The effect of quorum rules on voter
turnout in a binary referendum:
what happens when the preferences
of two groups differ in intensity?
Jeroen Pennings 10088830
MSc Economics
Track Behavioral Economics Master’s Thesis - 15 ECTS
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--- Statement of Originality
This document is written by Student Jeroen Pennings who declares to take full responsibility for the contents of this document:
“I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.”
Jeroen Pennings
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Summary1
This thesis builds on the growing body of literature on voter turnout, and more
specifically on the use of quorum rules on voter turnout. Using experimental methods, the author is able to replicate some previous findings that quorum rules have a negative effect on voter turnout, especially for majority group members. Moreover, higher
quorums have a larger effect than smaller ones. As an addition, asymmetric preference intensities are introduced in order to evaluate and understand some real life situations better. The author is unable to find any significant effect of this preference intensity treatment. This might be explained by shortcomings of the research, most notably in the recruitment of participants.
1 I am very grateful to Ailko van der Veen for his supervision throughout the process of writing my thesis and to the second corrector of this thesis for his time and effort. Moreover, I want to thank Joep
Sonnemans and Joël van der Weele for coordinating the master thesis seminar and all students and professors involved in that seminar for their comments on my ideas. Lastly, I cannot thank my friends and family enough for being more than willing to help me out with my experiment.
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Contents
1. Introduction 5
2. Literature review 7
3. The model and its predictions 15
4. Experimental design 20
5. Results 24
6. Conclusion 32
Reference list 34
Appendix A.1: Derivation of probabilities of being pivotal 37
Appendix A.2: Experiment instructions 44
Appendix A.3: Answer sheet and questionnaire 48
Appendix A.4: Round overview 50
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1. Introduction
On the 6th of April of 2016, a referendum was held in the Netherlands on whether or not to ratify a trade agreement between the EU and Ukraine. In the weeks before the referendum, there were campaigns from both the opponents and the supporters of ratification of the agreement. Although most people were trying to convince potential voters to vote either in favor or against, some of the supporters of ratification argued that a better strategy than voting yes was to abstain from voting. Ratification of the agreement would be the default option if the quorum would not be met anyway. Given that the consequences of organizing referendums can be far-reaching2 and the use of
referendums is becoming more and more popular across most of the world’s democracies3, tools for referendum design are becoming more important.
One of the tools governments can use when designing a referendum is a participation or approval quorum rule. Basically, a quorum rule adds an extra
restriction to the outcome of a referendum, namely that a minimum percentage of the electorate has to show up and vote. The underlying argument to impose such a rule is that in this way the most representative outcome is ensured. However, imposing a quorum rule can have a negative impact on voter turnout as well. It might lead to strategic abstaining, even to the point where the quorum percentage turnout is not met only because of the very existence of the quorum. This phenomenon is called the “no-show paradox”, first formalized by Fishburn and Brams (1983). Evidence that this phenomenon might be in place has been provided by many authors, e.g. Aguiar-Conraria et al. (2013), Hizen (2015) and Aguiar-Aguiar-Conraria and Magalhaes (2010).
2 The outcome of the referendum in the Netherlands was to not ratify the trade agreement between the EU and Ukraine. The Dutch government has been negotiating about the terms of the agreement since that day. Another illustration of the fact that referendums can have a big impact, was the Brexit referendum in the UK in 2016.
3 The IDEA Direct Democracy database (available at http://www.idea.int/db/fieldview.cfm?field=327) shows that no less than 151 countries in the world make use of direct democratic decision mechanisms like referendums.
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This thesis builds on previous research, more specifically that from experimental economics. Closely following the experimental design of Aguiar-Conraria et al. (2013), this thesis introduces a different intensity of preferences to the analysis of voter turnout in referendums. The addition of this factor makes the experiment resemble some real-life situations more closely. Below, the research question of this thesis is given:
To what extent do quorum rules affect voter turnout in binary (yes/no) referendums when the preferences of two groups differ in intensity?
Overall, this research cannot find any effect of a different preference intensity on voter turnout when a quorum rule is in place. This might be partly due to the
experimental design, where the treatment with asymmetric preference intensities might not have been ideal. However, the previous finding in the literature that a quorum has a negative effect on voter turnout can be confirmed. Higher quorums appear to have a bigger effect.
This thesis is organized as follows: section 2 gives a review of the most relevant literature. Section 3 then discusses the theoretical predictions of the game theoretical model that is used in this thesis and the hypotheses are formulated. The experimental design that is used to test these hypotheses is described in section 4. Section 5 reports the descriptive statistics, regression results and the possible limitations of the research. Section 6 provides the conclusion.
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2. Literature review
Firstly, this part starts with summarizing the rich literature on voter turnout in general, both theoretically and empirically. Secondly, the effects of adding a quorum rule on voter turnout are examined. Thirdly, the author discusses the two experimental papers that were the main source of inspiration. Lastly, the added value of this thesis to the existing body of literature is evaluated.
Voter turnout
The use of free elections to choose representatives is the foundation of all democracies around the world. People have the chance to vote for their preferred candidates for (supra)national, regional and local parliaments. Gaining a better understanding of the factors that influence voting behavior can help in designing elections in such a way that the outcome is a fair representation of the preferences of the population. Therefore, the importance of studying voter turnout is undisputed.
One of the earliest contributions to the field of voter turnout is an article by Downs (1957) who first came up with a model of instrumental voting, implying that someone votes if and only if the following formula holds for him:
𝑅 = 𝑃𝐵 − 𝐶 > 0 (eq. 1)
In this equation, ‘P’ is the probability of changing the outcome by casting a vote, ‘B’ is the net utility increase by casting a vote and ‘C’ is the cost of voting. One of the big challenges of this model is the paradox of (not) voting (Downs, 1957): if the number of eligible voters gets bigger, ‘P’ decreases to virtually zero. This means that in eq. 1, ‘R’ is never larger than 0 and all people with positive voting costs would abstain on election
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days. Hence, this model does not accommodate the empirical finding that turnout in almost all elections is significantly different from zero (Geys, 2006b).
Some other interesting observations can be made regarding the determinants of voter turnout. Firstly, as the size of the electorate gets bigger, turnout drops (Geys, 2006a). This finding is in line with the factor ‘P’ in eq. 1 decreasing. Secondly,
demographic characteristics4 play a role on the individual’s decision to vote. Thirdly,
factors involving the nature5 and design6 of the election play a role. Lastly, voters appear
to behave strategically sometimes depending on the situation.7 An example of this
strategic behavior is that turnout seems to increase if the election will be a close race between alternatives (Geys, 2006a).
For many years now, models have been proposed that would both incorporate an explanation for the paradox of (not) voting and accommodate the determinants of voter turnout above (Geys, 2006b). A first line of proposed models is to include some sort of benefit from voting ‘D’, for example by Riker and Ordeshook (1968):
𝑅 = 𝑃𝐵 − C + 𝐷 > 0 (eq. 2)
In eq. 2 ‘D’ is a measure of the extra utility that an individual gets from the process of casting a vote. This extra utility from voting can either be relatively self-centered (for example because getting the chance to express your opinion is satisfactory), or to some extent altruistic (Goodin & Roberts, 1975). In the remainder of this chapter, I refer to the
4 In general, individuals who are richer and higher-educated are more likely to vote. Furthermore, young voters and elderly are less likely to cast their vote whereas women vote more often (Lijphart, 1997). 5 For example, voter turnout is higher in ‘first order’ elections for national parliaments than in ‘second order’ elections for regional or local parliaments (Reif & Schmitt, 1980).
6 E.g. proportional elections result in a higher turnout compared to elections with a majority rule (Ladner & Milner, 1999). Furthermore, compulsory voting rules also increase the likelihood that individuals cast a vote (Geys, 2006a).
