting groups, we need to control

for these di¤erences. We constructed a variable called Di¤erence which is equal to the number

of computer votes for C subtracted from the number of voters whose rst preference is party A

when party A had more or the same number of supporters (voters with rst preference party

A) than party B (voters with rst preference party A). When party B had more supporters

Di¤erence equaled the number of computer votes for C subtracted from the number of voters

whose rst preference is party B:

13

Table 3: Multinomial Logit Estimation of Voter Choices, Abstained is Base OutcomeF & G Voters E & H Voters

Indep. Variable Coef. R. Std. Err. z Pr > jzj Coef. R. Std. Err. z Pr > jzjSincere Vote Sincere Vote

Party Label -0.24 0.16 -1.48 0.14 -0.16 0.22 -0.74 0.46Party Chat 0.44 0.24 1.84 0.07 0.01 0.29 0.02 0.98All Chat 0.85 0.23 3.73 0.00 0.48 0.32 1.50 0.13Vote Cost -0.05 0.01 -8.96 0.00 -0.04 0.01 -5.29 0.00Di¤erence 0.47 0.24 1.99 0.05 0.88 0.29 3.07 0.00Constant 0.70 0.18 3.78 0.00 0.80 0.28 2.84 0.01

Strategic Vote Other VoteParty Label 0.07 0.28 0.26 0.80 -0.74 0.78 -0.94 0.35Party Chat 1.11 0.31 3.58 0.00 0.80 0.68 1.18 0.24All Chat 1.01 0.30 3.34 0.00 1.00 0.71 1.41 0.16Vote Cost -0.06 0.01 -9.20 0.00 -0.06 0.02 -3.54 0.00Di¤erence -0.32 0.32 -1.00 0.32 0.28 0.68 0.42 0.68Constant 0.13 0.26 0.49 0.62 -1.26 0.59 -2.14 0.03

Voted C Voted CParty Label -0.81 0.69 -1.17 0.24 -32.80 0.79 -41.50 0.00Party Chat -1.38 1.09 -1.27 0.20 -33.54 0.88 -38.20 0.00All Chat -32.56 0.45 -71.82 0.00 -33.28 0.96 -34.74 0.00Vote Cost -0.03 0.02 -1.59 0.11 -0.11 0.03 -3.26 0.00Di¤erence -3.55 1.39 -2.55 0.01 -4.51 6.06 -0.74 0.46Constant -2.36 0.63 -3.74 0.00 -1.25 1.11 -1.13 0.26

Obs. = 1119, 88 clusters by subject Obs. = 453, 88 clusters by subjectLog pseudolikelihood = -1068.4106 Log psuedolikelihood = -359.16Pseudo R2 = 0:10 Pseudo R2 = 0:09

The multinomial logit estimation for voters of types F and G demonstrate that with commu-

nication voters make strategic choices signicantly more. However, we do not nd that strate-

gic voting is signicantly increased with the Party Label Treatment compared to the Baseline

Treatment nor do we nd a signicant di¤erence between the two communication treatments.

However, we nd that in the two communication treatments these voters also participate signif-

icantly more (both sincere and strategic voting signicantly increased). Although some of this

increase is a consequence of decreased voting for party C, most is at the expense of abstention.

Thus our results that communication increases both strategic voting and participation of these

voters is robust to controlling for voter costs.

14

The multinomial logit estimation for voters of types E and H, in contrast, do not show that

the participation increase observed in Table 2 is robust to controlling for voting costs. Beyond

the e¤ects of voting costs and Di¤erence, we nd that the di¤erent treatments have only a

signicant e¤ect on the tendency of these voters to vote for party C. But such an e¤ect is also

likely due to simply experience e¤ects since the baseline treatment took place in the rst ve

periods.

In summary, we nd little evidence that party labels lead to more strategic voting. We nd

signicant evidence that communication does increase both strategic voting and participation

in general of voters of voter types F and G; even controlling for voter costs. But we nd that it

makes little di¤erence whether the communication is conned within parties are allowed across

parties.

Group Behavior

We turn to Prediction 3 and group behavior. Table 4 summarizes the outcomes of the elections

in the groups by treatment. We nd signicant evidence that the three treatments decrease the

likelihood that C wins, with C winning more than 78% of the time in the Baseline Treatment

but less than 20% of the time in the Across Party Communication Treatment. Although the

reduction in wins is explained by an increase in tie elections, it is also explained by increased

wins by either party A or B: Thus, our examination of group behavior presents strong evidence

that the coordination mechanisms decrease the probability that C wins.

Table 4: Percentage Outcomes and TreatmentTreatment C Wins A or B tie with C A or B wins ObservationsBaseline 78.05 0 21.95 41

Party Label 56.67 13.33 30.00 60Party Chat 47.06 11.76 41.18 34All Chat 19.44 11.11 69.44 36

There were no three-way ties.

