Would letting people vote for multiple candidates yield policy moderation?

We investigate whether letting people vote for multiple candidates would yield policy moderation. We do so in a setting that takes three key features of elections into account, namely, strategic voting, endogenous candidacy and policy motivation on the part of the candidates. We consider two classes of voting rules. One class consists of the voting rules where each voter casts several equally-weighed votes for the different candidates. The other class consists of the voting rules where each voter rank-orders the candidates. We identify conditions under which these voting rules yield policy moderation. We also show that these voting rules may yield policy extremism instead of policy moderation if one (or several) of the conditions is not satisfied! Finally, we find that amongst these voting rules the extent of policy moderation is maximal under the Borda Count if we consider only equilibria where all candidates are serious contenders. However, this result does not carry over to spoiler equilibria, where Approval Voting can yield more moderate policy outcomes than the Borda Count.     

The welfare consequences of strategic behaviour under approval and plurality voting

This paper studies the welfare consequences of strategic behaviour under approval and plurality voting by comparing the utilitarian efficiencies obtained in simulated voting under two behavioural assumptions: expected utility-maximising behaviour and sincere behaviour. Under approval voting utilitarian efficiency is relatively high irrespective of the behavioural assumption, and under the plurality rule strategic voting significantly increases utilitarian efficiency.     

Voting by Successive Elimination and Strategic Candidacy

We study the impact of strategic choices of self-interested candidates of whether or not to enter an election. We focus on strategic candidacy in the context of the tree and binary voting procedures used by small groups such as committees. We offer a comprehensive analysis for the special but important case of voting by successive elimination. Strategic candidacy slightly enlarges the set of candidates that can be equilibrium outcomes relative to the traditional analysis which takes the set of candidates as fixed. Pareto-dominated candidates can be elected in equilibrium under voting by successive elimination when strategic candidacy is considered, in contrast with a fixed set of candidates. Journal of Economic Litterature Classification Numbers: D71, D72.     

Approval voting reconsidered

Summary. The merit of approval voting has been widely discussed in the past 25 years. The distinct property of this rule is the extent of flexibility it allows; any voter can approve as many alternatives/candidates as he wishes. Nevertheless, this advantage is the very reason for two drawbacks of approval voting: its extreme vulnerability to majority decisiveness (Theorem 1) and its extreme vulnerability to erosion of the majority principle (Theorem 2). On the one hand, under some feasible voting strategies any majority of more than 1/2 of the voters can guarantee the selection of its most favorable candidate, regardless of the preferences of the other voters. On the other hand, under alternative voting strategies even the largest majority cannot impose its common most preferred candidate. A simultaneous resolution of the two problems is possible by restricted approval voting (RAV), a voting rule that allows partial voter flexibility by restricting the minimal and maximal number of candidates that can be approved. Our main result (Theorem 3) clarifies how the foregone flexibility in voters sovereignty mitigates the above mentioned drawbacks under sincere and insincere coordinated voting. Our findings suggest a new possible justification of a particular voting rule which is based on the significance assigned to three considerations: the advantages of voters flexibility, immunity to majority decisiveness and immunity to erosion of the majority principle. Such justification can provide a possible explanation to the prevalent use of some special cases of RAV, notably, of the plurality rule and of approval voting.Received: 8 October 2003, Revised: 17 June 2004, JEL Classification Numbers: D71, D72. Correspondence to: Shmuel NitzanWe are indebted to Steve Brams, Remzi Sanver and an anonymous referee for their very useful comments and suggestions.     

The strategic sincerity of Approval voting

We show that Approval voting need not trigger sincere behavior in equilibrium of Poisson voting games and hence might lead a strategic voter to skip a candidate preferred to his worst preferred approved candidate. We identify two main rationales for these violations of sincerity. First, if a candidate has no votes, a voter might skip him. Notwithstanding, we provide sufficient conditions on the voters’ preference intensities to remove this sort of insincerity. On the contrary, if the candidate gets a positive share of the votes, a voter might skip him solely on the basis of his ordinal preferences. This second type of insincerity is a consequence of the correlation of the candidates’ scores. The incentives for sincerity of rank scoring rules are also discussed.     

On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.     

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by their equilibria in simple voting games with Poisson population uncertainty, using new techniques for computing pivot probabilities. Best-rewarding rules like plurality voting can generate discriminatory equilibria where the voters disregard some candidate as not a serious contender, although he may be universally liked, or may be symmetric to other candidates as in the Condorcet cycle. Such discriminatory equilibria are eliminated by worst-punishing rules like negative voting, but then even a universally disliked candidate may have to be taken seriously. In simple bipolar elections, equilibria are always majoritarian and efficient under approval voting, but not other scoring rules. Journal of Economic Literature Classification: D72.     