7 As Geys (2006b) argues: “voters defect from their true preferences in some cases to cast ‘insincere’ or ‘strategic’ votes”.
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factor ‘C − 𝐷’ as the ‘net voting costs’. Typically, this line of models explains high turnout rates for people with negative net voting costs. People with positive net voting costs abstain in this framework.
Palfrey and Rosenthal (1985) study the paradox of (not) voting game
theoretically. For small electorate groups under strategic uncertainty, their pivotal voter model makes nice predictions about whether people vote or abstain. They reason that if everybody votes, the chance of being pivotal ‘P’ becomes virtually zero. This makes it rational to abstain. But if everybody else abstains, the probability that you are pivotal is 100%. In this situation, it is rational to cast a vote. This leads to the conclusion that ‘P’ is not fixed, but it depends on the strategical interactions between individuals in the population. The main drawback of this class of models is that if the electorate size gets bigger, they predict high turnout rates for people with non-negative net voting costs. Again this is not in line with empirical findings.
More recent contributions are made incorporating group-based decision making, incomplete information situations and learning. However, for the current thesis these contributions are not very relevant.8
The use of models incorporating empirical findings to explain what drives voter turnout is very useful, but it has its limitations. Therefore, some authors resort to experimental evidence. The participation game in Palfrey and Rosenthal (1985) offers a framework to study the voter’s decision on whether or not to vote. For example,
Sonnemans and Schram (1996) show that participation increases if subjects are in a winner-takes-all scheme compared to a proportional representation scheme.
Furthermore, they provide evidence that group identification and the ability to communicate play a role in voter turnout. Later, Levine and Palfrey (2007) show that
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size of the experimental groups matters, as well as the intensity of competition (turnout is higher in referendums where a close-call majority is expected).
The effect of quorum rules on voter turnout
One of the first papers to theoretically examine the effect of quorum rules on voter turnout is written by Côrte-Real and Pereira (2004). Their analysis focuses on binary voting rules in situations where apart from a simple majority rule extra conditions like a quorum rule are in place. They show that conditions like a quorum rule might
incentivize some proportion of the electorate to abstain, a phenomenon sometimes referred to as the ‘quorum paradox’9. The ‘quorum paradox’ refers to the finding that
voter turnout might only exceed the quorum percentage without the existence of that very same quorum rule (Herrera & Mattozzi, 2010). Zwart (2010) builds on the previous literature by taking the model by Riker and Ordeshook (1968) where voters also have a ‘consumption benefit’ from voting. She argues that a quorum rule can have a
meaningful effect in making sure that the outcome of a vote is representative for the preference of the majority, but the success of such a condition depends on choosing the quorum height right. This task is very hard when information about preferences of people is not well-known. Setting the quorum too high might lead to a bigger disrupting effect than setting it too low. Other papers have confirmed these findings using different models10.
To test how well these theoretical models perform in the real world, one can look at some practical cases. One of the well-known cases where a quorum rule had an
important influence on voter turnout took place in Italy. In June 2005, a referendum was
9 This concept is closely linked to the no-show paradox. The first to formalize that it is sometimes better to abstain than vote were Fishburn and Brams (1983).
10 E.g. Herrera and Mattozzi (2010) use a group-based voter turnout model to demonstrate that quorum rules might lead to strategic abstention. Other variations on models have been proposed by e.g. Hizen and Shinmyo (2011) and Laruelle and Valenciano (2011).
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held there on whether or not to allow in vitro fertilization, commonly known as IVF11.
The Vatican strongly opposed IVF methods and tried to persuade people to abstain from voting, with Cardinal Camillo Ruini playing a central role. Turnout was 25,9% of the eligible voters, making the referendum invalid due to a participation quorum rule of 50% (Allen Jr., 2005). For a more detailed case study regarding the referendum in Italy, see Uleri (2002).
Although case studies, like the one in Italy, shed some light on the effects of quorum rules on turnout, the question is whether this finding can be generalized for all referendums. To test the effect of quorum rules on an aggregate level, Aguiar-Conraria and Magalhães (2010) took data from all 109 national binary (yes/no) referendums in member states of the European Union from 1970 until 2007. The authors estimate that imposing a participation quorum has a statistically significant negative effect on turnout of approximately 11 percentage points, with the effect being even stronger when the minority consists of the eligible voters who prefer the status quo.
Experimental evidence on the use of quorum rules on voter turnout
Obviously, empirical research brings the risk that other factors, both observable and unobservable, play a role in the decision to cast a vote or to abstain. Therefore, as a natural follow-up research, Aguiar-Conraria et al. (2013) conduct a laboratory
experiment. The authors test the consequences of introducing a participation quorum and an approval quorum in the pivotal voter model of Palfrey and Rosenthal (1985). In the remainder of this chapter, I focus specifically on the participation quorum. In their experimental design, 9 subjects are assigned the preference “Change” with probability μ or “Status Quo” with probability 1 - μ. Subjects who prefer “Change” are called
11 IVF refers to the process of human fertilization using techniques where the eggs of the female or fertilized outside of the body.
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Supporters, subjects who prefer the “Status Quo” are called Opponents. Probabilities are known to all players, but the actual preference is private knowledge. Subjects then get the opportunity to either vote for the option of their preference or abstain. Casting a vote has a cost uniformly distributed between 0 and 100 points. In principle the option that gets the majority of the vote wins and all subjects with that preference receive a payoff of 100 points, unless a quorum rule is in place in this round. The participation quorum rule says that a minimum number of 4 votes has to be cast to validate the outcome of the vote. Otherwise “Status Quo” wins the vote. Multiple rounds are played like this with different values of μ12.
A number of interesting results follows from this approach. Firstly, opponents are significantly less likely to cast a vote. Secondly, the quorum rule doesn’t have a significant effect on the likelihood to cast a vote for the supporters. Lastly, apart from influencing the likelihood to cast a vote, the quorum also influences the likelihood to ‘boycott’ the vote by choosing a willingness-to-pay of 0 if a quorum is in place.
In another laboratory experiment, Hizen (2015) uses an experimental design where the height of the quorum is changed. In their research 13 subjects are assigned the preference “yes” with probability s13 or “no” with probability 1 - s. Probability s is
known to all players, but the actual preference is private knowledge. As in Aguiar-Conraria et al. (2013) subjects either vote for the option of their preference or they abstain. In principle the option that gets the majority of the vote wins and all subjects with that preference receive a payoff of 200 yen, unless a quorum rule is in place in this round. If the quorum is not achieved, the payoff for every subject is 100 yen. Multiple
12 μ takes the value of 3/9, 4/9, 5/9 and 6/9 respectively in different rounds. Hence, the resulting comparison is within subjects.
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rounds are played like this with different heights of the quorum, namely 1, 3, 5, 7, 9, 11 and 13.
The authors find that as long as the quorum is 5 or lower, turnout rates are relatively high. As the size of the quorum gets bigger, the likelihood that especially minority group voters cast a vote drops. This increases the chance that the quorum is not met. Furthermore, turnout in a specific group gets bigger as the probability of being in that group is higher.
Added value of this thesis
This thesis builds mostly on the laboratory experiments in Aguiar-Conraria et al. (2013) and Hizen (2015), by introducing a different intensity of preferences to the analysis of voter turnout in referendums. This addition makes it possible to draw inferences for situations where ‘active’ minorities are involved, so it is important to realize that the proposed addition is already a step forwards towards more closely mirroring real life situations. To the best of my knowledge, the papers by Aguiar-Conraria et al. (2013) and Hizen (2015) are the only experimental research papers on the effect of participation quorum rules on voter turnout.
