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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November 28, 2008, Preliminary Draft; Do Not Cite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,
[email protected] - Center for Social Science
Methodology, University of Oldenburg, A6-3-322, Ammerlaender
Heerstrasse. 114 - 118, 26129 Oldenburg, +49 441 798 4528,
[email protected] of Politics, NYU, 19
West 4th Street, 2nd Floor, New York, NY 10012, re-
[email protected].
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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.
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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
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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
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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
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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
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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
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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
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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
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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:
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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
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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
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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
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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
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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:
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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
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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
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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
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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
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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
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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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