The effect of randomized school admissions on voter participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

A live experiment on approval voting

This paper presents a large-scale experiment on the Approval Voting rule that took place during the 2002 French presidential election. We describe the experiment and its main results. The findings are as follows: (i) Such an experiment is feasible, and very well accepted by voters. (ii) The principle of approval voting is easily understood and accepted. (iii) Within the observed political context, compared to the official first-round vote, approval voting modifies the overall ranking of candidates. (iv) The candidates Le Pen and Chirac, more than the others, were able to convert approval votes into official first-round votes. JEL Classification C93, D70, D72     

Redistributive policies with heterogeneous social preferences of voters

There is growing evidence on the roles of fairness and other-regarding preferences as fundamental human motives. Call voters with fair preferences, as in Fehr and Schmidt (1999), fair-voters. By contrast, traditional political economy models are based on selfish-voters who derive utility solely from “own” payoff. In a general equilibrium model with endogenous labor supply, a mixture of fair and selfish voters choose optimal policy through majority voting. First, we show that majority voting produces a unique winner in pairwise contests over feasible policies (the Condorcet winner). Second, we show that a preference for greater fairness leads to greater redistribution. An increase in the number of fair voters can also lead to greater redistribution. Third, we show that in economies where the majority are selfish-voters, the decisive policy could be chosen by fair-voters, and vice versa. Fourth, while choosing labor supply, even fair voters behave exactly like selfish voters. We show how this apparently inconsistent behavior in different domains (voting and labor supply) can be rationalized within the model.     

On the benefits of party competition

We study the role of parties in a citizen-candidate repeated-elections model in which voters have incomplete information. We first identify a novel “party competition effect” in a setting with two opposing parties. Compared with “at large” selection of candidates, party selection makes office-holders more willing to avoid extreme ideological stands, and this benefits voters of all ideologies. We then allow for additional parties. With strategic voting, citizens benefit most when the only two parties receiving votes are more moderate. With sincere voting, even with three parties, extreme parties can thrive at the expense of a middle party; and whether most citizens prefer two or three parties varies with model parameters.     

Unidimensional median voter results in probabilistic voting models

This paper studies the policy outcomes that can be expected to occur when candidates are uncertain about voter behavior. Its analysis begins with an example that illustrates how the ‘Comaner–Hinich effect’ (i.e., the possibility of non-median outcomes) can occur under such circumstances. This example is then modified in ways which restore a median outcome. After this is done, the method of restoration is generalized to obtain a unidimensional median voter result for probabilistic voting models.     

Compulsory versus voluntary voting: An experimental study

We report on an experiment comparing compulsory and voluntary voting institutions in a voting game with common preferences. Rational choice theory predicts sharp differences in voter behavior between these two institutions. If voting is compulsory, then voters may find it rational to vote insincerely, i.e., against their private information. If voting is voluntary so that abstention is allowed, then sincere voting in accordance with a voter's private information is always rational while participation may become strategic. We find strong support for these theoretical predictions in our experimental data. Moreover, voters adapt their decisions to the voting institution in place in such a way as to make the group decision accuracy differences between the two voting institutions negligible. The latter finding may serve to rationalize the co-existence of compulsory and voluntary voting institutions in nature.     

Size approval voting

We propose a new class of voting procedures, called Size Approval Voting, according to which, the effective weight of a vote from a given individual depends on how many other candidates that individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved candidates. Then, for a given profile of individual votes, all candidates with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting procedures is characterized by a set of natural properties.     

Counterexamples on the Superiority of Approval versus Plurality

We present a simple voting environment with three candidates where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability. We also analyze the robustness of such an example to changes in the number of voters and their preferences. To conclude, we present a generic four‐candidate voting environment with the same properties.     

Non-consequentialist voting

Standard theory assumes that voters’ preferences over actions (voting) are induced by their preferences over electoral outcomes (policies, candidates). But voters may also have non-consequentialist (NC) motivations: they may care about how they vote even if it does not affect the outcome. When the likelihood of being pivotal is small, NC motivations can dominate voting behavior. To examine the prevalence of NC motivations, we design an experiment that exogenously varies the probability of being pivotal yet holds constant other features of the decision environment. We find a significant effect, consistent with at least 12.5 percent of subjects being motivated by NC concerns.     

Deliberative voting

We analyze a model of jury decision making in which jurors deliberate before casting their votes. We consider a wide range of voting institutions and show that deliberations render these equivalent with respect to the sequential equilibrium outcomes they generate. In particular, in the context of a jury setup, all voting rules excluding the two types of unanimity rules (one requiring a unanimous consensus to acquit, one requiring a unanimous consensus to convict) induce the same set of equilibria outcomes. We show the robustness of our results with respect to several restrictions on communication protocols and jurors’ strategies. Furthermore, we demonstrate that our observations extend to practically all of the voting structures commonly studied in the voting literature. The paper suggests the importance of accounting for communication in models of collective choice.     

STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.