tactical coalition voting

Tactical Coalition Voting

Brian McCuen

United States Government

and

Rebecca B. Morton

Department of Politics New York University

4th Floor, 715 Broadway New York, NY 10003-6806

voice: 212-998-3706 sec: 212-998-8500 fax: 212-995-4184

[email protected]

Draft – not for citation without permission.

Abstract: Most research on voting in proportional representation electoral systems assumes that voters either choose sincerely for their most preferred parties or strategically if threshold constraints mean their party has little chance of winning a seat. Voters are assumed to ignore possible coalition implications of their choices. However, formal models of coalition formation in PR systems, such as Austen-Smith and Banks (1988), assume voters care about the ultimate coalition formation in the parliament and vote strategically in order to affect that coalition formation process, which we call “tactical coalition voting.” In this paper, we experimentally evaluate the extent voters in a PR system engage in tactical coalition voting. We find significant evidence that voters, even those non experienced with PR systems, do choose strategically to affect post election coalitions.

Tactical Coalition Voting page 1

Introduction

Traditionally, scholars have believed that voters in proportional representation

(PR) electoral systems should vote sincerely for their most preferred political party

(Duverger 1954; Lipset and Rokkan 1967). While Duverger argued that voters in

plurality rules systems who supported smaller parties would vote strategically, reducing

the number of viable parties, he believed these strategic concerns were absent in PR

systems since achieving near-majority status in the electorate is not necessary for a party

to have representation nationally. However, later research, both empirical, Leys (1959)

and Sartori (1968), and theoretical, Gibbard (1973) and Sattertwaite (1975) show that

even in PR systems strategic voting incentives exist. Nevertheless, most conclude that

voters largely choose sincerely in PR systems and that the strategic incentives are much

smaller and less significant than in plurality rule electoral systems.

In a seminal work, Cox (1997) has explored extensively the theoretical and

empirical effects of strategic voting across different electoral systems. He notes that

there are two types of strategic voting – “seat maximizing” which intends “to make votes

count in the allocation of legislative seats” and “portfolio-maximizing” which looks

“ahead to the government formation stage, and the coordination problems that arise at

that stage.” (p. 272). In plurality rule systems, seat maximizing voting is the force that is

contended to lead to bipartism and discussed by Duverger, while portfolio maximizing

voting is the type of voting emphasized by Alesina and Rosenthal (1989), Alesina,

Londregan, and Rosenthal (1993), and Fiorina (1992) to explain split ticket voting and

divided government in the United States. Most empirical research on strategic voting has

focused on the former over the latter variety, including Cox’s own work. This is


unfortunate because in PR systems one could argue that portfolio maximizing voting is

more likely to be relevant than the seat maximizing type. That is, the force to form a

winning coalition within the government to implement policy exists whether the voting

system is PR or plurality. If voters are myopic and do not look ahead to actual

government policy choices, then it appears that the incentive for strategic voting in PR

systems is less, and that the presumption of sincere voting may be reasonable. However,

if voters are forward looking such a conclusion is not obvious.

As Cox notes, there is little empirical exploration of the extent of portfolio-

maximizing voting in PR systems. In this paper, we present experimental evidence of

such voting, which we call “tactical coalition voting” or TCV. In the experiments, we

investigate voter choices in an experiment based on Austen-Smith and Banks’ (1988)

formal model of coalition formation under PR (ASB), which we review in the next

section. Then we present our experimental design and the results of the experiments. In

the final section we discuss future research.

Austen-Smith and Banks Coalition Formation Model

The ASB model has three political parties, α, β , γ, where Ω = α, β , γ.

These parties are competing in a one-dimensional policy space P ⊂ R. The parties are

competing for the votes of N voters, and N is assumed to be sufficiently large (N ≥ 15)

and odd. The model has three stages. First, the parties simultaneously announce their

policy positions in P, where p = (pα, pβ, pγ) indicates the policy positions of the parties.

Second, each voter casts one vote for one of the three parties. The parties receive seats in

the legislature in exact proportion to the number of votes that they received in the

election; however, a party must receive at least s votes to gain its proportionate share of


seats. A party that fails to receive at least s votes has its votes invalidated and the

proportion of votes cast for the remaining parties are normalized so that they sum to 1.