However, our results may also reect the fact that subjects are most likely to irrationally vote

for party C in the Baseline Treatment which took place in the rst ve periods. Thus, we could

be confounding experience e¤ects with treatment e¤ects. To determine if such experience e¤ects

15

may explain our results, we ran probit estimations where the dependent variable was whether

party C as a function of the period in the treatment which are available from the authors.

We nd that only in the Baseline Treatment does period in treatment have a signicant e¤ect

on the probability that C wins. This suggests that all the experience e¤ects occured in the

rst ve periods, which also ts with our observations on voting behavior above. Thus, the

high percentage of wins by C in the baseline treatment may simply reect voter errors that

lessen with experience. However, the di¤erences between the party label and communicaiton

treatments cannot be explained by such errors. This suggests that these di¤erences are robust

to the experience e¤ects on subject errors.

Concluding Remarks

In this paper we provide preliminary analysis of experiments on costly voting in multiparty

elections. To our knowledge, we are the rst to analyze such elections experimentally and

theoretically. Much of the existing research on multiparty elections focuses on mechanisms

by which voters can coordinate on common choices through strategic voting and the existing

research on costly voting in binary elections focuses on how voters who have been instilled with

social preferences may participate even though the cost of such voting might exceed the benets

to the voter. We argue that mechanisms by which voters coordinate in multiparty elections may

also increase participation of voters when voting is costly by increasing the value votersplace

on social activity. We focus in this paper on three mechanismsparty labels, communication

within parties, and communication across parties.

We nd signicant evidence that the communication treatments increase voter coordination.

We nd this through an increase in strategic voting as well as decreased wins by the party least

favored by the majority of voters. We also nd signicant evidence that communication also

increases turnout in general of some voters, which supports our hypothesis that coordination

mechanisms in multiparty elections may also a¤ect turnout of voters when voting is costly.

16

This paper presents work in progress. In our future work on this project we plan to focus

on the following:

1. We plan to analyze individual voter choices as a function of their particular voter costs as

compared to the critical costs predicted by the theory.

2. We plan to analyze the transcripts of communication by the subjects during the Within

Party and Across Party Communication Treatments. Specically, we plan to consider

how di¤erent types of messages a¤ect voter choices in the experiments.

3. We plan to conduct experiments that change the sequence of treatments to control for

possible experience e¤ects which may confound out results.

We expect that our results will provide important new evidence on how voters choose in

multiparty elections with costly voting and the e¤ects of party labels and communication in

such situations.

17

Appendix A: Distributions of Voter Types in Sessions with 22Subjects

Table A1: Distributions of Voter Types Used in Sessions with 22 SubjectsVoter Types

Distribution C Voters E Voters F Voters G Voters H Voters1 0 2 2 2 22 0 3 8 8 33 2 1 2 2 14 3 1 2 2 05 4 1 2 3 06 4 1 2 2 17 4 1 4 5 18 4 1 4 4 29 4 2 2 2 210 4 2 4 4 111 6 1 4 4 212 6 2 4 4 113 7 1 3 5 214 7 1 4 4 215 7 2 4 4 116 7 2 5 3 118 10 3 8 8 319 12 3 8 8 3

18

Table A2: Distribution of Voter Types By Period in Sessions with 22 SubjectsNP = Control, P = Party Label, C = Communication

Party A Party BTreatment-Period C Voters E Voters F Voters G Voters F Voters G Voters H Voters

NP-1, P-7 6 2 2 2 2 2 1NP-2, P-11 2 1 1 1 1 1 1NP-3, P-11 0 2 2 0 0 2 2

NP-3, P-8, C-13, C-18 4 1 0 2 2 1 0NP-3, P-8, C-13, C-18 3 1 0 1 2 1 0NP-4, P-12, C-16, C-19 7 1 2 2 2 2 2

NP-5 10 3 4 4 4 4 3P-6 4 2 2 2 2 2 1P-6 4 1 2 2 2 2 1

P-7, C-16, C-19 6 1 2 2 2 2 2P-9 12 3 4 4 4 4 3P-10 4 1 3 3 1 2 1P-10 4 1 1 2 3 3 1P-12 7 2 2 2 2 2 1C-14 4 1 1 1 1 1 1C-14 4 2 2 0 0 2 2C-15 0 3 4 4 4 4 3C-17 7 2 2 2 3 1 1C-17 7 1 1 3 2 2 2

Appendix B: Instructions for Sessions with Sequence 111

Welcome to the experiment! Please avoid talking to other participants of the experiment.

Please use only those functions of the workstation that are necessary for the experiment. This

experiment is about decision behaviour. You can earn real money. For your participation you

get 5e as a show-up fee. During the experiment your income will be displayed in points (the

experimental currency) instead of e. At the end of the experiment the points will be converted

in e at the following conversion rate: 2.5 points = 1e or 1 point = 40 cent.