Given the relative scarceness of experimental evidence on the use of quorum rules, it is fair to say that replication of the findings from the previous papers already adds value to the field. Both the design and different subject population give the
opportunity to check how influential some potential shortcomings in the literature were on previous findings. For example, Hizen (2015) tested the effect of different
probabilities of having a certain preference between subjects, whereas this research does so within subjects. Furthermore, one could argue that the use of non-neutral labels (“Status Quo” vs. “Change”) in Aguiar-Conraria et al. (2013) has an effect on the
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outcomes. This research uses the neutral labels “A” and “B” instead, which makes a check on the robustness of their findings possible.
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3. The model and its predictions
This section discusses the model used in this thesis and its parameters first. After that, the theoretical implications of changing these parameters are demonstrated. These implications are used to formulate the hypotheses that help to answer the research question of this thesis.
The model
Closely following Aguiar-Conraria et al. (2013)14, subjects in this thesis choose to vote or
not based on their belief of the probability of changing the outcome of the vote. In each voting round there are n15 possible voters who get assigned either preference “A” or
“B”. Everyone knows what the ex-ante probability μ is of being in the group with
preference “A”, namely 5/9 or 6/9. People decide either to vote or to abstain based on the actual assigned preference, which is private knowledge. If a person votes, he incurs voting costs ci, which is uniformly distributed between 0 and 100 points. In principal, the winning group is determined based on majority rule. However, a quorum rule might be in place: if the specified quorum is not met, people with preference “A” win. When a quorum is in place, quorum heights of 2, 3, 4 and 5 are considered. The default option if the quorum is not met, is always option “A”. Benefit 𝜋𝐴,𝑤𝑖𝑛 is the benefit of voters with preference “A” in case of a win, benefit 𝜋𝐵,𝑤𝑖𝑛 that of voters with preference “B” in case of a win. In case of a tie, each group wins with probability 50%. In case of a loss, 𝜋𝐴,𝑙𝑜𝑠𝑠 is 0 for A-players and 𝜋𝐵,𝑙𝑜𝑠𝑠 is 0 for B-players. Benefits are either symmetric (𝜋𝐴,𝑤𝑖𝑛 = 𝜋𝐵,𝑤𝑖𝑛 = 600 points) or asymmetric (𝜋𝐴,𝑤𝑖𝑛= 600 points, 𝜋𝐵,𝑤𝑖𝑛 = 400 points). Utility for individual voters is determined by the possible benefit they earn minus the possible voting costs they incur.
14 For an overview of the setup of Aguiar-Conraria et al. (2013), see section 2. 15 In all experiment sessions, groups had size n=9.
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For the purpose of this thesis it is important to look at the implications of
changing our parameters of interest on voter turnout. Define 𝜌(𝜐𝐴, 𝜐𝐵) as the probability person i attaches to the outcome that of the other (n-1) 16 people 𝜐
𝐴 vote “A” and 𝜐𝐵 vote “B”. Moreover, define 𝛾𝐴 and 𝛾𝐵 as the maximum voting cost an A- or B-player is
willing to incur to cast a vote. This notation allows us to write down the equilibrium conditions given in Table 1. In equilibrium, each person should equate the maximum voting cost he is willing to his expected benefit from voting, which is equal to the probability of being pivotal times the gain in 𝜋𝐴 or 𝜋𝐵. For a detailed overview of the derivation of these equilibrium conditions, see Appendix A.1 or Aguiar-Conraria et al. (2013).
Table 1: Equilibrium conditions of the model conditional on the quorum rule
Quorum height Group Equilibrium condition
No quorum A 𝛾𝐴= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=0 + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=0 ] 𝜋𝐴,𝑤𝑖𝑛 B 𝛾𝐵= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=0 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=0 ] 𝜋𝐵,𝑤𝑖𝑛 Quorum = 2 A 𝛾𝐴= [ 1 2 ∑ 𝜌(𝜐, 𝜐) + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) − 3 𝜐=1 1 2 𝜌(0,1) 4 𝜐=1 ] 𝜋𝐴,𝑤𝑖𝑛 B 𝛾𝐵= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=1 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=0 + 𝜌(0,1)] 𝜋𝐵,𝑤𝑖𝑛 Quorum = 3 A 𝛾𝐴= [ 1 2 ∑ 𝜌(𝜐, 𝜐) + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=1 4 𝜐=2 − 𝜌(0,2)] 𝜋𝐴,𝑤𝑖𝑛 B 𝛾𝐵= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=2 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=1 + 𝜌(1,1) + 𝜌(0,2)] 𝜋𝐵,𝑤𝑖𝑛 Quorum = 4 A 𝛾𝐴= [ 1 2 ∑ 𝜌(𝜐, 𝜐) + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=2 4 𝜐=2 − 1 2 𝜌(1,2) − 𝜌(0,3)] 𝜋𝐴,𝑤𝑖𝑛 B 𝛾𝐵= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=2 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=1 + 𝜌(1,2) + 𝜌(0,3)] 𝜋𝐵,𝑤𝑖𝑛 Quorum = 5 A 𝛾𝐴= [ 1 2 ∑ 𝜌(𝜐, 𝜐) + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=2 4 𝜐=3 − 𝜌(1,3) − 𝜌(0,4)] 𝜋𝐴,𝑤𝑖𝑛 B 𝛾𝐵= [ 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=2 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=2 + 𝜌(1,3) + 𝜌(0,4)] 𝜋𝐵,𝑤𝑖𝑛
Note: Equilibrium conditions are given for both A-players and B-players for the different possible quorum rules used in this thesis. In equilibrium, it should hold that the expected benefit of voting equals the maximum cost a player is willing to pay. The expected benefit of a vote is equal to the probability of being pivotal times the benefit in case the player is pivotal. A more detailed derivation of these equilibrium conditions is given in Appendix A.1.
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Predictions of the model
We can now make some predictions on what the impact is on voter turnout of changing the parameters of the model. Since this thesis does not focus on the effect of changing beliefs of individuals on voter turnout, we assume that 𝜌(𝜐𝐴, 𝜐𝐵) is stable when the parameters of the model change. Second order effects (e.g. an A-player updates his beliefs on the value of 𝜌(𝜐𝐴, 𝜐𝐵) if a B-player adjusts his cutoff value 𝛾𝐵) are explicitly ignored. Although this assumption might not hold up very well in reality, it allows us to draft some hypotheses.
Firstly, it is necessary to say something about the height of the benefit πA and πB. As said before, in the research design of this thesis half of the subjects faced the case where the benefits are symmetric (𝜋𝐴,𝑤𝑖𝑛= 𝜋𝐵,𝑤𝑖𝑛 = 600 points), whereas the other half faced the case of asymmetric benefits (𝜋𝐴,𝑤𝑖𝑛 = 600 points, 𝜋𝐵,𝑤𝑖𝑛 = 400 points). Holding all else equal, it is easy to see from the conditions in table 1 that if 𝜋𝐵 decreases, the cut-off value for a B-player decreases. Therefore, we would expect that a B-player is willing to pay less to cast a vote in sessions where benefits are asymmetric than in sessions where these are symmetric.
It is harder to determine the effect of adding a quorum directly. Holding all else equal, introducing a quorum of height 2 has the following effect on an A-player when compared to the case with no quorum: a vote by an A-player is no longer pivotal if 𝜐𝐴 = 0 and 𝜐𝐵= 0 or when 𝜐𝐴 = 0 and 𝜐𝐵 = 1. Actually, when 𝜐𝐴 = 0 and 𝜐𝐵= 1, voting will result in a tie instead of a sure win. Therefore, introducing a quorum leads to a lower expected probability of being pivotal by voting for an A-player. This should lead to a lower willingness to pay for an A-player. Higher quorums lead to even stronger
negative effects on the willingness to pay. The effect of introducing a quorum of height 2 on the behavior of a B-player is less straightforward. On the one hand, a B-player is no longer pivotal by voting if 𝜐𝐴 = 0 and 𝜐𝐵 = 0, but he gets an extra possibility to be
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pivotal if 𝜐𝐴 = 0 and 𝜐𝐵= 1. The expected probability of changing the outcome by voting thus depends on the beliefs 𝜌(0,0) and 𝜌(0,1). If 𝜌(0,0) > 𝜌(0,1), introducing the quorum with height 2 decreases the willingness to pay for a B-player. If 𝜌(0,0) < 𝜌(0,1), the quorum will lead to a higher willingness to pay. This confirms findings from the literature by e.g. Aguiar-Conraria et al. (2013) and Hizen (2015): we know that quorum rules lead to lower turnout for majority group voters, but the effect on minority group voters is less unambiguous.