Let w = (wα, wβ, wγ) indicate the proportion of votes that the parties received. Third, a

government is formed. A government is composed of a party or group of parties (a

coalition), which received a majority of votes in the election.

In the remaining description of the model, it is assumed that all parties receive at

least s votes and that a government coalition always has the minimum number of parties

necessary for a majority. The result of these two assumptions is that all government

coalitions are composed of only two parties. The government chooses a policy y ∈ P and

a distribution of transferable benefits among the parties. Let ∆(G) = gα, gβ, gγ) represent

the set of such distributions. These benefits represent portfolios in the new government.

The government formation process has three steps. First, the party with the

largest number of seats proposes a winning coalition (C1 ∈ S (Ω), whose members

received a majority of the votes), a policy (y1 ∈ P), and a distribution of benefits (g1 ∈

∆G). The party that the party with the largest number of seats proposes as its coalition

partner either accepts or rejects the coalition. If the coalition is accepted, then policy y1

and distribution g1 are implemented. If the first coalition is rejected, then the party that

received the second largest number of seats proposes a coalition, policy, and distribution.

If the second coalition fails then the third party makes its proposal. If the third party’s

coalition proposal is rejected then it is assumed that a caretaker government is elected.

The caretaker government is assumed to choose a policy and distribution of benefits that

results in the parties receiving zero utility.


Since the government formation process is a sequential game with perfect

information, Austen-Smith and Banks use backwards induction to solve the game.

Determining the equilibrium proposals generated at t = 3 and t = 2, allows the party with

the most votes to offer a coalition proposal at t = 1 that is accepted. The offer at t = 1 is

accepted since the largest party will offer a proposal that at least matches the utility that

its partner could receive at t = 2 or t = 3. Austen-Smith and Banks find that in

equilibrium the parties with the highest and lowest vote totals form a government. The

policy position of the government lies somewhere between the largest party’s most

preferred policy and the median point between the largest and smallest parties’ policy

positions. The exact position of the policy will depend on the distribution of votes among

the parties and the distance between the coalition members’ policy points. Therefore, the

equilibrium policy outcome from the government formation stage depends upon w, the

distribution of votes cast by the voters, and p, the policy positions of the parties. In

general, the equilibrium prediction will be unique for any (p, w).

Voters are assumed to be purely policy oriented. Their preferences are

characterized by quadratic utility functions uh(•) = u(•; xh) over the policy space P; xh

indicates voter h’s ideal point in P. It is assumed that x = (x1,…,xn) is common

knowledge. The voters are distributed symmetrically about the median voter’s ideal

point. A strategy for voter h is a function that indicates the probability that h votes for

each party given the electoral positions, σh: P × P × P → ∆ (Ω). Let σh(p) = (σh(α),

σh(β), σh(γ)), where σh(k) is the probability that voter h votes for party k and σ(p) =

(σ1(p),…,σn(p)). If there exists a probability distribution ζ(•) over P, then the expected

utility for voter h is: Εζ[uh (•)] = -(yζ - xh)2 - sζ, where yζ is the mean and sζ is the


variance of the distribution of ζ, despite uncertainty over the policy outcome of the

government formation stage.

Since the policy outcome of the government formation stage is dependent on p

and w, the voters can determine the final policy outcome for any p and any set of voting

strategies σ(p). This relationship means that the equilibrium voting behavior of the

voters is an n-tuple σ*(p) such that ∀ p, ∀ h ∈ N, ∀σh(p): Επ(σ*, p) [uh(y)] ≥ Ε π(σh,

σ*- h, p) [uh(y)]. Therefore, a voting equilibrium is a Nash equilibrium of the game with

N players and payoffs induced by the equilibrium behavior in the government formation

stage. Recall that voters base their vote decisions on the final policy outcome and not the

position of individual party positions. Interestingly, Austen-Smith and Banks find that if

all voters are forced to vote sincerely then there is no equilibrium set of party policy

positions.

