Partnership dissolution and proprietary information

This article analyzes simple rules for dissolving a common value partnership in which one partner holds proprietary information. The winner’s bid auction and the loser’s bid auction are payoff equivalent and both favor the informed partner. If it is verifiable which partner is informed, the cake-cutting mechanism (CCM) generates a “fair” allocation by making the informed partner the proposer. If that information is not verifiable and the identity of the proposer is determined through a lottery, the CCM favors the informed partner, too. Moreover, CCM is fairer than the auctions for common distributions of the asset value.     

On the (sequential) majority choice of public good size and location

This article studies majority voting over the size and location of a public good when voters differ both in income and in their preferences for the public good location. Public good provision is financed either by a lump sum tax or by a proportional income tax. We analyze both the simultaneous and the sequential determinations of the public good’s size and location. We show that, while the choice of the type of public good follows the traditional median logic, the majoritarian determination of the taxation rate need not coincide with the preferences of a median income citizen. With lump sum financing, income heterogeneity plays no role and the sequential equilibrium consists of the median location together with the public good level most-preferred by the individual located at the median distance from the median. This policy bundle also constitutes an equilibrium with simultaneous voting in the special case of a uniform bivariate distribution of individuals’ income and location. With proportional taxation, there is no policy equilibrium with simultaneous voting. We offer a complete characterization of the equations describing the sequential equilibrium in the general case and we show why and how our results depart from those most-preferred by the median income individual located at the median distance from the median. We also compare these majority voting allocations with the socially optimal one.     

The Generosity Game and calibration of inequity aversion

In the Generosity Game the agreement payoff of the proposer is fixed whereas that of the responder can be varied by the proposer who chooses the pie size. Increasing the pie size increases the (generosity of the) offer by the same amount. We define a unit-square class of Generosity Games by weakening the payoff consequences resulting from a veto by the responder and discuss how the dictator variants can be used to test inequity aversion parameters. Experimental findings, however, so far question inequity aversion as a dominant motive and thus discourage such attempts of assessing its parameters.     

Voting rules as statistical estimators

We adopt an ‘epistemic’ interpretation of social decisions: there is an objectively correct choice, each voter receives a ‘noisy signal’ of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori (MAP) estimator or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common ‘quasiutilitarian’ voting rules can be interpreted as EUM.     

Democratically Elected Aristocracies

The article suggests a formal model of a two-tier voting procedure, which unlike traditional voting systems does not presuppose that every vote counts the same. In deciding a particular issue voters are called in the first round to assign categories of their fellow-citizens with differential voting power (or weights) according to the special position or concern individuals are perceived to have with regard to that issue. In the second stage, voters vote on the issue itself according to their substantive view and their votes are counted in the light of the differential weights assigned in the first round. We analyze formal and philosophical reasons that support the model.     

Voting under the threat of secession: accommodation versus repression

We build a simple model of secession crises where a majority of voters may wish to accommodate a minority in order to prevent a secession attempt. We first show the existence of a majority voting equilibrium, where the median voter is decisive and most prefers a government’s type that is biased in favor of the minority. We propose a measure of the secession risk at equilibrium, which depends upon the comparison of the willingness to secede by the minority and to accommodate by the majority. We show that focusing only on the willingness to secede, as previous literature has done, is misleading when studying the impact on the risk of secession of the size of the minority region, the probability that a secession attempt by the minority is successful, and the cultural heterogeneity in the country.     

Generalized average rules as stable Nash mechanisms to implement generalized median rules

We consider a problem in which a policy is chosen from a one-dimensional set over which voters have single-peaked preferences. While Moulin (Public Choice 35:437–455, 1980) and others subsequent works have focused on strategy-proof rules, Renault and Trannoy (Mimeo 2011) and Renault and Trannoy (J Pub Econ Theory 7:169–199, 2005) have shown that the average rule implements a generalized median rule in Nash equilibria and provide an interpretation of the parameters in Moulin’s rule. In this article, we first extend their result by showing that a wide range of voting rules which includes the average rule can implement Moulin’s rule in Nash equilibria. Moreover, we show additionally that within this class, generalized average rules are Cournot stable. That is, from any strategy profile, any best response path must converge to a Nash equilibrium.     

SOCIAL PREFERENCES AND TAX POLICY DESIGN: SOME EXPERIMENTAL EVIDENCE

This article reports the results of a set of experiments designed to examine whether a taste for fairness affects people's preferred tax structure. Using the Fehr and Schmidt model, we devise a simple test for the presence of social preferences in voting for alternative tax structures. The experimental results show that individuals demonstrate concern for their own payoff and inequality aversion in choosing between alternative tax structures. However, concern for redistribution decreases as the deadweight loss from progressive taxation increases. Our findings have important implications for tax policy design. ( JEL C92, D63, H21, H23)     

An extension of Bowen’s dynamic voting rule to many dimensions

 We ask in this paper about the effect on social decisions of limiting the size of changes that voters may propose each time in an otherwise standard dynamic social choice model. The voting rule we study can be seen as an extension of Bowen’s dynamic “majority voting” rule, and is closely related to the dynamic procedures for public good allocation in the literature (Drèze and de la Vallée Poussin 1971; Malinvaud 1971; Laffont and Maskin 1983; Chander 1993). Under general assumptions we prove existence and Pareto efficiency of equilibrium, and show that our rule motivates voters not to misrepresent preferences (more precisely, the rule is Strongly Locally Individually Incentive Compatible). Under Euclidean preferences we find that electoral cycles do not arise (i.e., the rule is convergent), that there is a unique equilibrium, and that the equilibrium coincides with the solution to an old problem of geometry, first addressed by Fermat, Torricelli, and Cavallieri. Received: 20 September 1994/Accepted: 6 August 1996     