It is hard to make any predictions about the effect of changing the ex-ante probability of being in group A, without discarding the assumption that beliefs on the value of 𝜌(𝜐𝐴, 𝜐𝐵) are not updated if the parameters of the model change. If μ is higher, two opposing effects might affect 𝛾𝐴 and 𝛾𝐵. On the one hand, we know that in
participation games cooperation drops as groups get larger. Following this logic, A-players might lower 𝛾𝐴. This makes it easier for B-players to win the vote, so they might increase 𝛾𝐵. However, if A-players expect that B-players increase 𝛾𝐵, they might choose themselves to increase 𝛾𝐴. Therefore, our model cannot provide an estimate for the net effect in our model on the willingness to pay to cast a vote. Therefore, we turn to the literature. Almost every article in the literature gives evidence that overall voter turnout increases if in a certain elections percentage of people in the majority group is close to that percentage in the minority group (e.g. Levine & Palfrey (2007)).
Hypotheses
The findings from the literature in section 2 combined with the theoretical findings of this section lead to the following hypotheses to answer the research question:
H1: If majority group voters have a higher payoff in case of a win than minority
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group voters and a lower willingness to pay for the minority group when a quorum is in place.
The logic is that in the absence of a quorum rule voters are willing to pay more to cast a vote if they have more to gain. Adding a quorum to the vote gives majority group voters an extra possible strategy, namely to abstain. Suppose the quorum is not met: in this case the majority group always wins the vote. Therefore, majority group voters are more likely to abstain when facing a minority group with a higher payoff in case of a win. Conversely, minority group voters are willing to pay more to cast a vote if the payoff in case of a win is higher.
Besides this hypothesis, that is mostly related to the main research question of this thesis, the experimental design used in this thesis allows for the replication of earlier results from laboratory research by Aguiar-Conraria et al. (2013) and Hizen (2015). The possible replication of earlier results allows me to check whether the experiment performed in this thesis has any shortcomings. To replicate these findings, the hypotheses below are formulated:
H2: A more asymmetric population distribution (μ =6/9 vs. μ=5/9) leads to a stronger effect of quorum rules on voter turnout.
H3a: Willingness to pay to vote is higher for minority group voters under a
participation quorum rule than in the absence of a quorum rule.
H3b: Willingness to pay to vote is lower for majority group voters under a
participation quorum rule than in the absence of a quorum rule.
H4: If the quorum gets larger, the effects of the quorum rule on voter turnout are larger, both for majority group and minority group voters.
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4. Experimental design
From June 22 until 26 in 2016, experiment sessions took place both in Rosmalen at the home of the author’s parents and in Amsterdam at the University of Amsterdam. Participants for the research were recruited amongst the family and friends of the author.17 In total 6 sessions were held, where in every session 9 subjects took part. This
led to a total subject pool of 54 people, of which 42,6% was female. The age of the subjects ranged from 20 to 68 years, with an average of 32,4 years. The educational background of the subjects was very diverse, ranging from high school level to university level18. Almost half of the subject population (48,1%) was familiar with
laboratory research. One necessary comment to make regarding the subject recruitment, is that most of the subjects knew the author beforehand. Therefore, it was inevitable that some of them already knew each other before the experiment. In the planning of the experiments, the author tried to prevent (good) friends from being in the same experiment session as much as possible.
At the start of the experiment, subjects were randomly placed by picking seating cards (1-9). The subjects were then given instructions in Dutch. An English translation of the instructions can be found in Appendix A.2. The experimenter read the instructions together with the subjects and answered questions if necessary. From this point
onwards no communication was allowed until the end of the experiment. The entire experiment was conducted with pen and paper.
An individual round proceeded as follows: subjects were informed about the probability of being in group A and the quorum rule in that round. Quorum rules were always defined as follows: “If fewer than [quorum height] votes are cast, option A will
17 Due to both monetary and time constraints, it was not feasible to recruit subjects other than friends and family of the author.
18 79,6% of the subjects held a degree at the level of university of applied sciences (Dutch: HBO) or higher. Of the participants, 53,7% had followed courses in economics at a university.
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automatically win. If [quorum height] votes or more are cast, the option with most votes will win. In case of a tie, a random choice is made (50/50).” Subjects were then asked to pick a ball indicating either “A” or “B” from an urn. They wrote down their pick on their individual answer sheet (see Appendix A.3). Subjects then wrote down their willingness to pay (WTP) to cast a vote on a scale from 0 to 100. After they wrote down their WTP, the experimenter asked each subject to determine his/her individual voting cost (VC). This was done using an online random number generator (www.random.org) ranging from 1 to 100. The following voting rule applied for each individual: if the WTP was higher than the VC for a subject, a vote was cast in favor of the option of the group the individual belonged to. If the WTP was lower than the VC, no vote was cast. The experimenter then collected all answer sheets and calculated how many votes were casts, whether the quorum was met and which group was the winner of that specific round. The experimenter indicated what the payoff of the subject was in that specific round. This payoff was equal to 𝜋𝐴,𝑤𝑖𝑛− 𝑉𝐶 in case the individual belonged to group A and that group won, 𝜋𝐵,𝑤𝑖𝑛− 𝑉𝐶 in case the individual belonged to group B and that group won, and 0 − 𝑉𝐶 in case his group lost. The experimenter then gave the answer sheets back to the corresponding subjects, and another round began.
The main source of inspiration for the choices made in the research design was the Aguiar-Conraria et al. (2013) research. Every experiment session performed for this thesis lasted for 10 rounds, following a 2 x 2 x 5 design to investigate the consequences of different intensity of preferences (𝜋𝐴,𝑤𝑖𝑛 = 600 points and 𝜋𝐵,𝑤𝑖𝑛 = 400 points vs. 𝜋𝐴,𝑤𝑖𝑛= 𝜋𝐵,𝑤𝑖𝑛= 600 points), the effect of population distribution (μ = 5/9 vs. μ = 6/9) and the presence and height of the quorum (no quorum rule vs. quorum rules with heights 2, 3, 4 and 5). The different intensity of preferences was tested between subjects and the effect of different population distribution and the height of the quorum was tested using treatments within subjects. Compared to the Aguiar-Conraria et al. (2013)
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research, the within subject treatments were only slightly changed. My experiment focused on the difference in intensity preference between subjects, where the other research looked at the difference between approval and participation quorum rules
between subjects. For a graphical overview of the research design, see Table 2.
Table 2: Overview of the research design Treatment group
𝜋𝐴,𝑤𝑖𝑛= 600 points / 𝜋𝐵,𝑤𝑖𝑛= 400 points
Control group
𝜋𝐴,𝑤𝑖𝑛= 600 points / 𝜋𝐵,𝑤𝑖𝑛= 600 points
μ = 6/9 μ = 5/9 μ = 6/9 μ = 5/9
No quorum 05AxNT 06AxNT 05AxT 06AxT
Quorum = 2 25AxNT 26AxNT 25AxT 26AxT
Quorum = 3 35AxNT 36AxNT 35AxT 36AxT
Quorum = 4 45AxNT 46AxNT 45AxT 46AxT
Quorum = 5 55AxNT 56AxNT 55AxT 56AxT
Note: Every round is given a code name according to the following structure: βδAx(N)T, where β indicates the quorum height (0 if no quorum was in place, otherwise 2, 3, 4 or 5) and δ indicates the number of A-balls in the urn. NT indicates that subjects were in the symmetric intensity of preferences group, T indicates they were in the asymmetric case. For an overview of the order in which the rounds were played, see Appendix A.4.