In equilibrium, one party adopts the median voter’s policy position and the other

two parties position themselves equidistant from the median voter. The equilibrium

voting strategies for this distribution of party positions results in the median party

receiving exactly s (the minimum threshold level) votes and the two non-median parties

dividing the remaining votes among themselves. This result means that the non-median

parties have an equal probability of being the largest party. The party that wins the tie-

breaking procedure then forms a government with the median party and the government

policy point is set halfway between the coalition partners.

The equilibrium party positions are shown in Figure 1. The points Pl, Pm, Pr show

the policy positions of respectively, the left, middle, and right parties. The middle party

adopts the median voter’s policy position. The left and right parties adopt policy


positions that are equidistant from the middle party. The points Plm and Pmr represent the

median points between the left and middle parties and the middle and right parties. In

addition, these points represent the possible coalition policy points.

Figure 1: Equilibrium Party Positions in ASB Model

Note: n = number of voters

Note: s = threshold level

The voters that engage in TCV are those voters who sincerely prefer the middle

party but vote for the closest non-median party. These voters behave in this manner

(increasing the vote share of their second most preferred party and decreasing the vote

share of their most preferred party) since the government formation process always

results in a coalition of the largest and smallest parties. The defection of voters who

sincerely prefer the middle party continues until the middle party has s votes. The

defection stops at this point since the failure of the middle party to enter the legislature

Pm Plm Pl Pmr Pr

Individuals who vote strategically

(n-s)/2 voters

Vote L

(n-s)/2 voters

Vote R

s voters

Vote M


would cause the final policy outcome to move away from the median and towards the

ends of the distribution.

Experimental Design

In the experiment there are three parties are named B, C and D which compete on

a one-dimensional policy space. There are 23 voters (n = 23) who are symmetrically

distributed around the median voter. In the ASB model, the voting threshold is odd and

has the following range s ∈ [3, n/3). Given that n = 23, the possible values for s in the

experiment are 3, 5 and 7.

In ASB, the equilibrium distribution of the parties in the policy space depends

upon the number of voters and the threshold level. The equilibrium middle party’s policy

position is at the median voter’s policy position (PC = xµ). The other two parties (B and

D) in equilibrium are equidistant from the median voter’s policy position and their

distance from the median voter is d, where d ≥ ((8/3) * ((µ + ((s-1)/2)) - xµ)). The value

of this equation equals the minimum number of voters that must be between the policy

position of the non-median parties and the policy position of the median party. Using the

three possible values for s (s = 3, s = 5 and s = 7) results in d ≥ 2.6, d ≥ 5.3 and d ≥ 8

respectively. In our design d ≥ 8. Using this value of d allows us to use the same

distribution of parties regardless of the value of s. Using the same distribution permits us

to compare directly how the different threshold levels influence voting behavior. Figure

2 indicates the distribution of parties and voters in the experiment. Figures 3, 4, 5, and 6

indicate the equilibrium voting choices as a function of the s. The positions B/C and C/D

indicate the coalition policy positions of these two possible coalition governments. Note

in particular that as s increases, we expect to find less tactical coalition voting.


Sincerely Prefers Party B

B

Figure 2: Distribution of Parties and Voting Types

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16

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23

Sincerely Prefers Party C

Sincerely Prefers Party D

B/C

C

C/D

D


Figure 3: Equilibrium Voting Behavior when the Threshold = 3

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B

B/C

Votes for Party B

C

C/D

D

Votes for Party C

Votes for Party D

Votes Sincerely

Votes Tactically

Votes Sincerely

Votes Tactically

Votes Sincerely



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B

B/C

C

C/D

D

Votes for Party B

Votes for Party C

Votes for Party D

Votes Sincerely

Votes Sincerely

Votes Sincerely

Votes Tactically

Votes Tactically



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B

B/C

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C/D

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Votes for Party B

Votes for Party C

Votes for Party D

Votes Sincerely for B

Votes Sincerely for C

Votes Sincerely for D


The experiment consisted of five sessions (the differences between the sessions

will be explained in the next section) and each session involved 23 subjects. The subjects

were recruited from students at the University of Iowa. The subjects are primarily

undergraduates enrolled in political science classes and are drawn from a pool of students

that had volunteered to participate in political science research projects.

