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10 September 19

Mardi 8 octobre, 12:00, salle C129 (Lamsade-LEDA seminar)

Clemens Puppe

Title : Impact and Participation: A Field Experiment on Voting over Resource Allocation

Abstract : (joint work with Jana Rollmann)

With their work on rational choice theory and the calculus of voting, Downs (1957), Tullock (1967) as well as Riker and Ordeshook (1968) provide a decision-theoretic model of participa- tion in elections. The question these models face is why a rational individual would vote if the return from voting is often outweighed by the costs that emerge in the voting process. Even if the costs to participate in an election are rather small, the probability that a single vote affects the outcome is almost zero in large electorates. The rational choice model predicts turnout levels that are far below the actual participation rates in elections. This discrepancy is referred to as the paradox of voting.

Palfrey and Rosenthal (1983, 1985) and Ledyard (1984) formulate the pivotal voter model in a game-theoretic approach. In the participation game, two groups of subjects prefer either one or another candidate. Each subject may vote at a certain cost for his preferred candidate (voting for the opponent is strictly dominated in the two-candidate case) or abstain. The candidate that receives the majority of votes wins. In their equilibrium analysis, Palfrey and Rosenthal (1983) show that there exist not only low turnout levels but also equilibria with substantial turnout when participants face identical costs and complete information on the distribution of preferences. Ledyard (1984) endogenizes pivotality and highlights that the participation decision of all subjects is made simultaneously. The model implements uncertainty about preferences as well as costs, and turnout levels lie somewhere in-between zero and full participation in equilibrium. Building on Ledyard (1984), Palfrey and Rosenthal (1985) implement uncertainty about the individual voting costs and show that this lack of information causes individuals to abstain even though participation would have been optimal under full information in large electorates. These authors’ participation game is used widely in the literature for testing the pivotal voter model especially in lab experiments. In particular, the vast majority of both the theoretical foundations and the empirical tests of the pivotal voter model has assumed two alternatives or candidates and simple majority voting as the decision rule.

We contribute to the literature by studying the pivotal voter model in the context of a simple resource allocation problem with single-peaked preferences. In this setting, an alternative is given by the fraction of a budget to be used for a given public project, with the understanding that the non-used budget will be spent for some other purpose. A ‘vote’ can thus be identified with a real number between 0 and 100 (percent). In our analysis, we concentrate on two ‘focal’ voting rules: the mean and the median rule.

Under the mean rule, the social outcome is given as the sum of all votes divided by the number of participants. By contrast, the median rule selects the middle vote if the number of participants is odd or the average of the two middle votes if the number of participants is even. We assume that voting is costly and, for simplicity, that participation costs are identical for all subjects. In our theoretical model, we assume single-peaked preferences, sometimes also under the additional assumption that preferences are symmetric around the peak (‘Euclidean’ preferences).

Without participation costs, it is well-known that (i) truth-telling is a weakly dominant strategy under the median rule (Moulin (1980)), and (ii) there is a unique Nash equilibrium under the mean rule with complete information (Renault and Trannoy (2005)). By contrast, the game-theoretic analysis of both the median and the mean rule becomes quite complex if voting is costly. In particular, in Mu ̈ller et al. (2019) we show that the corresponding voting games in general have multiple equilibria, frequently with different sets of participants, both under complete and incomplete information.1

Due to the existence of multiple equilibria and the complexity of the task to determine the equilibria, we hypothesize in this study that the individual participation decision is in practice not driven by equilibrium considerations but by other factors: the impact of a vote on the social outcome (or the belief about the impact) and risk attitude. We measure the impactby the length of the option set, i.e. the distance between the interval boundaries, which are achieved by the minimal and maximal value of a subject’s vote. While the impact of a vote on the social outcome under the mean rule is small for large electorates, it is certain and always greater than zero. By contrast, the impact under the median rule has large variance. We theoretically analyze the individual impact on the social outcome for different preference distributions under the mean and the median rule. For some preference distributions theexpected impact on the social outcome is larger under the median rule than under the mean rule. This raises the question whether the difference in the individual impact has effects on the participation rates under different voting rules.2

In a field experiment we test whether, and how, voter turnout varies with the voting rule. To this end, we conduct an election using either the mean or the median rule to determine the allocation of a donation on two public projects on the university campus. Our main focus lies on the voter turnout under either rule, and on the role of impact and risk attitude. Subsequent to the vote, we implement a survey in order to elicit beliefs about the allocation result, about the participation rate and about the real impact of the individual’s vote on the social outcome. Additionally, we ask for strategic voting behavior and elicit risk preferences via a standard lottery choice procedure.

The mean rule is in many ways ‘simpler’ than the median rule. In particular, the individual impact can be computed without knowledge of the votes of the other participants (it depends only on the number of the participants). By contrast, the impact under the median rule depends on the distribution of the votes of all other participants. Moreover, with an odd number of participants, ex-post generically only one vote determines the outcome under the median rule. We therefore have the following hypothesis:

(H1) The belief about the real impact is higher under the mean rule as compared to the median rule.

Related to the previous point, while the impact under the mean rule is certain and always strictly positive, the impact is uncertain under the median rule and its expectation can be smaller or larger than the corresponding impact under mean rule with the same number of participants.3 We thus hypothesize a ‘selection effect,’ i.e. that the participants under the mean rule are more risk averse.

(H2) Participants are more risk averse in mean voting as compared to median voting.

Together with standard assumptions about individual preferences, in particular about risk preferences, we thus have the following hypothesis about voter turnout:

(H3) The actual number of participants is higher under the mean rule as compared to the median rule.

Our data show that the average individual real impact on the social outcome is significantly lower under the mean rule. Nevertheless, this difference does not occur for the participants’ beliefs about their impact. We find a slightly higher belief about the real impact for mean participants, but the difference is not statistically significant, which means our data do not support H1. Under both rules, subjects overestimate their real impact. We do find a selection effect in support of H2: the participants are more risk averse in mean voting which implies that more risk averse subjects are less likely to participate in median voting. Regarding voter turnout, we find weak evidence that the participation rate over all groups is higher under the mean rule, on average 29.0% as compared to 25.9% under the median rule, which supports H3.