Characterization of self-selective social choice functions on the tops-only domain

Self-selectivity is a new kind of consistency pertaining to social choice rules. It deals with the problem of whether a social choice rule selects itself from among other rival such rules when a society is also to choose the choice rule that it will employ in making its choice from a given set of alternatives. Koray [3] shows that a neutral and unanimous social choice function is universally self-selective if and only if it is dictatorial. In this paper, we confine the available social choice functions to the tops-only domain and examine whether such restriction allow us to escape the dictatoriality result. A neutral, unanimous, and tops-only social choice function, however, turns out to be self-selective relative to the tops-only domain if and only if it is top-monotonic, and thus again dictatorial. Received: 8 October 2001/Accepted: 4 June 2002     

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.     

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.     

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.     

STATE LIQUOR LICENSING, IMPLICIT CONTRACTING, AND DRY/WET COUNTIES

Local option liquor laws are generally interpreted as granting voters the right to choose between allowing and prohibiting alcoholic beverage sales. This paper argues that the real choice confronting voters is between legal sales according to state-prescribed rules and illegal sales according to an informal set of locally-determined rules. Given this choice, rational voters will choose the option with the lower relative price. State laws restricting the number of licenses that can be issued in legally wet jurisdictions prove to be more powerful than religious preferences in explaining the pattern of dry counties.     

Ensuring Pareto Optimality by Referendum Voting

We consider a society confronting the decision of accepting or rejecting a list of (at least two) proposals. Assuming separability of preferences, we show the impossibility of guaranteeing Pareto optimal outcomes through anonymous referendum voting, except in the case of an odd number of voters confronting precisely two proposals. In this special case, majority voting is the only anonymous social choice rule which guarantees Pareto optimal referendum outcomes.     

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     

Identification of domain restrictions over which acyclic, continuous-valued, and positive responsive social choice rules operate

We consider a social choice problem in various economic environments consisting of n individuals, 4≤n<+∞, each of which is supposed to have classical preferences. A social choice rule is a function associating with each profile of individual preferences a social preference that is assumed to be complete, continuous and acyclic over the alternatives set. The class of social choice rules we deal with is supposed to satisfy the two conditions; binary independence and positive responsiveness. A new domain restriction for the social choice rules is proposed and called the classical domain that is weaker than the free triple domain and holds for almost all economic environments such as economies with private and/or public goods. In this paper we explore what type of classical domain that admits at least one social choice rule satisfying the mentioned conditions to well operate over the domain. The results we obtained are very negative: For any classical domain admitting at least one social choice rule to well operate, the domain consists only of just one profile.     

On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.     

The vulnerability of four social choice functions to coalitional manipulation of preferences

The vulnerability of a social choice function to coalitional manipulation of preferences is defined as the proportion of voting situations in which the social choice function can be manipulated by a coalition of individuals. In this paper, we provide exact relations giving the vulnerability of four specific social choice functions (plurality rule, anti-plurality rule, plurality with runoff, anti-plurality with runoff) in three-alternative elections. Plurality with runoff appears to be less vulnerable than the other three rules.     

Is it ever safe to vote strategically?

There are many situations in which mis-coordinated strategic voting can leave strategic voters worse off than they would have been had they not tried to strategise. We analyse the simplest of such scenarios, in which a set of strategic voters all have the same sincere preferences and all contemplate casting the same strategic vote, while all other voters are not strategic. Most mis-coordinations in this framework can be classified as instances of either strategic overshooting (too many voted strategically) or strategic undershooting (too few). If mis-coordination can result in strategic voters ending up worse off than they would have been had they all just voted sincerely, we call the strategic vote unsafe. We show that under every onto and non-dictatorial social choice rule there exist circumstances where a voter has an incentive to cast a safe strategic vote. We extend the Gibbard–Satterthwaite Theorem by proving that every onto and non-dictatorial social choice rule can be individually manipulated by a voter casting a safe strategic vote.     