At the beginning of each session, the 23 subjects were seated separately at a

computer terminal. Partitions were placed between the subjects so that they could not

observe the voting behavior of the other subjects. Each subject was assigned a unique

identification number. A set of instructions (see Appendix B) was given to each subject.

The instructions were read aloud and all questions were answered publicly, ensuring that

all instructional information was common knowledge. The subjects were not allowed to

communicate among themselves during the experiment session. Once we reviewed and

answered all questions concerning the instructions, the first election was conducted.

At the beginning of each election, the computer program randomly assigned each

subject to one of the 23 voter policy positions (see Figure 2). The 23 policy positions are

called voting types. Since each voting type occupies a unique policy position, the

outcome of the election has a different impact upon each subject. In the ASB model

voters maximize expected utility from the government’s policy position. The distance

between the subject's policy position and the government's policy position determines the

subject's utility. As the government's policy position converges upon the subject's policy

position, the utility received by the subject increases. In the experiment, monetary

payoffs were used to represent utility. The payoff each subject earns from each election

is determined by a function that transforms the linear distance between the subject's


policy position and the government's policy position into an amount that ranges from

$1.70 to $0.35. The function is: i's payment = 1.70 – ((|xg - xi|/100) * 12), where xg is the

policy position of the government and xi is the policy position of subject i. Each subject

is given a complete payoff schedule that indicates the amount of money each voting type

would receive for all the possible outcomes (see Appendix B).

After the assignment phase was complete, the voting phase began. The program

privately displayed to each subject his or her voting type for that election. The program

informed the subjects about the threshold level (the s value in the ASB model) for the

election and the subjects were asked to vote. They cast one vote for a party (B, C or D)

or they abstain. The subject's vote is displayed to the subject and the subject is asked to

confirm the vote. After the subjects confirmed their vote, the program collects the votes.

Once all the votes were collected, the program determined the winner of the

election and displayed the results. The program follows the ASB government formation

parameters, where the largest and smallest parties form a coalition government if no

single party receives a majority of the votes. The government policy position is set

halfway between the two coalition partners and the payoffs for each subject is calculated.

In the case of ties between two or more parties, the computer randomly determined the

winner. The percentage of valid votes cast for each party and the composition of the new

government was then displayed to all the subjects. Each subject's vote and payoff for that

election was privately displayed to each subject. Once the subjects finished reviewing

the results, a new election began with the program randomly reassigning voting types to

the subjects. The subjects participated in 20 elections. After the 20th election, the


subjects filled out a questionnaire concerning their voting behavior and were paid their

cumulative election payoffs in cash.

In the experiments, we varied the information subjects had about the voting

environment. In the high information treatment, the payoff schedule included a small

table that summarized the distribution of the most preferred party preferences of the

subjects (see Appendix B). Given the voting rules and government formation rules, the

table should help the subjects realize that the equilibrium outcome of the election is a

coalition government between either B/C or C/D. The payoff schedule in the low

information treatment did not include the most preferred party table.

Experimental Results

In the treatments with thresholds equal to 3 and 5, we expect to observe 240

voters whose first preference is party C voting strategically for their second preferred

party (either B or D) and all other voter choices to be sincere. Table 1 reports the results

of a logistic estimation of the probability that a voter chooses tactically for her second

preference (more detailed data summaries are provided in Appendix A) as a function of

her voter type, the information level of the experiment, and the value of the threshold.

Specifically, the null case in the estimation is a voter whose first preference is party C,

choosing under high information with a threshold equal to 7. In this case, all voters

should choose sincerely. Variable TCV*(s = 3) equals 1 if a voter should vote tactically

when the threshold equals 3, 0 otherwise; TCV*(s = 5) equals 1 if a voter should vote

tactically when the threshold equals 5, 0 otherwise; s = 3 equals 1 if the threshold is 3, 0

otherwise, s = 5 equals 1 if the threshold is 5, 0 otherwise; Election equals the election

period in the treatment and takes values from 1 to 20; Low Infor. equals 1 if subjects are


provided with low levels of information; 0 otherwise; 1st Pref. B equals 1 if voters’ first

preference is party B, 0 otherwise; and 2nd Pref. D equals 1 if voters’ first preference is

party D, 0 otherwise.