During the first, fourth and sixth experiment session, the case of asymmetric intensity of preferences was tested. In the other sessions, the preference intensity was symmetric. This allowed for a between subjects comparison of different preference intensities. In addition, each round used a different combination of population
distribution in the population and the height of the quorum. To control for learning and order effects, the order of these within subjects treatments were reversed between
experiment sessions. To prevent subjects from attaining negative payoffs, each subject got a show-up fee of 1000 points.
After the last round, subjects filled out a questionnaire. Besides questions on demographic characteristics such as age, gender and level of education, the
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One of the subjects was then asked to randomly determine which subject was selected for payoff based on the seating number. The author chose to pay only one of the
subjects19. Payoffs were calculated for that particular subject according to the results of
all rounds, with a payoff rate of €1 for every 500 points. The average number of points attained by the subjects was 4333 points (the equivalent of €8,67). After filling out the questionnaire, subjects were asked not to share the decisions they made with others or the payoff they attained with these decisions. Furthermore, they were explicitly asked not to share any details with people that would still participate. In this way subjects were unaware about the group assignment of other subjects during and after the
experiment, but the experimenter knew at all times what the group assignment and the decisions of a subject were. Experiments lasted on average 55 minutes, with the
minimum length being 54 minutes and the maximum length being 58 minutes.
19 Before the experiment the author chose to only pay one of the subjects due to both time and logistic constraints. However, all of the subjects indicated at the end of the experiment that they did not accept any monetary payoff.
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5. Results
Firstly, this section reports descriptive statistics and the results of non-parametric tests for the difference in means between the treatment variables. Secondly, because simple non-parametric tests fail to incorporate all available data, some regressions are run to estimate the effects of the several variables on the willingness to pay (WTP) to vote. Lastly, the limitations of the research are discussed.
Descriptive statistics and preliminary tests
Before I go in depth on the results of the experiment, it is necessary to give some descriptive statistics, such as means and standard deviations. For aesthetic purposes, these are reported conditional on μ, which was either 5/9 or 6/9 in the experiment. Table 3 and 4 report the means and standard deviations of the WTP for different quorum heights and for asymmetric or symmetric preference intensities.
To gain further insights, some non-parametric tests were performed. P-values associated with the Mann-Whitney U test are given in the last column, for the null that the means are the same under both symmetric and asymmetric preference intensities. The fact that not even 1 of the 20 possible comparisons shows a significant difference at the 5% confidence level (and only 2 of them are significant at the 10% confidence level), doesn’t give support for the hypothesis H1.
Preliminary result 1: There is no significant difference in mean willingness to pay of both
A- and B-players in the treatment sessions with asymmetric payoffs compared to the control sessions with symmetric payoffs.
Based on this fact, the next comparisons in this section are given for all subjects, regardless of whether they were in a session with symmetric or asymmetric preferences.
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Table 3: Descriptive statistics and preliminary statistics for rounds where μ =5/9 Asymmetric payoffs 𝜋𝐴,𝑤𝑖𝑛= 600 points / 𝜋𝐵,𝑤𝑖𝑛= 400 points Symmetric payoffs 𝜋𝐴,𝑤𝑖𝑛= 600 points /𝜋𝐵,𝑤𝑖𝑛= 600 points Asymmetric vs. symmetric
Mean WTP St. dev. Mean WTP St. dev. P-value
A -pla y er s No quorum 64,67 28,92 84,71 19,61 0,0511* Quorum = 2 55,92 37,03 62,15 31,96 0,6815 Quorum = 3 62,4 37,91 54 37,04 0,4724 Quorum = 4 35,56 41,42 39,29 33,21 0,6569 Quorum = 5 50 45,39 46,4 44,68 0,8069 B -pla y er s No quorum 31,67 29,15 52 30,11 0,0911* Quorum = 2 36,53 32,57 57,14 33,02 0,1101 Quorum = 3 28,67 27,30 50,73 40,65 0,1540 Quorum = 4 50,22 34,85 43,92 43,45 0,6153 Quorum = 5 21,54 39,52 38,92 43,28 0,1496
Notes: Means and standard deviations of the WTP for all rounds where μ = 5/9 are given for different quorum heights. A division is made between groups with asymmetric or symmetric preferences. A Mann-Whitney U-test is then performed for the difference in means between the asymmetric and the symmetric payoff group, for which the p-values are given in the fifth column.
* Statistically significant at a 10%-level
Table 4: Descriptive statistics and preliminary statistics for rounds where μ = 6/9 Asymmetric payoffs 𝜋𝐴,𝑤𝑖𝑛= 600 points / 𝜋𝐵,𝑤𝑖𝑛= 400 points Symmetric payoffs 𝜋𝐴,𝑤𝑖𝑛= 600 points / 𝜋𝐵,𝑤𝑖𝑛= 600 points Asymmetric vs. symmetric
Mean WTP St. dev. Mean St. dev. P-value
A -pla y er s No quorum 69,26 29,98 78,19 24,94 0,3822 Quorum = 2 64,44 35,18 54 37,78 0,4411 Quorum = 3 54,29 40,76 52,63 41,15 0,5682 Quorum = 4 46,4 41,65 55,59 40,46 0,5862 Quorum = 5 38,11 45,91 57,69 46,75 0,2523 B -pla y er s No quorum 31 43,66 43,91 38,37 0,2443 Quorum = 2 34,78 36,28 40,62 43,29 0,8127 Quorum = 3 32,38 36,87 32,75 38,44 0,8551 Quorum = 4 29,67 31,86 10 17,32 0,1491 Quorum = 5 23,78 32,67 27,36 35,37 0,9486
Note: Means and standard deviations of the WTP for all rounds where μ = 6/9 are given for different quorum heights. A division is made between groups with asymmetric or symmetric preferences. A Mann-Whitney U-test is then performed for the difference in means between the asymmetric and the symmetric payoff group, for which the p-values are given in the fifth column.
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An overview of the results conditional on being in either of the two groups is given in Tables A3a and A3b in Appendix A.5.
Table 5 shows the means and standard deviations of the WTP conditional on the value of μ. It is clear that the mean WTP for A-players is almost similar for both groups, whereas B-players tend to decrease their WTP when μ goes from 5/9 to 6/9. The p-values, again calculated using a Mann-Whitney U test for the difference in means, reported in the last column show that both in the absence as well as in the presence of quorum rules there is no significant change in WTP. On the basis of this analysis, the hypothesis H2 is rejected.
Preliminary result 2: There is no significant difference in mean willingness to pay of both
A-players and B-players between rounds where μ=5/9 and rounds where μ=6/9.
Table 5: Descriptive statistics and preliminary statistics conditioned on the different value of μ
μ = 5/9 μ = 6/9 Difference in means?
Mean WTP St. dev. Mean St. dev. P-value
A -pla y er s No quorum 74,4 26,50 73,34 27,75 0,9904 Quorum = 2 59,81 33,50 59,88 36,13 0,7764 Quorum = 3 58,06 37,08 53,33 40,35 0,6253 Quorum = 4 37,19 37,51 51,86 40,62 0,0777* Quorum = 5 48,26 44,33 46,32 46,53 0,7764 B -pla y er s No quorum 42,37 30,66 38,47 40,02 0,6176 Quorum = 2 43,09 33,40 38,23 39,76 0,3817 Quorum = 3 39,22 35,37 32,52 36,51 0,5150 Quorum = 4 46,5 39,39 23,88 29,29 0,0585* Quorum = 5 30,61 41,54 25,96 33,62 0,8490
Notes: Means and standard deviations of the WTP are given for different quorum heights. A division is made between the rounds where μ = 5/9 and where μ = 6/9. A Mann-Whitney U-test is then performed for the difference in means between the asymmetric and the symmetric payoff group, for which the p-values are given in the fifth column.