After the end of the session your overall earnings from the experiment will be paid in privately

and in cash together with the 5 e show-up. None of other participants will be informed about

your decisions and your income neither during or after the experiment. The data collection is

purely anonymous and observations cannot be matched with the identities of the participants.

11The instructions used were in German and below is a translation into English. For a copy of the originalGerman instructions, please contact the authors.

19

Before the experiment starts there will be a short comprehension quiz to ensure that everyone

understood the instructions.

Duration: The experiment will last 120 minutes and consists of 19 periods. These 19

periods are divided into 3 independent phases. You will receive detailed instructions in each of

theses phases. This means that only after phase 1 you will receive the instructions for phase 2

etc. If you have any questions after reading the instructions or the procedures please raise your

hand. The experimenter will answer your questions privately. You can also ask questions at any

point during the experiment.

Groups: The experiment is executed simultaneously with several groups of participants

(experiment groups) one group represents one Experiment. All following instructions refer

to one experiment group. All displayed information on voters, parties, the elections etc. always

refer to one group of participants. However, you are randomly assigned to one experiment

group in each period. It is therefore possible that your group changes several times during the

experiment. Your tasks, payo¤ etc. are identical in each group.

Payo¤s: Out of the 19 experimental periods only four are chosen at random for the payo¤.

The mean of your earnings in these four periods will be calculated, converted to Euros and

paid in cash. At the end of the experiment the four selected periods and your earnings in these

periods as well as the mean earnings your actual payo¤ will be displayed.

Phase 1

Basic Experimental Procedures: In this experiment elections will be held. In each elec-

tion phase (each period) there will be three parties: A, B and C. You will have the opportunity

to vote for party A, party B, party C, or abstain. The computer will also have M votes, which

the computer will always cast for party C. The party that receives the most votes (a simple

majority of the total votes cast) will win the election. If there are more parties with the same

number of votes, a winner will be randomly elected from these parties.

Party Membership and Voter Types: In each election period you will be assigned a

20

voter type E, F, G or H. The voter type will be randomly determined in each period. Before

each election you will learn your voter type for that respective period and the numbers of voters

and their voter types for that period, including yourself. If a voter type is indicated as 0, this

voter type does not appear in this period.

Payo¤s: You will receive an election payo¤ which depends on your voter type and which

party wins, according to the following table:

Voter Type Party A wins Party B wins Party C winsE 155 75 75F 155 105 55G 105 155 55H 75 155 75

Your receive your payo¤ depending on which party receives the most votes in the election,

even if you did not vote in the election or you voted for a di¤erent party. For example, you

are voter type E. Party B wins the election, you voted for party A. You will receive a payo¤

of 75 points. Alternatively, suppose you are voter type H, Party C wins the election, and you

abstained. You will receive a payo¤ of 75 points. Your payo¤ depends solely on which party

wins, not on how you voted or whether you voted at all.

Election Costs: As mentioned above, in each election you have the option to vote or to

abstain. In fact, if you choose to vote you have to pay election costs. If you abstain you do

not have to pay these costs. The amount of your election costs is randomly assigned by the

computer in each period. The election costs range between 0 and 55 points. The amount of the

elections costs does not depend on your voter type or your decisions in previous periods. As the

election costs are assigned separately for each participant, di¤erent participants will typically

have di¤erent election costs. Your elections costs will be displayed before your option to vote.

You will never learn the election costs of the other participants. You only know that they have

election costs between 0 and 55. Your election costs are deducted from your payo¤, independent

of the party you voted for. If you abstain nothing will be deducted from your payo¤.

Suppose you are voter type E. Suppose party A wins. You will receive a payo¤ of 155 points

21

if you do not vote. If you vote, however, you will receive a payo¤ of 155 points less election

costs. If you have election costs of 55 points, this will be 155 55 = 100. If you have election

costs of 0 points you will receive a payo¤ of 155 points, without any deduction.

Phase 2

The experimental procedure remains unchanged with one exception

Additional to the voter type you will be randomly assigned to be a member of party A or

party B in each period. Before each election you will again learn your voter type and your party

membership for that respective period and the numbers of voters and their voter types for that

period, including yourself. In phase 2 the numbers of voter types will be displayed separately

for each party. If a voter type is indicated as 0, this voter type does not appear in this period.

The party membership does not inuence on the payo¤s or the voting costs.

Apart from the party membership, there will be no di¤erences to phase 1!

Phase 3

The experimental procedure remains unchanged as, in addition to the previous procedures

you will be given the opportunity to communicate with them members of your party.

Chat: You have the option to send online messages to other members of your party before

you can cast your vote or abstain. Your messages will be displayed to all members of your party.

For the chat, you receive an identication number in each period which is displayed next to your

messages. This identication number may change in each period.