Table1: Logistic Estimation of Probability of Voting Strategically for 2nd Preference (Null case: s = 7, 1st preference is C, voter should choose sincerely, high information)

Coefficient Std. Error z Pr>|z|

TCV*(s = 3) 1.69 0.23 7.39 0.00

TCV*(s = 5) 1.59 0.27 5.91 0.00

s = 3 -0.42 0.16 -2.64 0.01

s = 5 -0.16 0.15 -1.09 0.27

Election 0.02 0.01 1.95 0.05

Low Infor. -0.24 0.12 -2.09 0.04

1st Pref. B 0.35 0.16 2.19 0.03

1st Pref. D 0.63 0.16 4.03 0.00

Constant -1.69 0.18 -9.23 0.00

Log Like. -1166.7415

# of Obser. 2300

Pseudo R2 0.0383

Both TCV dummy variables are highly significant, which shows that voters

predicted to vote tactically are significantly more likely to do so than other voters whose

first preference is party C. Strategic voting also is more likely to increase with the

election period, demonstrating some degree of learning. Similarly, the low information

treatment leads to significantly less strategic voting. Finally, voters whose first


preference is either B or D are significantly more likely to vote strategically than voters

whose first preference is C and strategic voting is significantly less likely when the

threshold is 3 than 7 (the dummy variable representing a threshold of 5 is insignificant).

As the coefficients of logistic results are difficult to interpret, Table 2 presents the

predicted probability of voting tactically by voter type, threshold level, and information

for the last election period (Election = 20).

Table 2: Predicted Probability of Voting Tactically

Should Not Vote Tactically

Threshold

Should Vote

Tactically 1st Pref. B 1st Pref. C 1st Pref. D

7 NA 27% 21% 33%

5 52% 24% 18% 29%

High

Information 3 48% 20% 15% 25%

5 46% 20% 15% 25% Low

Information 3 42% 16% 12% 20%

In general, even voters predicted to vote tactically are estimated to have a higher

probability of voting sincerely than tactically and there is a baseline tendency to vote

strategically when thresholds and information is high and voters have extreme

preferences. This is not a surprise since the subjects were not experienced with PR

systems, but are with plurality rule where this type of strategic voting is normal.

However, the probability of voting tactically is highest when a voter is predicted to vote

tactically by the theory, even though these voters are moderates.


Conclusions


Appendix A – Summaries of Experimental Results

Figure A1: Voting Behavior in the High Information Treatment when the Threshold = 3

Figure A2: Voting Behavior in the Low Information Treatment when the Threshold = 3

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Voting Type

(%)

Second Most Preferred Most Preferred

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Voting Types

(%)



Table A1: Comparison of Voting Behavior in the High Information Treatment when the Threshold = 3

Predicted Voting Behavior

Actual Voting Behavior

Voting Types that

should Vote Sincerely (1-8, 11-13, 16-23)

Voting Types that

should Vote Tactically

(9-10, 14-15)

Sincere

77.7% (275)

43.7% (31)

Tactical

22.3% (79)

56.3% (40)

Total

100% (354)

100% (71)

Number of Cases = 425, χ2 = 33.954, significant at the 0.05 level


Table A2: Comparison of Voting Behavior in the Low Information Treatment when the Threshold = 3



Voting Types that


Voting Types that


(9-10, 14-15)

Sincere

84.1% (301)

64.9% (48)

Tactical

15.9% (57)

35.1% (26)

Total

100% (358)

100% (74)



Figure A3: Voting Behavior in the High Information Treatment When the Threshold = 5

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Voting Types

(%)



Figure A4: Voting Behavior in the Low Information Treatment when the Threshold = 5

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Voting Types

(%)



Table A3: Comparison of Voting Behavior in the High Information Treatment When the Threshold = 5



Voting Types that


Voting Types that


(9, 15)

Sincere

77.1% (297)

50.0% (19)

Tactical

22.9% (88)

50.0% (19)

Total

100% (385)

100% (38)



Table A4: Comparison of Voting Behavior in the Low Information Treatment When the Threshold = 5