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Table 5 also gives an insight into the finding that the introduction of a quorum tends to lower the WTP for both the A-players and the B-players in both population distributions. Figure 1 gives a better overview of this result.
Note: Figure 1 provides a graphical overview of the mean WTP for the different possible quorum rules, conditional on being an A-player or a B-player and μ being 5/9 or 6/9. It is clear from the figure that the mean willingness to pay decreases as a quorum is introduced. Moreover, it seems that higher quorum heights lead to sharper decreases.
Table 6 reports the P-values for the Mann-Whitney U test for the null that the means are the same. This analysis is not conditioned on population distribution, but it is noteworthy here that such conditioning does not alter the results. For completeness, tables A4a and A4b in Appendix A.5 provides analyses with conditioning. Table 6 can be read as follows: e.g. the mean WTP for A-players when the quorum is 5 differs significantly from the mean WTP when there is no quorum (p-value: 0,0032). These results give support to my hypothesis H3b, whereas H3a cannot be verified.
0 10 20 30 40 50 60 70 80 90 100
No quorum Quorum = 2 Quorum = 3 Quorum = 4 Quorum = 5
Willingn es s to p ay to v o te
Figure 1: Adding a quorum rule results in lower willingness to pay to vote
μ=5/9, A-player μ=5/9, B-player μ=6/9, A-player μ=6/9, B-player
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Table 6: Descriptive statistics and preliminary statistics: P-values for difference in mean WTP for different quorum rules
A-players B-players Quorum height 2<Q<5 Q=2 Q=3 Q=4 Q=5 2<Q<5 Q=2 Q=3 Q=4 Q=5 No quorum 0,0001** 0,2914 0,0109** 0,0000** 0,0032** 0,2670 0,6276 0,4770 0,5390 0,0432** Quorum=2 0,5576 0,2652 0,1751 0,8009 0,6905 0,0935* Quorum=3 0,0955 0,2578 0,8941 0,2051 Quorum=4 0,9291 0,1242
Notes: This table gives an overview of the results of a Mann-Whitney U-test for the difference in mean willingness to pay for the different quorum rules, conditional on being an A-player or a B-player. The table can be read as follows: the test for the difference in mean WTP between the cases where there is no quorum and the cases where there is a quorum, can be found by looking up the cell for which the vertical axis says ‘no quorum’ and the horizontal axis says 2<Q<5. For an A-player, the p-value is 0,0001. Moreover, e.g. the p-value for the difference in means between quorum height 2 and quorum height 4 is 0,2652 for an A-player.
** Statistically significant at a 5%-level; * Statistically significant at a 10%-level
Preliminary result 3: The introduction of a quorum decreases the willingness to pay of
majority group voters. For minority group voters, this effect is only observed when the quorum height is 5.
Table 6 also provides interesting insights in the effect of different quorum heights. It is clear that for A-players, p-values for the difference in mean WTP between the case with and the case without a quorum tend to decrease as the quorum height increases. This gives support for my hypothesis H4, at least for majority group voters.
Preliminary result 4: In case there is a quorum, a higher quorum decreases the WTP of
majority group voters more than a lower quorum. For minority group voters, no significant relationship is found.
Regression results
Although the non-parametric tests performed in the previous section are informative, testing in this way has its limitations. The main drawback of this method is that not all information regarding individual actions can be used. Therefore, some OLS regression
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models were estimated using WTP as the dependent variable. Table 7 provides the regression results. Explanatory variables in specification 1 were whether subjects had been in a group with symmetric or asymmetric preference intensities, whether they were an A-player and the population distribution in a particular round. Specification 2 adds interaction variables of the dummy of being an A-player with the quorum
dummies and μ=6/9 dummy. Specification 3 and 4 control for subject characteristics like age, gender, education level, experience in economics and experience with economic experiments. In all specifications, data is treated as panel data.
The regression results confirm the findings in the non-parametric tests of section 5. People are willing to pay more if they are in group A, a difference that is highly significant. Moreover, the introduction of a quorum leads to a significant decrease in WTP for A-players as can be seen from specification 2 and 4. Having asymmetric instead of symmetric preference intensities decreases WTP, but again this difference is
insignificant. A higher quorum height has a stronger effect. Lastly, it is noteworthy to say here that personal characteristics such as age, gender and education appear to have no influence, a finding that is not in line with the previous findings in the literature (Lijphart, 1997).
Limitations
An obvious shortcoming of the analyses above lies in the number of statistically independent observations. In total, 6 groups of 9 individuals are recruited for the experiment. This results in a subject population of 54 people. This has an obvious negative effect on the power of the performed tests. Moreover, it is possible that no effect of asymmetric preference intensity is observed because of a flaw in the research design. In the asymmetric preference intensity treatment 𝜋𝐴,𝑤𝑖𝑛> 𝜋𝐵,𝑤𝑖𝑛, whereas the control group was confronted with a situation where 𝜋𝐴,𝑤𝑖𝑛= 𝜋𝐵,𝑤𝑖𝑛. Since B-players
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Table 7: The determinants of willingness to pay to cast a vote
(1) (2) (3) (4) R² = 0,1129 R² = 0,1267 R² = 0,1255 R² = 0,1403 A-player 19,52005** (3,213518) 30,33568** (7,931568) 19,33252** (3,223752) 30,381** (7,939685) μ = 6/9 -2,469038 (3,04182) -8,027175 (4,916077) -2,464177 (3,04131) -8,101247* (4,915117) Asymmetric preference intensity -6,257185
(4,21792) -6,656843 (4,23391) -4,90147 (4,501683) -5,058137 (4,566163) QH 2 -8,989627* (4,811049) 1,123673 (7,882328) -9,000045* (4,810252) ,875222 (7,881337) QH 3 -13,37852** (4,811049) -2,10895 (7,893792) -13,38893** (4,810252) -1,742484 (7,892237) QH 4 -19,90259** (4,807828) -3,428967 (8,133813) -19,90433** (4,807009) -3,086671 (8,13967) QH 5 -21,46148** (4,813625) -10,16467 (7,828676) -21,47537** (4,812844) -9,692758 (7,824885) A-player * μ = 6/9 9,463778 (6,348567) 9,60424 (6,353081) A-player * QH 2 -15,60861 (10,07138) -15,17852 (10,08006) A-player * QH 3 -17,70768* (10,09499) -18,31746* (10,10104) A-player * QH 4 -25,90237** (10,21254) -26,44155** (10,23246) A-player * QH 5 -17,67217* (10,09939) -18,47931* (10,10151) Age ,3231076 (,2323144) ,3574534 (,2363485) Male 6,178854 (4,711366) 6,612038 (4,773968) Higher education 5,725573 (9,111915) 6,268309 (9,239744) Economic experience -2,289033 (8,176169) -2,66422 (8,286491) Experimental experience -1,849188 (7,853792) -,9356693 (7,968322) N 540 540 540 540
Notes: dependent variable: mean WTP. The table presents the coefficients from OLS regressions, where all regressions control for individual fixed effects. ‘A-player’ takes the value of 1 if the player was in group A. ‘μ = 6/9’ takes the value of 1 if μ=6/9. ‘Asymmetric preferences’ takes the value of 1 if benefits where asymmetric (𝜋𝐴,𝑤𝑖𝑛 = 600 points, 𝜋𝐵,𝑤𝑖𝑛 = 400 points). The dummy variables QH2, QH3, QH4 and QH5 indicate that a quorum rule was in place, with the height of the quorum being 2, 3, 4 or 5 respectively. Interaction dummies are added for the variables ‘A-player’ and ‘μ = 6/9’, QH2, QH3, QH4 and QH5. ‘Male’ takes the value 1 for male participants. ‘Higher education’ takes the value 1 if a participant had a highest obtained degree of at least ‘university of applied sciences (Dutch: HBO). ‘Economic experience’ takes the value 1 if the participant had a background study in economics. ‘Experimental experience’ takes the value 1 if the participant had participated in economic experiments before at least 5 times. ** Statistically significant at a 5%-level; * Statistically significant at a 10%-level; Standard errors are given in parentheses.