What are you calling intuitive? Subject heterogeneity as a driver of response times in an impunity game

Studies on the intuitive or deliberate nature of human actions often use time constraints for identification, assuming that constrained individuals fall back to intuitive behavior. This identification strategy disregards individual heterogeneity and self-priming, i.e. the behavioral rule that subjects can form during the instructions phase, and then apply irrespective of the time constraint. We use respondent data from an impunity game as an example of how subject heterogeneity can drive results. 24 respondents face 240 more or less unfair allocation proposals out of a small or large pie and can accept or reject the offer. Upon rejection respondents burn their own money, but not the proposer’s. Respondents decisions are communicated to the proposer. On average, emotional rejections take longer than deliberate acceptances. Including individual heterogeneity, though, we find that subjects who mostly accept (reject) take more time to reject (accept). Faster decisions are the ones conforming with the modal early reaction. We attribute this finding to heterogeneity in self-priming. Since self-priming is orthogonal to time constraints, it has the capacity to invalidate their use in the identification of dual decision modes.     

The undercut procedure: an algorithm for the envy-free division of indivisible items

We propose a procedure for dividing a set of indivisible items between two players. We assume that each player’s preference over subsets of items is consistent with a strict ranking of the items, and that neither player has information about the other’s preferences. Our procedure ensures an envy-free division—each player receives a subset of items that it values more than the other player’s complementary subset—given that an envy-free division of “contested items,” which the players would choose at the same time, is possible. We show that the possibility of one player’s undercutting the other’s proposal, and implementing the reduced subset for himself or herself, makes the proposer “reasonable,” and generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is manipulable and its envy-free allocation may be Pareto-inferior, each player’s maximin strategy is to be truthful. Applications of the procedure are discussed briefly.     

Policy convergence in a two-candidate probabilistic voting model

We propose a generalization of the probabilistic voting model in two-candidate elections. We allow the candidates have general von Neumann–Morgenstern utility functions defined over the voting outcomes. We show that the candidates will choose identical policy positions only if the electoral competition game is constant-sum, such as when both candidates are probability-of-win maximizers or vote share maximizers, or for a small set of functions that for each voter define the probability of voting for each candidate, given candidate policy positions. At the same time, a pure-strategy local Nash equilibrium (in which the candidates do not necessarily choose identical positions) exists for a large set of such functions. Hence, if the candidate payoffs are unrestricted, the “mean voter theorem” for probabilistic voting models is shown to hold only for a small set of probability of vote functions.     

Does uncertainty lead to sincerity? Simple and complex voting mechanisms

We ask whether the absence of information about other voters’ preferences allows optimal voting to be interpreted as sincere.We start by classifying voting mechanisms as simple and complex according to the number of message types voters can use to elect alternatives. We show that while in simple voting mechanisms the elimination of information about other voters’ preferences allows optimal voting to be interpreted as sincere, this is no longer always true for complex ones. In complex voting mechanisms, voters’ optimal strategy may vary with the size of the electorate. Therefore, in order to interpret optimal voting as sincere for complex voting mechanisms, we describe the optimal voting strategy when voters not only have no information but also have no pivotal power, i.e., as the size of the electorate tends to infinity.     

Rationalizations of Condorcet-consistent rules via distances of hamming type

In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem.     

Enlargement and the balance of power: an experimental study

Theoretical analysis suggests that enlargement of a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members.     

Simple guilt and cooperation

We introduce simple guilt into a generic prisoner’s dilemma (PD) game and solve for the equilibria of the resulting psychological game. It is shown that for all guilt parameters, it is a pure strategy equilibrium that both players defect. But if the guilt parameter surpasses a threshold, a mixed strategy equilibrium and a pure strategy equilibrium in which both players cooperate emerge. We implement three payoff constellations of the PD game in a laboratory experiment and find in line with our equilibrium analysis that first- and second-order beliefs are highly correlated and that the probability of cooperation depends positively on these beliefs. Maximum likelihood estimations of a model of noisy introspection reveal that experimental data is best fitted with positive guilt levels and that omission of guilt results in a substantial increase in the noise parameters.     

ENDOGENOUS TIMING IN CONTESTS WITH DELEGATION

We study two‐player contests in which each player hires a delegate, and the delegates decide endogenously when to expend their effort. First, we look closely at the delegates' decisions on when to expend their effort, given contracts between the players and the delegates, and look at the players' decisions on their contracts. Then, we compare the outcomes of the endogenous‐timing framework with those of the simultaneous‐move framework. We show that the higher‐valuation player offers her delegate greater contingent compensation than her opponent, the delegate of the higher‐valuation player chooses his effort level after observing his counterpart's, the equilibrium expected payoff of the delegate of the higher‐valuation player is greater than that of his counterpart, and economic rent for each delegate exists. We show that, in the endogenous‐timing framework, each player offers her delegate better contingent compensation, each delegate's expected payoff is greater, and each player's expected payoff is smaller, as compared with the simultaneous‐move framework. (JEL D72)     

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     

Exploiting polyhedral symmetries in social choice

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet’s paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.