Voting Types that


Voting Types that


(9, 15)

Sincere

77.5% (310)

55.3% (21)

Tactical

22.5% (90)

44.7% (17)

Total

100% (400)

100% (38)



Figure A5: Voting Behavior in the High Information Treatment When the Threshold = 7

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Voting Types

(%)



Table A5: Comparison of Voting Behavior in the High Information Treatment When the Threshold = 7

Voting Types


Voting Types

Previously Predicted to Vote Sincerely

When the Threshold = 3

(1-8, 9-13, 16-23)

Votes Types

Previously Predicted to Vote Tactically

When the Threshold = 3 (9-10, 14-15)

Sincere

73.8% (268)

78.2% (62)

Tactical

26.2% (95)

21.5% (17)

Total

100% (363)

100% (79)

Number of Cases = 442, χ2 = 0.742


Table A6: Comparison of Voting Behavior in the Low Information Treatment When the Threshold = 7

Voting Types


Voting Types

Previously Predicted to Vote Sincerely


(1-8, 10-14, 16-23)

Votes Types

Previously Predicted to Vote Tactically


(9, 15)

Sincere

74.4% (299)

77.5% (31)

Tactical

25.6% (103)

22.5%

(9)

Total

100% (402)

100% (40)



Table A7: Comparison of the Voting Behavior of the Voting Types (9-10, 14-15) that should Vote Tactically in the

High Information Treatment and Low Information Treatment When the Threshold = 3

Treatments


High Information

Treatment

Low Information

Treatment

Sincere

43.7% (31)

64.9% (48)

Tactical

56.3% (40)

35.1% (26)

Total

100% (71)

100% (74)



Table A8: Comparison of the Voting Behavior of the Voting Types (9, 15) that should Vote Tactically in the High

Information Treatment and Low Information Treatment When the Threshold = 5

Treatments


High Information

Treatment

Low Information

Treatment

Sincere

50.0% (19)

55.3% (21)

Tactical

50.0% (19)

44.7% (17)

Total

100% (38)

100% (38)



Table A9: Comparing the Voting Behavior of the Voting Types in all the Voting Sessions (s = Threshold)

Treatment One

Treatment Two

Voted

According to ASB

Predictions

s = 3

s = 5

s = 7

s = 3

s = 7

Overall Totals

Yes

68.7%

68.5%

71.7%

71.1%

71.1%

70.2%

No

31.3%

31.5%

28.3%

28.9%

28.9%

29.78%

Total

100%

100%

100%

100%

100%

100%


Figure A6: Distribution of the Voters in all Voting Sessions who Voted According to the ASB Predictions

0

2

4

6

8

10

12

14

16

100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

Percentage of Voters Voting According to the ASB Predictions

Number of Voters


Appendix B: Experiment Instructions

The instructions will be read aloud and we ask that you wait until the reader has

finished reading all the instructions before you ask any questions. The number at the top

of this sheet is your identification number. Please do not hit any keys on the keyboard

until we are ready to begin the experiment.

General

This experiment is part of a study examining voting behavior. The experiment

will consist of a series of 20 separate elections. During each election you will vote for

one of three parties; they are labeled B, C, and D. The votes cast will determine the

winner in each election. A party must receive a majority of the votes, twelve, to win the

election. The party that wins the election determines how much money you will receive

for that election. You will be paid in cash at the end of the experiment. The exact

amount will depend upon the decisions made by you and the other participants.

Election Process

At the beginning of each election you will be randomly assigned a voting type.

There are 23 voting types and each person is assigned to one voting type. Your voting

type is indicated by the assignment screen (see figure 1). The first line indicates your

identification number, which remains constant throughout the experiment (the number at

the top of this sheet). The second line indicates your voting type for the current election.

All the possible voting types are displayed on the voting schedule (see handout). The

simplified voting schedule shows you which party is most preferred by each voter. A

voter’s most preferred party is the party that the voter will receive the most money if that

party wins the majority of the votes. The individual voting schedule shows the amount of

money each voting type will receive depending on the outcome of the election. For

example, if you were assigned to voting type one, then you would look at the row labeled

1 in the voting schedule. If party B won a majority of the votes then you would receive

$1.67 for this election. And, if party C won a majority of the votes then you would

receive $1.04, and so forth. The amount of money that you receive depends solely upon

the outcome of election. The last column reminds you that only one person is assigned to

each voting type.