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already had two disadvantages, both from being the ex-ante minority group and from not being the default option in case the quorum rule was not met, it might have been more logical to add a third treatment where 𝜋𝐴,𝑤𝑖𝑛< 𝜋𝐵,𝑤𝑖𝑛.
Although order effects are already controlled for in the experiment by reversing the order of the rounds between groups, it is possible that a learning effect is present. If people change their behavior as the experiment progresses, this would influence the results. Therefore, several regressions are estimated excluding the results from the first, second and third round. This analysis does not provide evidence that there is a learning effect. For a full overview, see Table A5 in Appendix A.5.
Lastly, a limitation of the research is the fact that participants are recruited amongst the friends and family of the author. This implies that most of the subjects knew each other beforehand. For an experiment like the one reported in this game, we know that a high level of group identification might bias the results towards
cooperation (Schram & Sonnemans, 1996). Specifically in this experimental design, this bias would then show up as a higher willingness to pay to vote regardless of the
circumstances in that round (e.g. whether there was a quorum). The author tried to prevent that people who knew each other relatively well before the experiment, ended up in the same experiment session. Moreover, given that the subjects knew the
experimenter, the likelihood that an experimenter effect was in place is high. Although the author tried to prevent this by promising that per session one of the subjects would get a monetary payoff, all of the chosen participants rejected the payoff. If these subjects had already decided beforehand that they would not accept the monetary payoff, their motivation could have been solely to help the experimenter. When the author
confronted some of the subjects after the experiment with this possibility, nobody indicated that he or she was not driven by the goal of accumulating as much points as possible.
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6. Conclusion
The aim of this thesis is to examine the effect of quorum rules on voter turnout, specifically in situations where two rival groups have a different preference intensity. From the literature, there is a big body of evidence both theoretically and empirically that a negative relationship is present between the presence of a quorum rule and voter turnout. An interesting new direction of research, started by Aguiar-Conraria et al, (2013) and Hizen (2015), tries to examine this effect in an experimental way. This thesis builds on this literature and more specifically on these two papers, both by replicating some previous findings and by introducing asymmetric preference intensities so that some real life situations are more closely mirrored.
The author is able to replicate two previous findings from Aguiar-Conraria et al, (2013) and Hizen (2015): introducing a quorum rule decreases the likelihood that a person will vote, and higher quorum rules lead to a bigger effect. Unfortunately, this thesis is unable to find any significant difference of asymmetric preference intensity compared to symmetric preference intensity. This might be due to problems with the recruitment of participants. Subjects were recruited amongst the family and friends of the author, which limits the number of subjects to 54 subjects. Moreover, it is hard to say to which extent these subjects were influenced by the experimenter effect.
Taking the limitations of the research into account, it is fair to say that this thesis adds extra evidence to the finding that quorum rules have a negative effect on voter turnout. Future research should focus on ways to overcome this negative effect, for example by communication. Another possible research direction is to look at what the effect is of showing real-life voter turnout percentages during election days, which might lead people to update their beliefs about the outcome percentage. This happened during the referendum on the 6th of 2016 in the Netherlands, as Dutch television
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problematic, as it gives people the possibility to behave more strategically in their
decision whether or not to vote. As we have seen in this thesis, strategic voting behavior might lead to an outcome that is not a fair representation of the preferences of a
population. Lastly, future experimental evidence might focus more on the ways people update their beliefs, something that is explicitly ignored throughout this thesis.
However, it is realistic to argue that people update their beliefs, and it would be interesting to see in which ways this process influences voter turnout.
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Reference list
Aguiar-Conraria, L., & Magalhães, P. (2010). Referendum design, quorum rules and turnout. Public Choice(144(1-2)), 63-81.
Aguiar-Conraria, L., Magalhães, P., & Vanberg , C. A. (2013). Experimental evidence that quorum rules discourage turnout and promote election boycotts.
Experimental Economics, 1-24.
Allen Jr., J. (2005, July 1). Cardinal Ruini's victory; low voter turnout for in vitro
referendum is ascribed to the church's political muscle in Italy. National Catholic
Reporter. Retrieved June 14, 2016, from
http://www.thefreelibrary.com/Cardinal+Ruini's+victory%3B+low+voter+turnout +for+in+vitro+referendum...-a0134008198
Coate, S., Conlin, M., & Moro, A. (2008). The performance of pivotal-voter models in small-scale elections: Evidence from Texas liquor referenda. Journal of Public
Economics(92(3)), 582-596.
Côrte-Real, P., & Pereira, P. (2004). The voter who wasn’t there: referenda, representation and abstention. Social Choice and Welfare(22(2)), 349-369.
Downs, A. (1957). An economic theory of political action in a democracy. The journal of
political economy, 135-150.
Ferejohn, J. A., & Fiorina, M. P. (1974). The paradox of not voting: A decision theoretic analysis. American political science review, 525-536.
Fishburn, P., & Brams , S. (1983). Paradoxes of preferential voting. Mathematics
Magazine(56(4)), 207-214.
Geys, B. (2006a). Explaining voter turnout: A review of aggregate-level research.
35
Geys, B. (2006b). Rational’theories of voter turnout: a review. Political Studies
Review(4(1)), 16-35.
Goodin, R. E., & Roberts, K. W. (1975). The Ethical Voter. . The American Political Science
Review(69(3)), 926-928.
Herrera, H., & Mattozzi, A. (2010). Quorum and turnout in referenda. Journal of the
European Economic Association(8(4)), 838-871.
Hizen, Y. (2015). A referendum experiment with participation quorums. (No.
SDES-2015-6) Kochi University of Technology, School of Economics and Management.
Hizen, Y., & Shinmyo, M. (2011). Imposing a turnout threshold in referendums. Public
Choice(148(3-4)), 491-503.
Ladner, A., & Milner, H. (1999). Do voters turn out more under proportional than majoritarian systems? The evidence from Swiss communal elections. Electoral
Studies(18(2)), 235-250.
Laruelle, A., & Valenciano, F. (2011). Majorities with a quorum. Journal of Theoretical
Politics(23(2)), 241-259.
Levine, D., & Palfrey, T. (2007). The paradox of voter participation? A laboratory study.
American political science Review(101(01)), 143-158.
Lijphart, A. (1997). Unequal participation: Democracy's unresolved dilemma. American
political science review(91(01)), 1-14.
Palfrey, T., & Rosenthal, H. (1985). Voter participation and strategic uncertainty.
36
Reif, K., & Schmitt, H. (1980). Nine second‐order national elections – A conceptual framework for the analysis of European election results. European journal of
political research(8(1)), 3-44.
Riker, W. H., & Ordeshook, P. C. (1968). A Theory of the Calculus of Voting. American
political science review(62(01)), 25-42.
Schram, A., & Sonnemans, J. (1996). Voter turnout as a participation game: An
experimental investigation. International Journal of Game Theory(25(3)), 385-406.
Uleri, P. V. (2002). On referendum voting in Italy: YES, NO or non–vote? How Italian parties learned to control referendums. European Journal of Political Research(41(6)), 863-883.
