A Strategy‐Proofness Characterization of Plurality Rule

• Date: 01 August 2016
• Published date: 01 August 2016
• Author: DONALD E. CAMPBELL,JERRY S. KELLY
• DOI: http://doi.org/10.1111/jpet.12198

ASTRATEGY-PROOFNESS CHARACTERIZATION OF PLURALITY RULE

DONALD E. CAMPBELL

The College of William and Mary

JERRY S. KELLY

Syracuse University

Abstract

Assuming at least four individuals and at least four alternatives, a social

choice function on the domain of profiles at which there is an alterna-

tive ranked first by more individuals than any other alternative is non-

dictatorial, strategy-proof, and has full range if and only if it is plurality

rule.

1. Introduction

A social choice function selects a feasible alternative as a function of individual prefer-

ences. It is dictatorial if it selects a fixed individual’s most-preferred alternative at every

configuration of individual preferences. It is strategy-proof if one can never secure the

adoption of a preferred alternative by submitting an ordering different from one’s true

preferences.

This paper continues the investigation initiated in Campbell and Kelly (2003, 2016),

which established that the Condorcet rule is the only nondictatorial and strategy-proof

social choice function on the domain of profiles at which there is an alternative that

defeats every other by a strict majority. (Those papers assumed that the number of in-

dividuals is odd, there are at least three alternatives, and the rule has full range.) This

paper considers social choice functions on the domain Pof profiles (configurations of

individual preferences) at which there is an alternative that is ranked first by more indi-

viduals than any other alternative. Plurality rule is the only social choice function on P

with full range that is both nondictatorial and strategy-proof.

For many social choice problems, we need a rule that is defined on the unre-

stricted domain. We also want it to be strategy-proof. Of course, that leads to dictatorship

(Gibbard 1973; Satterthwaite 1975). We have to demand less. One way to proceed is to

seek a social choice function that is defined on the unrestricted domain but require

strategy-proofness only of its restriction to some significant subset of the full domain. P

is that subdomain in the present paper.

Donald E. Campbell, Department of Economics and the Program in Public Policy, The College of

William and Mary, Williamsburg, VA 23187-8795 (decamp@wm.edu). Jerry S. Kelly, Department of

Economics, Maxwell School of Citizenship and Public Affairs, Syracuse University, Syracuse, NY 13244-

1090.

We are grateful for the advice of our associate editor and referees. Their suggestions led to a number

of improvements.

Received October 20, 2014; Accepted June 9, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (4), 2016, pp. 610–623.

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