Voluntary voting: Costs and benefits (original) (raw)

Introduction

Should voting be a right or a duty? Faced with declining turnouts in elections, many countries have concluded that voting should be a duty—a requirement to be enforced by sanction—rather than a right.1 On a smaller scale, voting is considered a duty in most committees as well. Attendance is usually required, and members are encouraged to “make their voice heard” through actually casting votes rather than abstaining. In some committees, abstentions count as “no” votes.

Advocates of voting as a duty offer several arguments in support. First, high turnout may confer legitimacy to those elected. Second, compulsory voting may give greater voice to poorer sections of society who would otherwise not participate [17]. Third, by aggregating the opinions of more individuals, compulsory voting may have informational benefits. In this paper, we do not directly address the first two arguments. Rather we examine the right versus duty question on informational grounds. Which regime produces better decisions?

The analysis of voting on informational grounds begins with Condorcetʼs celebrated Jury Theorem which states that, when voters have common interests but differential information, sincere voting under majority rule produces the correct outcome in large elections. There are two key components to the theorem. First, it postulates that voting is sincere—that is, voters vote solely according to their private information. Second, that voter turnout is high.

Recent work shows, however, that sincerity is inconsistent with rationality—it is typically not an equilibrium to vote sincerely. The reason is that rational voters will make inferences about othersʼ information and, as a result, will have the incentive to vote against their own private information [2]. Equilibrium voting behavior involves the use of mixed strategies—with positive probability, voters vote against their private information. Surprisingly, this does not overturn the conclusion of the Jury Theorem: In large elections, there exist equilibria in which the correct candidate is always chosen despite insincere voting [8].2 These convergence results, while powerful, rest on equilibrium behavior that may be deemed implausible. Voting is not only insincere but random. Moreover, some voters have negative returns to voting—they would rather not vote at all—this is a manifestation of the “swing voterʼs curse” [7].

These generalizations of the Jury Theorem rely on the assumption that voter turnout is high. Indeed it is implicitly assumed that voting is compulsory, so all eligible voters show up and vote for one of the two alternatives. When voting is voluntary and costly, however, there is reason to doubt that voters will turn out in large enough numbers to guarantee correct choices. Indeed, even if there were no swing voterʼs curse, rational voters would correctly realize that a single vote is unlikely to affect the outcome, so there is little benefit to voting. This is the “paradox of not voting” [6].

In this paper, we revisit the classic Condorcet Jury model but relax the assumption that voting is compulsory (i.e., it is not possible to abstain). We study two variants of the model: in one, voting is costless but abstention is possible; in the other, voters incur private costs of voting and may avoid these by abstaining. Voters in our model are fully rational, so the twin problems of strategic voting and the paradox of not voting are present. Throughout, we compare institutions on the basis of ex ante expected utilitarian welfare inclusive of voting costs (if any). Because of the common interest specification in Condorcetʼs model, this is just the ex ante probability of a correct decision less voting costs.

For our analysis, we adopt the Poisson model introduced by Myerson [21], [22], [23]. In this model, the size of the electorate is random. As Myerson [21] has demonstrated, in large elections, the qualitative predictions of Poisson voting models are identical to those with a fixed electorate. The analysis is, however, much simpler.

We find:

To summarize, our results point to the advantages of voting as a right over voting as duty. Welfare is higher. Moreover, equilibrium behavior under the voluntary scheme is simple and intuitive. Strategic behavior is no longer at odds with sincerity.

The following example may be used to illustrate our main results.3 Three voters must decide between two candidates, A and B. Voters have equal priors over who is the better candidate but receive private signals. When A is best, each voter receives an a signal for sure. When B is best, however, a voter receives a b signal only with probability s strictly between 12 and 1. Notice that a single b signal indicates that B is the best candidate for sure.

First, suppose that all voters participate and vote sincerely. While this leads to the correct outcome when A is best, it produces errors when B is best. The most likely error occurs when two voters receive a signals and only one receives a b signal (this is more likely than the event that all three receive a signals). The situation improves if a voters were to participate at slightly lower rates. The first order effect of this change is to reduce the errors when B is best without affecting the error rate when A is best. Thus, full participation with sincere voting is not optimal.

Next, suppose that voting is compulsory. If the other two voters voted sincerely, a voter with an a signal would correctly reason that she is decisive only when the vote is split. But this can only happen if one of the other voters has a b signal. And since even one b signal predicts perfectly that B is the better candidate, it is optimal to vote for B. Therefore, such an a voter would be well-advised to vote insincerely.

In contrast, under voluntary voting, voters with a signals would come to the polls less often than those with b signals. This is because b voters are certain that B is the best candidate while a voters are unsure. How should an a voter vote if she does decide to come to the polls? She is decisive in two cases—on a split vote when B is best and when she is the only voter and A is best. If the participation rates are such that an a voter rates the latter case as more likely, she would vote sincerely, that is, for A. Our results will show that the participation rates are indeed such that they induce sincere voting. Finally, since full participation with sincere voting is not optimal, this reduction in participation may have the beneficial effect of also reducing the error rate. Indeed, in equilibrium, we show that it minimizes the error rate when voting is costless.

Early work on the Condorcet Jury Theorem viewed it as a purely statistical phenomenon—an expression of the law of large numbers. Perhaps this was the way that Condorcet himself viewed it. Game theoretic analyses of the Jury Theorem originate in the work of Austen-Smith and Banks [2]. They show that sincere voting is generally not consistent with equilibrium behavior.

Feddersen and Pesendorfer [8] derive the (“insincere”) equilibria of the voting games specified above—these involve mixed strategies—and then study their limiting properties. They show that, despite the fact that sincere voting is not an equilibrium, large elections still aggregate information correctly. Using a mechanism design approach, Costinot and Kartik [5] investigate optimal voting rules under a variety of behavioral assumptions including strategic and sincere voting. They show that there is a unique voting rule, independent of voter behavior, that aggregates information. McLennan [19] views such voting games, in the abstract, as games of common interest and argues on that basis that there are always Pareto efficient equilibria of such games. Apart from the fact that voting is voluntary, and perhaps costly, our basic setting is the same as that in these papers—there are two candidates, voters have common interests but differential information (sometimes referred to as a setting with “common values”).

A separate strand of the literature is concerned with costly voting and endogenous participation but in settings in which voter preferences are diverse (sometimes referred to as “private values”). Palfrey and Rosenthal [26] consider costly voting with privately known costs but where preferences over outcomes are commonly known (see [15] and [16] for models in which preferences are also privately known). These papers are interested in formalizing Downsʼ paradox of not voting. Börgers [4] studies majority rule in a costly voting model with private values—that is, with diverse rather than common preferences. He compares voluntary and compulsory voting and argues that individual decisions to vote or not do not properly take into account a “pivot externality”—the casting of a single vote decreases the value of voting for others. As a result, participation rates are too high relative to the optimum and a law that makes voting compulsory would only worsen matters. Krasa and Polborn [13] show that the externality identified by Börgersʼ is sensitive to his assumption that the prior distribution of voter preferences is 50–50. With unequal priors, under some conditions, the externality goes in the opposite direction and there are social benefits to encouraging increased turnout via fines for not voting.

Ghosal and Lockwood [10] reexamine Börgersʼ result when voters have more general preferences—including common values—and show that it is sensitive to the private values assumption. They show that, under some conditions, compulsory voting may be welfare superior to voluntary voting even in a pure common values setting. This, however, relies on there being a small number of voters. (Our Proposition 10 shows the reverse is true in large elections.) We discuss the connection between their findings and ours in more detail below. Finally, Feddersen and Pesendorfer [7] examine abstention in a common values model when voting is costless. The number of voters is random, some are informed of the state, while others have no information whatsoever. Abstention arises in their model as a result of the aforementioned swing voterʼs curse—in equilibrium, a fraction of the uninformed voters do not participate. McMurray [20] studies a similar model in which the information that voters have differs in quality. In large elections, a positive fraction of voters with imprecise information continue to vote even though there are voters with more precise information.

Much of this work postulates a fixed and commonly known population of voters. Myerson [21], [22], [23] argues that precise knowledge of the number of eligible voters is an idealization at best, and suggests an alternative model in which the size of the electorate is a Poisson random variable. This approach has the important advantage of considerably simplifying the analysis of pivotal events. Myerson illustrates this by deriving the mixed equilibrium for the majority rule in large elections (in a setting where signal precisions are asymmetric). He then studies its limiting properties as the number of expected voters increases, exhibiting information aggregation results parallel to those derived in the known population models. We also find it convenient to adopt Myersonʼs Poisson game technology but are able to show that there is a sincere voting equilibrium for any (expected) size electorate.

Feddersen and Pesendorfer [9] use the Poisson framework to study abstention when voting is costless but preferences are diverse—voters differ in the intensity of their preferences, given the state. In large elections, a positive fraction of the voters abstain even though voting is costless. Nevertheless, information aggregates. Our model and results differs from theirs in three respects. First, we allow for costly voting and so, in large elections, the fraction of voters who abstain is typically large—only those with low costs turn out to vote. We show that information aggregates in this environment nevertheless. Second, the Feddersen and Pesendorfer results may be interpreted as saying that whether or not abstention is allowed or not is irrelevant—in large elections, information aggregates under both institutions. We argue that the abstention option actually results in higher welfare, and this is true whether or not there are voting costs. Finally, we show that with costly voting, equilibrium voting behavior is particularly simple. All those who vote do so sincerely.

Herrera and Morelli [11] also use a diverse preference Poisson model to compare turnout rates in proportional and winner-take-all parliamentary elections.

The paper is organized as follows. In Section 2 we introduce the basic environment and Myersonʼs Poisson model. As a benchmark, in Section 3 we first consider the model with compulsory voting and establish (a) even if voting is sincere, full participation is not optimal; and (b) under full participation, sincere voting is not an equilibrium. In Section 4, we introduce the model with voluntary voting. We show that all equilibria entail sincere voting and positive participation. Section 5 compares the performance of voluntary and compulsory voting schemes when voting is costless. Our main finding is that voluntary voting produces the correct outcome more often than compulsory voting and hence is preferred. Section 6 studies the limiting properties of the equilibria when voting is costly. We show that, despite the “paradox of not voting,” in the limit, information fully aggregates and the correct candidate is elected with probability one under voluntary voting. Compulsory voting also produces the correct outcome in the limit, but at higher cost; hence, voluntary voting is again superior.

Omitted proofs are collected in Appendix A Equilibrium, Appendix B Large elections, Appendix C Uniqueness.

Section snippets

The model

There are two candidates, named A and B, who are competing in an election decided by majority voting, with ties decided by the toss of a fair coin. There are two equally likely states of nature, α and β.4 Candidate A is the better choice in state α while candidate B is the better choice in state β. Specifically, in state α the payoff of any citizen is 1 if A is elected and 0 if B is

Compulsory voting

We begin by examining equilibrium voting behavior under compulsory voting. By compulsory voting we mean that each voter must cast a vote for either A or B. While many countries have compulsory voting laws, these can, at best, only compel voters to come to the polls; under most voting systems, they are still free to cast “spoilt” or “blank” ballots.7 But this is not the intent of compulsory voting laws—it only highlights the conflict

Voluntary voting

In this section, we replace the compulsory voting assumption with that of voluntary voting. We now allow for the possibility of abstention—every citizen need not vote. In effect, this gives voters a third option. A second aspect of our model concerns whether or not voters incur costs of voting. We study two separate models. In the costless voting model, voters incur no costs of going to the polls. In the costly voting model, they have heterogeneous costs of going to the polls, which can be

Welfare

The informational comparison between voluntary and compulsory voting is influenced by the following trade-off. Under voluntary voting, (i) not everyone votes; but (ii) everyone who votes, does so sincerely. On the other hand, under compulsory voting, (i) everyone votes; but (ii) voters do not vote sincerely (see Proposition 2). Put another way, under voluntary voting, there is less information provided but it is accurate. Under compulsory voting, there is more information provided but it is

Large elections

The previous section showed that when voting is costless, voluntary voting is superior to compulsory voting. Precisely, for n⩾n(r,s), the ex ante probability of a correct decision under costless voluntary voting, denoted by WnV(0) is strictly greater than the same probability under compulsory voting, denoted by WnC. The same is true for costly voting when the distribution of voting costs is close to zero. Precisely, if we denote by WnV(F) the ex ante probability of a correct decision under

Partisans

Under compulsory voting, asymmetry of signals in our model (r≠s) leads voters to vote insincerely (Proposition 2). Voluntary voting, by permitting voters to express preferences with their feet as well as at the polls, restores the incentives to vote sincerely (Proposition 4). Other kinds of asymmetry have the same effect under compulsory voting. For instance, introducing partisans—voters favoring one candidate (say A) regardless of the state—also destroys the incentives to vote sincerely under

Conclusions

In situations where informed voters have a common interest in making the right decision, we have shown that mandatory voting requirements and the elimination or suppression of the option to abstain are positively harmful. On informational grounds, voting should be a right rather than a duty. Many situations involve common interests: In committee-like settings there are votes by corporate boards of directors with a shared interest in the profitability of the company, votes for hiring and

Cited by (41)

2014, Games and Economic Behavior
The validity of Condorcet's assumption was first questioned by Austen-Smith and Banks (1996) who showed that if voting is compulsory, then rational voters may have incentives to vote strategically, i.e., sometimes voting against their private information (see also Feddersen and Pesendorfer, 1996, 1997, 1998; Myerson, 1998). On the other hand, Krishna and Morgan (2012, henceforth K–M) have recently shown that if voting is voluntary so that abstention is possible, then in the same common preference, Condorcet jury model, sincere voting, i.e., voting in accordance with one's private information, is always rational when voters face private costs of voting. In K–M's voluntary voting framework, participation decisions become strategic and will depend on the private costs of voting (if there are such costs).2 View all citing articles on Scopus

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