Zwart, S. (2010). Ensuring a representative referendum outcome: the daunting task of setting the quorum right. Social Choice and Welfare(34(4)), 643-677.
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Appendix A.1: Derivation of probabilities of being pivotal
The tables A1 a-e provide an insight in the way the probabilities of being pivotal are calculated. Black squares indicate a win for group A, white squares indicate a win for group B and grey cells indicate a tie. The numbers in the cells indicate the impact of voting compared to abstaining. The first number indicates the increase or decrease in the probability of a win seen from the perspective of an A-player, the second number does so for a B-player. E.g. in table A1-a player i faces a situation where 3 people vote B and 4 people vote A. If player i has preference A, he cannot increase the chance of winning the vote, so the first number is 0. If player i has preference B, he can increase the chance of winning the vote by 50%, namely shifting the outcome from a sure loss to a tie.
Therefore, the second number is 0,5.
Based on this reasoning, the expected increase in the probability that group A (or B) earns 𝜋𝐴 (or 𝜋𝐵) instead of 0 if an A-player (B-player) i votes is can be calculated. As a benchmark case, we consider the situation where there is no quorum rule first. A person can be pivotal in two ways: by voting he either achieves a win instead of a tie or a tie instead of a loss for his group. Therefore, an A-player’s belief that he changes the
outcome of the election is based on the belief he has of the probabilities 𝜌(𝜐𝐴, 𝜐𝐵) for the cases where 𝜐𝐴 = 𝜐𝐵20 and 𝜐𝐴− 1 = 𝜐𝐵21. Remember that the expected value of a tie is 50% of either 𝜋𝐴,𝑤𝑖𝑛 or 𝜋𝐵,𝑤𝑖𝑛. This means that if a person by voting turns a tie into a win for his group, he will double the probability of having the benefit from 50% to 100%. If a person by voting turns a loss into a tie for his group, he will change the probability of having that benefit from 0% to 50%. Summarizing, a person’s belief about his
probability of being pivotal by voting is equal to all cases where 𝜐𝐴 = 𝜐𝐵 and 𝜐𝐴− 1 = 𝜐𝐵. In all these cases, voting increases the probability of winning the election by
20 If 𝜐
𝐴= 𝜐𝐵, voting is pivotal for an A-player as it changes the outcome from a tie into a win for group A.
21 If 𝜐
𝐴− 1 = 𝜐𝐵, voting is pivotal for an A-player as it changes the outcome from a loss into a tie for group
38
50%. Therefore, the expected increase in the probability that A earns 𝜋𝐴,𝑤𝑖𝑛 instead of 0 if A-player i votes is:
1 2 𝜌(0,0) + 1 2 𝜌(1,1) + 1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(0,1) + 1 2 𝜌(1,2) + 1 2 𝜌(2,3) + 1 2 𝜌(3,4) (eq. 3) , or alternatively: 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=0 + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=0 (eq.4)
Following this logic, the expected increase in the probability that B earns 𝜋𝐵,𝑤𝑖𝑛 instead of 0 if a B-player i votes is:
1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=0 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=0 (eq. 5)
We now consider the cases where a quorum rule is in place. The existence of a quorum rule that has “A” as default option changes the probabilities of being pivotal. Starting with the case where the quorum height is 2, two things now differ compared to the case without a quorum rule for A-players: they can now be decisive by voting in an
unfavorable way if 𝜐𝐴 = 0 and 𝜐𝐵 = 1 (a vote by player A now reduces the probability that “A” wins from 100% to 50%) and it is no longer possible for an A-player to be pivotal if 𝜐𝐴 = 0 and 𝜐𝐵= 0. Therefore, the expected increase in the probability that A earns 𝜋𝐴,𝑤𝑖𝑛 instead of 0 if A-player i votes is:
1 2 𝜌(1,1) + 1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(1,2) + 1 2 𝜌(2,3) + 1 2 𝜌(3,4) − 1 2 𝜌(0,1) (eq. 6) , or alternatively:
39 1 2 ∑ 𝜌(𝜐, 𝜐) + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) − 1 2 𝜌(0,1) 3 𝜐=1 4 𝜐=1 (eq. 7)
For B-players, voting has no impact on the chance of winning the vote for group B if 𝜐𝐴 = 0 and 𝜐𝐵 = 1 in the absence of a quorum. In the new situation, voting increases the chance of winning the election from 0% to 100%. Therefore, the expected increase in the probability that B earns 𝜋𝐵,𝑤𝑖𝑛 instead of 0 if a B-player i votes is:
1 2 𝜌(1,1) + 1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(1,0) + 1 2 𝜌(2,1) + 1 2 𝜌(3,2) + 1 2 𝜌(4,3) + 𝜌(0,1) (eq. 8) , or alternatively: 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=1 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=0 + 𝜌(0,1) (eq. 9)
The following holds for the case with quorum height 3 compared to the case where the quorum height is 2. If 𝜐𝐴 = 1 and 𝜐𝐵 = 1, a vote by player A does not change the probability of winning: not voting means that the quorum is not reached implying a win by group A, voting means that group A wins. So in this case voting is not pivotal. If 𝜐𝐴 = 0 and 𝜐𝐵 = 1, voting is not pivotal, because in both cases the quorum is not met implying a victory by group A. Instead, it is now possible to be pivotal if 𝜐𝐴 = 0 and 𝜐𝐵 = 2. In this case voting changes the outcome from a sure win by A (because the quorum is not met) into a sure loss by A. Therefore, the expected increase in the probability that A earns 𝜋𝐴,𝑤𝑖𝑛 instead of 0 if A-player i votes is:
1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(1,2) + 1 2 𝜌(2,3) + 1 2 𝜌(3,4) − 1 𝜌(0,2) (eq. 10) , or alternatively:
40 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=2 + 1 2 ∑ 𝜌(𝜐, 𝜐 + 1) 3 𝜐=1 − 𝜌(0,2) (eq.11)
For B-players things change as well, compared to the case with quorum height 2. If 𝜐𝐴 = 1 and 𝜐𝐵 = 1, voting increases the chance of winning the election from 0% to 100%. The same holds for the case where 𝜐𝐴 = 0 and 𝜐𝐵 = 2. Therefore, the expected increase in the probability that B earns 𝜋𝐵,𝑤𝑖𝑛 instead of 0 if a B-player i votes is:
1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(2,1) + 1 2 𝜌(3,2) + 1 2 𝜌(4,3) + 𝜌(1,1) + 𝜌(0,2) (eq. 12) , or alternatively: 1 2 ∑ 𝜌(𝜐, 𝜐) 4 𝜐=2 + 1 2 ∑ 𝜌(𝜐 + 1, 𝜐) 3 𝜐=1 + 𝜌(1,1) + 𝜌(0,2) (eq. 13)
For the case with quorum height 4 compared to the case where the quorum height is 3, the following is true. If 𝜐𝐴 = 1 and 𝜐𝐵 = 2, a vote by player A changes the outcome of the vote from a sure win into a tie, and therefore the probability of winning decreases from 100% to 50%. Moreover, voting is not pivotal in case 𝜐𝐴 = 1 and 𝜐𝐵 = 1, or in case 𝜐𝐴 = 0 and 𝜐𝐵= 2. Instead, it is now possible to be pivotal if 𝜐𝐴 = 0 and 𝜐𝐵 = 3. In this case voting changes the outcome from a sure win by A (because the quorum is not met) into a sure loss by A. Therefore, the expected increase in the probability that A earns 𝜋𝐴,𝑤𝑖𝑛 instead of 0 if A-player i votes is:
1 2 𝜌(2,2) + + 1 2 𝜌(3,3) + 1 2 𝜌(4,4) + 1 2 𝜌(2,3) + 1 2 𝜌(3,4) − 1 2 𝜌(1,2) − 1 𝜌(0,3) (eq. 14) , or alternatively:
