Voting on redistribution with tax evasion

This paper analyzes voting on a linear income tax whose proceeds are redistributed lump sum to the taxpayers. Individuals can evade taxes, which leads to penalties if evasion is detected. Since preferences satisfy neither single peakedness nor single crossing, a voting equilibrium may not exist. When an equilibrium does exist, there are several possible outcomes. There may be ‘conventional’ equilibria where the rich are expropriated by the poor and middle class. There may be equilibria without full expropriation where redistribution is limited by the threat of evasion. Finally, there may be equilibria where redistribution goes from the middle class to the rich and poor.     

Inefficient committees: small elections with three alternatives

We consider small committees which have to elect one of three alternatives using the simple plurality rule. Committee members have common, state-dependent preferences and receive imprecise private signals about the state of nature prior to the election. We are interested in whether the committee decision is efficient, that is whether the probability with which the committee elects the correct alternative is higher than the probability with which one single individual alone—on behalf of the others—would. It has been shown that there exists a unique efficient equilibrium in elections with two alternatives. We show that this result does not extend to elections with more alternatives. Multiple equilibria may exist for the same committee, and there may be both efficient and inefficient ones. Informative voting may or may not be an equilibrium. Also contrary to two-alternative elections, there exist responsive equilibria in which voters vote ‘against’ their signal. As a consequence, only two alternatives receive positive expected vote shares and the outcome is inefficient.     

Implementation in perfect equilibria

This paper considers implementation when the feasible outcomes are lotteries over a finite set of alternatives. The following weak condition is sufficient for implementation in trembling hand perfect equilibria (with three or more players): if all but one player agree on which alternative is the best, this alternative is (among those that are) chosen by the social choice rule, and if all but one player agree on which alternative is the worst, this alternative is not chosen. Many interesting social choice rules that are not Nash implementable satisfy this condition. On the other hand, there are social choice rules that are implementable in Nash equilibria but not in perfect equilibria.I am grateful to Luis Corchón, Eric Maskin, William Thomson, seminar participants at Harvard and Rochester, and two anonymous referees for helpful comments and suggestions. This research was supported by grants from the Royal Swedish Academy of Sciences and the Bank of Sweden Tercentenary Foundation.     

Sophisticated voting and equilibrium refinements under plurality rule

In this paper we show in the context of voting games with plurality rule that the “perfect” equilibrium concept does not appear restrictive enough, since, independently of preferences, it can exclude at most the election of only one candidate. Furthermore, some examples show that there are “perfect” equilibria that are not “proper”. However, also some “proper” outcome is eliminated by sophisticated voting, while Mertens' stable set fully satisfies such criterium, for generic plurality games. Moreover, we highlight a weakness of the simple sophisticated voting principle. Finally, we find that, for some games, sophisticated voting (and strategic stability) does not elect the Condorcet winner, neither it respects Duverger's law, even with a large number of voters. Received: 16 March 1999/Accepted: 25 September 1999     

Probabilistic voting and platform selection in multi-party elections

The literature on stochastic voting to date has focused almost exclusively on models with only two candidates (or parties). This paper studies multiparty competition with stochastic voting. We look at two different models in which candidates aim to maximize their expected vote, as well as a model where the objective of candidates is rank minimization. The equilibria of these models are derived and characterized. We show that the properties of the equilibria are quite different from those derived in deterministic models. Furthermore, the analysis shows that deterministic voting models are not robust since the introduction of even a minute level of uncertainty leads to a drastic change in predictions. Consequently, we argue that the deterministic model provides a misleading benchmark. Stochastic models provide a much richer framework, and the nature of the uncertainty in voter choice is a key determinant of the qualtitative properties of the equilibria.The authors thank Martin Osborne and Maurice Salles for useful comments and suggestions. The first author would also like to thank the Bankard Fund for financial support.     

Limiting distributions for continuous state Markov voting models

This paper proves the existence of a stationary distribution for a class of Markov voting models. We assume that alternatives to replace the current status quo arise probabilistically, with the probability distribution at time t+1 having support set equal to the set of alternatives that defeat, according to some voting rule, the current status quo at time t. When preferences are based on Euclidean distance, it is shown that for a wide class of voting rules, a limiting distribution exists. For the special case of majority rule, not only does a limiting distribution always exist, but we obtain bounds for the concentration of the limiting distribution around a centrally located set. The implications are that under Markov voting models, small deviations from the conditions for a core point will still leave the limiting distribution quite concentrated around a generalized median point. Even though the majority relation is totally cyclic in such situations, our results show that such chaos is not probabilistically significant.We acknowledge the support of NSF Grants #SOC79-21588, SES-8106215 and SES-8106212.     

First and second best voting rules in committees

A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases.

“Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller, Catch-22

     

Single-Crossing, Strategic Voting and the Median Choice Rule

This paper studies the strategic foundation of the Representative Voter Theorem (Rothstein in: Pub Choice 72:193–212, 1991), also called the “second version” of the Median Voter Theorem. As a by-product, it also considers the existence of strategy-proof social choice functions over the domain of single-crossing preferences. The main result shows that single-crossing constitutes a domain restriction over the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median rule, which is found to be group strategic-proof over the full set of alternatives and over every nonempty subset. In addition, the paper also examines the relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median rule to prove that the outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism. This mechanism is a two-stage voting procedure in which, first, individuals select a representative among themselves, and then the winner chooses a policy to be implemented by the planner.     

Some Further Results on the Manipulability of Social Choice Rules

A typology of electoral environments in which strategic manipulation of voting rules can occur is proposed. From this typology, six different concepts of equilibria (or quasi-equilibria) are defined, including the usual ones. Then, focusing on three alternative elections, we derive some analytical representations for the vulnerability of a large number of voting rules to strategic manipulation by considering successively each type of equilibrium. Our results show that the hierarchy of the rules changes when the voting framework is modified. However, some rules are clearly dominated and some others (among which the Borda and the Nanson rules) appear to be uniquely the best in some specific contexts.     

Costly voting when both information and preferences differ: is turnout too high or too low?

We study a model of costly voting over two alternatives, where agents’ preferences are determined by both (i) a private preference in favour of one alternative e.g. candidates’ policies, and (ii) heterogeneous information in the form of noisy signals about a commonly valued state of the world e.g. candidate competence. We show that depending on the level of the personal bias (weight on private preference), voting is either according to private preferences or according to signals. When voting takes place according to private preferences, there is an unique equilibrium with inefficiently high turnout. In contrast, when voting takes place according to signals, turnout is locally too low. Multiple Pareto-ranked voting equilibria may exist and in particular, compulsory voting may Pareto dominate voluntary voting. Moreover, an increase in personal bias can cause turnout to rise or fall, and an increase in the accuracy of information may cause a switch to voting on the basis of signals and thus lower turnout, even though it increases welfare. This is a substantially revised version of Department of Economics University of Warwick Working Paper 670, “Information Aggregation, Costly Voting and Common Values”, January 2003. We would like to thank B. Dutta, M. Morelli, C. Perrroni, V. Bhaskar and seminar participants at Warwick, Nottingham and the ESRC Workshop in Game Theory for their comments. We would also like to thank the editor and an anonymous referee for their comments.     

Modeling large electorates with Fourier series, with applications to Nash equilibria in proximity and directional models of spatial competition

 In this paper we introduce harmonic analysis (Fourier series) as a tool for characterizing the existence of Nash equilibria in two-dimensional spatial majority rule voting games with large electorates. We apply our methods both to traditional proximity models and to directional models. In the latter voters exhibit preferences over directions rather than over alternatives, per se. A directional equilibrium can be characterized as a Condorcet direction, in analogy to the Condorcet (majority) winner in the usual voting models, i.e., a direction which is preferred by a majority to (or at least is not beaten by) any other direction. We provide a parallel treatment of the total median condition for equilibrium under proximity voting and equilibrium conditions for directional voting that shows that the former result is in terms of a strict equality (a knife-edge result very unlikely to hold) while the latter is in terms of an inequality which is relatively easy to satisfy. For the Matthews [3] directional model and a variant of the Rabinowitz and Macdonald [7] directional model, we present a sufficiency condition for the existence of a Condorcet directional vector in terms of the odd-numbered components of the Fourier series representing the density distribution of the voter points. We interpret our theoretical results by looking at real-world voter distributions and direction fields among voter points derived from U.S. and Norwegian survey data. Received: 7 July 1995 / Accepted: 14 May 1996     

AN EXPRESSIVE VOTING THEORY OF STRIKES

Union members may vote for a strike even if they do not expect to thereby increase their wages. For under majority voting any one member's vote for a strike is unlikely to be decisive. A union member who obtains a non-infinitesimal emotional benefit from the act of voting for a strike may therefore vote in its favor. This hypothesis can explain the existence of strikes and the conditions which make strikes especially likely.     

On the positive association of parliamentary social choice functions

Intuitively, a voting rule satisfies the condition of positive association if it guarantees that an improvement for an alternative in the preferences expressed by voters results in a change, if there is any, of the social status of that alternative in the same direction. In this article, we consider two interpretations of this notion, and for parliamentary voting procedures, we provide results showing under the impartial anonymous culture (IAC) hypothesis how often the positive association is (not) satisfied. Furthermore, our analysis also permits us to investigate the relationships between these notions.     