The third line in figure 1 indicates the threshold. The threshold is the minimum

percentage of votes that a party must receive. If a party fails to receive the minimum

number of votes then those votes that were cast for the party are voided and the party is

thrown out of that election. The minimum threshold for all the elections is 20 % of the

votes. This threshold level means that each party must receive at least five votes to cross

the threshold.

-Example 1: Suppose the following occurred: Party B receives 11 votes Party C receives 10 votes Party D receives 2 votes The final result is party B wins with 11 votes and Party C receives 10 votes and party D

receives 0 votes since it did not receive at least 5 votes.

The fourth and fifth lines indicate the names of the parties. The sixth line should

be ignored.

Voting

Figure 2 shows the voting screen. Once you are finished with the assignment

screen you need to press the ‘C’ to move to the voting screen. The first line indicates

which election is being conducted (there will 20 elections). The second line indicates

your voting type for this election. The third line asks you to vote. You must choose

either party B (Push ‘B’), party C (Push ‘C’), party D (Push ‘D’), or abstain (Push ‘O’).

Abstaining means that you are not going to vote for any of the parties. You will be asked

to push either ‘Y’ to confirm your vote choice or ‘N’ to cancel your vote and to cast a

new vote.

Results

Once everyone has voted, I will tell you to press ‘1’. This will move you to the

results screen (see figure 3). The first section of the results screen tells you which party

you voted for, your type, and the amount of money that you earned. The second section

tells you the percentage of votes that each party received and the voting threshold. The

last line tells you the result of the election.


When I tell you, everyone will push ‘1’ to start the new election. After pushing

‘1’ you will be returned to the assignment screen which will randomly assign you a

voting type for the new election.

As you may have noticed in the voting schedule, the result of the election can be a

single party (B, C, or D) or a combination of parties (B/C, C/D, B/D). A single party

wins the election if that party receives more than 50% of the votes. If no party wins more

than 50% of the votes then the winner of the election will be a combination (a coalition)

of parties.

-Example 2: Suppose the following results occur: Party B receives 1 vote Party C receives 9 votes Party D receives 13 votes Party B fails to cross the threshold so its one vote is voided, Party C receives 9 votes, and

party D wins the election since it received over 50% of the valid votes cast. If you were

voting type 23 in this election then you would receive $1.67 (see Voting Schedule).

If no single party receives over 50% of the votes then the parties with the most

and least numbers of votes forms a coalition.

-Example 3: Party B receives 5 votes Party C receives 11 votes Party D receives 7 votes The result would be a coalition between parties B and C (B/C) since party C received the

most votes (11) and party B received the least number of votes (5) but still received the

minimum number of votes (5). If you were voting type 23 in this election then you

would receive $0.70 (see Voting Schedule).

Tie-Breaking

Whenever two or three parties receive the same number of votes, the computer

randomly breaks the tie determining the winner.

Notification and Recording

The computer keeps track of your type, party vote, and winnings in each election.

In case of unforeseen circumstances, we suggest that you keep a paper record (see figure

4) of type, party vote, and winnings in each election.


Conclusion

When the experiment is concluded, we will hand out a questionnaire, which will

ask you about your voting behavior. Once you finished the questionnaire, we will pay

you your winnings.

If you have any questions during the experiment, raise your hand and wait for

someone to help you. Otherwise, you must keep silent until the experiment is completed.


