A characterization of social choice correspondences that implement the core of simple games

In a coalitional voting game, an alternative is said to be in the core when no majority is willing to replace it with another alternative. A social choice correspondence is a mapping which associates any profile of voters’ preferences with a non-empty subset of the set of alternatives, which is understood as the set of selected outcomes. We characterize the social choice correspondences which always select the core of a simple game for any profile of preferences. This work was completed when B. Tchantcho was Visiting assistant Professor at UTA (University of Texas at Arlington). We acknowledge the support of the Department of Mathematics of UTA. We are most grateful to R. Pongou of Brown University, USA for his help and advice. We sincerely thank N.G Andjiga for his helpful comments and we are indebted to two anonymous referees for their helpful comments.     

Axioms for minimax regret choice correspondences

This paper unifies and extends the recent axiomatic literature on minimax regret. It compares several models of minimax regret, shows how to characterize the according choice correspondences in a unified setting, extends one of them to choice from convex (through randomization) sets, and connects them by defining a behavioral notion of perceived ambiguity. Substantively, a main idea is to behaviorally identify ambiguity with failures of independence of irrelevant alternatives. Regarding proof technique, the core contribution is to uncover a dualism between choice correspondences and preferences in an environment where this dualism is not obvious. This insight can be used to generate results by importing findings from the existing literature on preference orderings.     

Anonymous monotonic social welfare functions

This paper presents two results about preference domain conditions that deepen our understanding of anonymous and monotonic Arrovian social welfare functions (ASWFs). We characterize the class of anonymous and monotonic ASWFs on domains without Condorcet triples. This extends and generalizes an earlier characterization (as Generalized Majority Rules) by Moulin (Axioms of Cooperative Decision Making, Cambridge University Press, New York, 1988) for single-peaked domains. We also describe a domain where anonymous and monotonic ASWFs exist only when there are an odd number of agents. This is a counter-example to a claim by Muller (Int. Econ. Rev. 23 (1982) 609), who asserted that the existence of 3-person anonymous and monotonic ASWFs guaranteed the existence of n-person anonymous and monotonic ASWFs for any n>3. Both results build upon the integer programming approach to the study of ASWFs introduced in Sethuraman et al. (Math. Oper. Res. 28 (2003) 309).     

On the topological social choice model

The main goal of this paper is to show that if a finite connected CW complex admits a continuous, symmetric, and unanimous choice function for some number n>1 of agents, then the choice space is contractible. On the other hand, if one removes the finiteness, we give a complete characterization of the possible spaces; in particular, noncontractible spaces are indeed possible. These results extend earlier well-known results of Chichilnisky and Heal.     

Non-dictatorial extensive social choice

Summary. Different social planners may have different opinions on the well-being of individuals under different social options (Roberts, 1980). If utilities are translation- or ratio-scale measurable, or if the social ranking might be incomplete, or if interplanner comparability is allowed; then there exist non-dictatorial aggregation rules. We propose extensions, intersections, and mixtures of the Pareto, utilitarian, leximin, Kolm-Pollak, and iso-elastic rules.Received: 16 May 2001, Revised: 18 November 2003, JEL Classification Numbers: D63, D71. Correspondence to: Erwin OogheErwin Ooghe, Luc Lauwers: We are extremely grateful to the referee who was willing to review this paper many times. Her/his extensive and in-depth comments had a strong impact. Further thanks are due to Bart Capéau, Marc Fleurbaey, Maurice Salles, Erik Schokkaert, and Alain Trannoy. The first author gratefully acknowledges the financial support by the TMR network Living Standards, Inequality and Taxation (ERBFMRXCT 980248) of the European Communities.     

Salience and social choice

The axioms of expected utility and discounted utility theory have been tested extensively. In contrast, the axioms of social welfare functions have only been tested in a few questionnaire studies involving choices between hypothetical income distributions. In a controlled experiment with 100 subjects placed in the role of social planners, we test five fundamental properties of social welfare functions to determine the efficacy of traditional social choice models in predicting social planner allocations when presented with choice sets designed to test the axioms of the theory. We find that three properties of the standard social welfare functions tested are systematically violated, producing an Allais paradox, a common ratio effect, and a framing effect in social choice. We find support for scale invariance and a preference for tail-increasing transfers. Our experiment also enables us to test a model of salience-based social choice which predicts the systematic deviations and highlights the close relationship between these anomalies and the classical paradoxes for risk and time.

     

Lebesgue measure and social choice trade-offs

Summary An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome spaceX with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fractiont, either some individual dictates over a subset ofX of measuret or more, or at least a fraction 1–t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integer (less than the total number of individuals), there is some subsetH of society consisting of all but persons such that the fraction of outcome pairs (x, y) that are social ranked without consulting the preferences of anyone inH, whenever no individual is indifferent betweenx andy, is at least 1–1/4.We are grateful to Roy Mathias and Daniel Waterman for help with some technical matters, and to chairman Jim Follain and the Syracuse University Economics Department for financing the exchange that launched this project. Campbell's research was funded by National Science Foundation grants, SES 9007953 and SES 9209039.     

Candidate stability and nonbinary social choice

Summary. The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of their impossibility theorems. Received: August 15, 2001; revised version: March 11, 2002 RID="*" ID="*" Parts of this article were previously circulated in somewhat different form in a working paper with the same title by the second author. We are grateful to Michel Le Breton and an anonymous referee for their comments. Correspondence to:J.A. Weymark     

Gains from manipulating social choice rules

Gibbard–Satterthwaite analysis is extended by examining the size of the potential gains that can be achieved from manipulation. The authors are grateful for an invitation from the University of Athens to visit their Ph D program where some of this work was done.     

Structure of neutral and monotonic binary social decision rules with quasi-transitive individual preferences

The paper investigates the structure of neutral and monotonic binary social decision rules with unrestricted domain under the assumption that individual weak preference relations are reflexive, connected, and quasi-transitive. Among other results, neutral and monotonic binary social decision rules on this domain are characterized for alternative social rationality assumptions.     

Losses due to manipulation of social choice rules

In a companion paper, “Gains from Manipulating Social Choice Rules,” we analyzed the incentive to manipulate by considering the maximum number of ranks someone can gain in their preference ordering by manipulation. This paper treats the number of ranks someone else can lose due to manipulation. We find large classes of rules where that loss is very large, a few rules where the loss can be significantly smaller, and even some rules where no one ever loses—even though manipulation will take place.     

Working part time: by choice or by constraint

The selection of workers into part-time jobs and the wages they earn are analysed using the 1989 Labour Market Activity Survey. We focus on the distinction between voluntary and involuntary part-time workers, since involuntary part-time workers earn substantially lower wages than other workers. We find that the selection of individuals into involuntary part-time work is more closely tied to job characteristics than personal or human capital characteristics. The lower wage earned by involuntary part-time workers is largely due to differences in returns and selection effects, rather than differences in endowments. JEL Classification: J22, J23, J31     

Designing social security - a portfolio choice approach

Public social security systems may provide diversification of risks to individuals’ life-time income. Capturing that a pay-as-you-go system (paygo) may be considered as a “quasi-asset”, we study the optimal size of the paygo system as well as the optimal split between funded and unfunded pension saving by means of a theoretical portfolio choice framework. A low-yielding paygo system can benefit individuals if it contributes to hedge other risks to their lifetime resources. Numerical calculations indicate that optimal social security systems should be at least partly paygo financed in many economies. The optimal magnitude of the paygo system depends on the specified risk concept as well as the stochastic properties of stock market returns and implicit paygo-returns.     

Fertility choice under child mortality and social norms

In most demographic transitions, declines in child mortality precede declines in net fertility rates. Variants of the Barro-Becker model of fertility fail to deliver this link. A simple extension, the inclusion of social norms regarding fertility, generates the desired effect.     

Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

On fixed point theorems and social choice paradoxes

This note explores the relationship of social choice paradoxes to fixed point theorems. A special case of the paradox proven in Chichilnsky (forthcoming), the non-existence of a continuous anonymous rule that respects anonymity with two voters and two dimensional choice spaces, is proven here to be equivalent to a fixed point problem. We indicate also how the results can be extended to higher dimensional choice spaces and any finite number of agents.     

Theorems on correspondences and stability of the core

In this note two theorems strengthening Grodal's (1971) Theorem on correspondences are proved. The first drops the convexity assumption. The second strengthens that theorem further for the case when the range is the positive orthant. In this case, the conclusion of Grodal's Theorem - the intersection of the integral with the interior of the range being open- is modified to read as the integral being a relative open subset of the positive orthant. An example is provided to show that, such a strengthening is not valid in general. This allows us to dispense with the requirment of convexity of preferences in Grodal's (1971) theorems on the closedness of the set of Pareto optimal allocations, the core, and the continuity of the core correspondence for pure exchange economies. We apply this result to show that blocking coalitions in a large economy are stable. Received: September 30, 1998; revised version: September 18, 2001 RID="*" ID="*" The author is grateful to an anonymous referee for helpful comments. The usual disclaimer applies.