Strategy-proofness on Euclidean spaces

 In this paper we characterize strategy-proof voting schemes on Euclidean spaces. A voting scheme is strategy-proof whenever it is optimal for every agent to report his best alternative. Here the individual preferences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if (α) its range is a closed Cartesian subset of Euclidean space, (β) the outcomes are at a minimal distance to the outcome under a specific coordinatewise veto voting scheme, and (γ) it satisfies some monotonicity properties. Neither continuity nor decomposability is implied by strategy-proofness, but these are satisfied if we additionally impose Pareto-optimality or unanimity. Received: 18 October 1993/Accepted: 2 February 1996     

FISCAL POLICY, EXPECTATION TRAPS, AND CHILD LABOR

This paper develops a dynamic model with overlapping generations where there are two possible equilibria: one without child labor, and one with it. It is shown that intergenerational transfers can eliminate the child labor equilibrium and that this intervention is Pareto improving. However, if society does not believe that the government will implement the transfer program, it won't, reinforcing society's expectations. This is true even if the transfer program would have been implemented in the absence of uncertainty. Thus a government may be powerless to prevent the child labor equilibrium if it does not command the confidence of their populace, leaving the country in an expectations trap. ( JEL D91, E60, J20, O20)     

Simple plurality versus plurality runoff with privately informed voters

This paper compares two voting methods commonly used in presidential elections: simple plurality voting and plurality runoff. In a situation in which a group of voters have common interests but do not agree on which candidate to support due to private information, information aggregation requires them to split their support between their favorite candidates. However, if a group of voters split their support, they increase the probability that the winner of the election is not one of their favorite candidates. In a model with three candidates, due to this tension between information aggregation and the need for coordination, plurality runoff leads to higher expected utility for the majority than simple plurality voting if the information held by voters about the candidates is not very accurate. Received: 12 September 2000/Accepted: 8 November 2001     

Sophisticated voting rules: the case of two tournaments

A voting rule maps voter preferences into outcomes, and is called sophisticated if there exists a voting tree whose sophisticated outcomes coincide with the voting rule for every voter preference. As yet, no complete characterization of such rules is available. In this paper, we provide an important step toward this characterization by completely solving the problem when there are two possible sets of voter preferences.The second author was supported by the Office of Naval Research, Grant N00014-92-J-1387.     

The two-party system under alternative voting procedures

Countries that elect their policy-makers by means of Plurality Voting tend to have a two-party system. This observation can be explained by the strategic behavior of voters. This article derives two broad classes of voting procedures under which strategic voting behavior induces a two-party system under standard assumptions on voter preferences. One class consists of the voting procedures with unique top-score, i.e., under which a voter can cast a top-score vote for only one candidate (e.g., Plurality Voting, Borda Count). The other class consists of the voting procedures that permit truncated ballots, i.e., under which voters do not have to cast all their votes (e.g., Approval Voting). This analysis suggests that the key for strategic voting behavior to induce a two-party system is that voters can always cast a different score for the two candidates they rank first and second on their ballots.     

Impartiality,friendship-networks and voting behavior: Evidence from voting patterns in the Eurovision Song Contest

What is the extent to which a country's political institutions impact aggregate voting behavior in a comparative perspective? More specifically, are citizens in some countries more inclined vote on the basis of ‘quality’ or ‘merit’ over ‘friendship’ or ‘loyalty’, and if so, why? This paper seeks to address how the extent to which a country's political institutions are impartial (treats all citizens equally, free from corruption, strong rule of law) impact aggregate citizen behavior. When political institutions are more (less) impartial, success in society is more often on the basis of merit (patrimonial ties). This test cases is voting in the Eurovision Song Contest (ESC) from 1975 to 2012 among pairs and blocs of ‘voting friends’. The theory elucidates that given that certain pairs or blocs exhibit systematic voting bias for one another over time, the bias will be considerably less among impartial states than those with highly partial institutions. Using several measures of ‘friendship’, I find strong empirical evidence for this claim, even when controlling for myriad alternative factors and taking into account various voting regimes. The analysis gives us new insights on how political institutions condition aggregate citizen behavior in general and that although there is much bias in ESC voting, not all bias is equal among friend-countries.     

Anonymous implementation of the Lindahl correspondence: possibility and impossibility results

This paper deals with the existence of anonymous mechanisms to realize the Lindahl correspondence. We consider, in turn, constant and decreasing returns to scale technologies for producing public goods. In each case, we provide a continuous (but not smooth) and weakly balanced mechanism, which meets the two conditions. We then remark that they satisfy a property (see property NC), which is related to, but in fact stronger than anonymity. Finally, we prove that if a mechanism has this property, if it is weakly balanced and implements the Lindahl correspondence, then it cannot be differentiable around Nash equilibria.