The chat will last 10 minutes at most. In principle the content of the chat is not constricted,

however, you are not allowed to reveal personal details about yourself, e. g. name, age, address,

gender (please use gender-neutral terms), your eld of study (including names of lecturers,

lectures and their contents, which would hint at your eld of study) or the like that could

identify yourself (e. g. your seat number, row or seat). Furthermore, it is not allowed to arrange

side-payments (gratication or punishment). Those who violate the communication rules are

excluded from the experiment by the experimenter and wont receive any payo¤ for the whole

22

experiment.

Apart from the chat, there will be no di¤erences to phase 2!

End

After you lled in a short questionnaire you will be displayed your total earnings. You will

be called separately for the private payment. Please bring the voucher and the card indicating

the number of your seat with you for the payment.

References

[1] Coate, Steven and Michael Conlin. 2002. "Voter Turnout: Theory and Evidence from Texas

Liquor Referenda." American Economic Review

[2] Cox, Gary W. 1997. Making Votes Count. Cambridge: Cambridge University Press.

[3] Downs, Anthony. 1957. An Economic Theory of Democracy. New York: Harper and Row.

[4] Du¤y, John and M. Tavits. 2008. American Journal of Political Science

[5] Feddersen, Timothy (2004). Rational Choice Theory and the Paradox of Not Voting. Journal

of Economic Perspectives 18: 99-112.

[6] Feddersen, Timothy and Alvaro Sandroni (2006a). A Theory of Participation in Elections.

American Economic Review.

[7] Feddersen, Timothy and Alvaro Sandroni (2006b). Ethical Voters and Costly Information

Acquisition. Quarterly Journal of Political Science 1(3).

[8] Forsythe R, Myerson RB, Rietz TA, Weber RJ (1993) An experiment on coordination in

multicandidate elections: The importance of polls and election histories. Social Choice and

Welfare 10:223-247

23

[9] Ledyard, John. 1981. "The Paradox of Voting and Candidate Competition: A General

Equilibrium Analysis," in Essays in Contemporary Fields of Economics. George Hoorwich

and James P. Quick, eds. Lafayette: Purdue University Press, pp. 54-80.

[10] Ledyard, John. 1984. "The Pure Theory of Two Candidate Elections." Public Choice. 44:1,

pp. 7-41. Leighly, Jan. 19

[11] Levine, David, and Thomas Palfrey. American Political Science Review. 2007.

[12] Morton RB, Rietz TA (1994) Majority requirements and minority representation. University

of Iowa Working Paper

[13] Morton, Rebecca. 1987. "A Group Majority Model of Voting." Social Choice and Welfare.

4:2, pp. 117-31.

[14] Morton, Rebecca. 1991. "Groups in Rational Turnout Models." American Journal of Po-

litical Science. August, 35, pp. 758-76.

[15] Myerson RB, Rietz TA, Weber RJ (1994) Compaign nance levels as coordinating signals

in three-way, experimental elections. Kellogg Graduate School of Management, Department

of Finance Working Paper 150

[16] Myerson RB, Weber RJ (1993) A theory of voting equilibria. American Political Science

Review 87: 102-114

[17] Palfrey, Thomas and Howard Rosenthal. 1983. "A Strategic Calculus of Voting." Public

Choice. 41:1, pp. 7-53.

[18] Palfrey, Thomas and Howard Rosenthal. 1985. "Voter Participation and Strategic Uncer-

tainty." American Political Science Review. 79:1, pp. 62-78. Pollock, Phillip H. III. 1982.

"Organizations as

24

[19] Rietz TA (1993) Comportamiento estrat~gico en elecciones con mltiples alternatives: Una

revisi6n de alguna evidencia experimental. Cuardernos Economicos de ICE 54 2:129-170

(Available in English as: Strategic behavior in multi-alternative elections: A review of some

experimental evidence. Kellogg Graduate School of Management Department of Finance

Working Paper 149)

[20] Schram, A.J.H.C. 1991. Voter Behavior in Economic Perspective, Studies in Contemporary

Economics. Heidelberg: Springer Verlag.

[21] Schram, A.J.H.C. 1992. "Testing Economic Theories of Voter Behavior Using Micro-Data."

Applied Economics. 24:4, pp. 419-28.

[22] Schram, A.J.H.C. and J. Sonnemans. 1996a. "Voter Turnout and the Role of Groups: Par-

ticipation Game Experiments." International Journal of Game Theory. 25:3, pp. 385-406.

[23] Schram, A.J.H.C. and J. Sonnemans. 1996b. "Why People Vote: Experimental Evidence."

Journal of Economic Psychology. 17:4, pp. 417-42.

[24] Uhlaner, Carol. 1989. "Rational Turnout: The Neglected Role of Groups." American Jour-

nal of Political Science. 33:2, pp. 390-422.

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