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.     

Public information and social choice

We examine the value of public information when a society uses a social choice rule to decide among a set of outcomes. We require that a social choice function satisfies unrestricted domain, non-decisiveness and the Pareto principle. We show that there exist payoff structures for every social choice function, such that an arbitrary subset of voters is worse off by public information. We apply the proposition to collective information acquisition and to irreversible investments. Received: 2 June 1997/Accepted: 30 September 1998     

Aversion to inequality in Italy and its determinants

The main goal of this paper is to estimate the preferences of the Italian society towards equity in order to verify whether preferences (i) have changed across the years, and (ii) can be related to specific socio-demographic characteristics. Introducing equity concerns in the implementation of economic policies is a fundamental problem faced by both economists and policy makers. This paper uses a social welfare function à la Jorgenson and Slesnick to estimate society’s aversion towards inequality by implementing a voting scheme for compiling individuals’ equity preferences into a social choice by majority rule. The results show that preferences are highly polarized toward a low and a high concern for equity aversion and that this concern is significantly related with several sociodemographic characteristics. Among them, income plays an important role with richer people tending to favor less equity. Results also show that preferences towards equity have changed across the years.     

Topological aggregation of preferences: the case of a continuum of agents

 This paper studies the topological approach to social choice theory initiated by G. Chichilnisky (1980), extending it to the case of a continuum of agents. The social choice rules are continuous anonymous maps defined on preference spaces which respect unanimity. We establish that a social choice rule exists for a continuum of agents if and only if the space of preferences is contractible. We provide also a topological characterization of such rules as generalized means or mathematical expectations of individual preferences. Received: 30 November 1994/Accepted: 22 April 1996     

Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings

The aim of the present paper is to provide an axiomatic analysis of incomplete social judgments. In particular, we clarify the underlying power structure of Arrovian collective choice rules when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness and investigate the properties of the collection of quasi-decisive sets associated with an Arrovian collective choice rule. In the course of this, we offer a series of applications.     

Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.     

Ensuring every candidate wins under positional voting

Given a fixed set of voter preferences, different candidates may win outright given different scoring rules. We investigate how many voters are able to allow all n candidates to win for some scoring rule. We will say that these voters impose a disordering on these candidates. The minimum number of voters it takes to impose a disordering on three candidates is nine. For four candidates, six voters are necessary, for five candidates, four voters are necessary, and it takes only three voters to disorder nine candidates. In general, we prove that m voters can disorder n candidates when m and n are both greater than or equal to three, except when m = 3 and n ≤ 8, when n = 3 and m ≤ 8, and when n = 4 and m = 4 or 5.     

Manipulability measures of common social choice functions

All social choice functions are manipulable when more than two alternatives are available. I evaluate the manipulability of the Borda count, plurality rule, minimax set, and uncovered set. Four measures of manipulability are defined and computed stochastically for small numbers of agents and alternatives.  Social choice rules derived from the minimax and uncovered sets are found to be relatively immune to manipulation whether a sole manipulating agent has complete knowledge or absolutely no knowledge of the preferences of the others. The Borda rule is especially manipulable if the manipulating agent has complete knowledge of the others. Received: 5 January 1996/Accepted: 31 July 1998     

Choosing an electoral rule: Values and self-interest in the lab

We study the choice of multi-person bargaining protocols in the context of politics. In politics, citizens are increasingly involved in the design of democratic rules, for instance via referendums. If they support the rule that best serves their self-interest, the outcome inevitably advantages the largest group. In this paper, we challenge this pessimistic view with an original lab experiment, in which 252 subjects participated. In the first stage, these subjects experience elections under plurality and approval voting. In the second stage, they decide which rule they want to use for extra elections. We find that egalitarian values that subjects hold outside of the lab shape their choice of electoral rule in the second stage when a rule led to a fairer distribution of payoffs compared to the other one in the first stage. The implication is that people have consistent ‘value-driven preferences’ for decision rules.