Figure 1 Your ID# is 999 in election 1 You are type 1 The threshold value is 20% Party names are: B, C, D Current government is 0 Press c to continue Figure 2 This is the 1 th election Your type is 1 Now it is time for you to vote Please enter the party name for which you are voting or O to abstain Your vote: Figure 3 You voted for party B Your type was 1 The amount you earned this election is $1.67 Percentage of votes received by each party: Party B received 52 percent of the votes Party C received 48 percent of the votes Party D received 0 percent of the votes The threshold value was 20% The new government is B


Figure 4 ID#:

Election Your Vote

Your Type

Outcome Money Won

Votes for B

Votes for C

Votes for D

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20


Voting Schedule Simplified Voting Schedule

Voting Types

Most Preferred

Party

Total

1-8 B 8 9-15 C 7 16-23 D 8

Individual Voting Schedule

Possible Outcome

Voting Type

B

B/C

C

B/D

C/D

D

# of

Voters

1

1.67

1.39

1.04

1.04

.70

.35

1

2

1.64

1.42

1.07

1.07

.73

.38

1

3

1.61

1.45

1.10

1.10

.76

.41

1

4

1.58

1.48

1.13

1.13

.79

.44

1

5

1.57

1.49

1.14

1.14

.80

.45

1

6

1.56

1.50

1.15

1.15

.81

.46

1

7

1.55

1.51

1.16

1.16

.82

.47

1

8

1.54

1.52

1.17

1.17

.83

.48

1

9

1.34

1.69

1.37

1.37

1.03

.68

1

10

1.28

1.63

1.43

1.43

1.09

.74

1


Possible Outcomes

Voting Type

B

B/C

C

B/D

C/D

D

# of

Voters

11

1.04

1.39

1.67

1.67

1.33

.98

1

12

1.01

1.36

1.70

1.70

1.36

1.01

1

13

.98

1.33

1.67

1.67

1.39

1.04

1

14

.74

1.09

1.43

1.43

1.63

1.28

1

15

.68

1.03

1.37

1.37

1.69

1.34

1

16

.48

.83

1.17

1.17

1.52

1.54

1

17

.47

.82

1.16

1.16

1.51

1.55

1

18

.46

.81

1.15

1.15

1.50

1.56

1

19

.45

.80

1.14

1.14

1.49

1.57

1

20

.44

.79

1.13

1.13

1.48

1.58

1

21

.41

.76

1.10

1.10

1.45

1.61

1

22

.38

.73

1.07

1.07

1.42

1.64

1

23

.35

.70

1.04

1.04

1.39

1.67

1


ID#: Name: During the experiment were you ever voting type 1 to 8? If you were one of these voting types then Party B was your most preferred party. When you were one of these voting types did you ever vote for party C or D? Please explain why you thought voting for Party C would be useful? Please explain why you thought voting for party D would be useful? During the experiment were you ever voting type 9 to 15? If you were one of these voting types then Party C was your most preferred party. When you were one of these voting types did you ever vote for party B or D? Please explain why you thought that voting for party B would be useful? Please explain why you thought that voting for party D would be useful? During the experiment were you ever voting type 16 to 23? If you were one of these voting types then Party D was your most preferred party. When you were one of these voting types did you ever vote for party B or C? Please explain why you thought voting for party B would be useful? Please explain why you thought voting for party C would be useful?


References

Alesina, Alberto and Howard Rosenthal. 1995. Partisan Politics, Divided Government,

and the Economy. Cambridge: Cambridge University Press. Austen-Smith, David and Jeffrey Banks. 1988. “Elections, Coalitions, and Legislative Outcomes.” American Political Science Review 82: 405-422. Cox, Gary W. 1997. Making Votes Count: Strategic Coordination in the World’s

Electoral Systems. Cambridge: Cambridge University Press.

Duverger, Maurice. 1954. Political Parties: Their Organization and Activity in the Modern State. New York: John Wiley and Sons. Fiorina, Morris P. 1992. Divided Government. New York: Macmillan. Gibbard, Alan. 1973. “Manipulation of Voting Schemes: A General Result.”

Econometrica 41: 587-601. Leys, Colin. 1959. “Models, theories and the Theory of Political Parties.” Political

Studies 7: 127-146. Lipset, Seymour Martin and Stein Rokkan. 1967. Party Systems and Voter Alignments: Cross-National Perspectives. New York: Free Press. Sartori, Giovanni. 1968. “Political Development and Political Engineering.” In John D.

Montgomery an Albert O. Hirschmann, eds. Public Policy. Cambridge: Cambridge University Press.

Satterthwaite, Mark Alan. 1975. “Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions.” Journal of Economic Theory 10: 187-217.

tactical coalition voting

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