Efficient and strategy-proof voting rules: A characterization

Abstract The paper provides a characterization of all efficient and strategy-proof voting mechanisms on a large class of preference domains, the class of all generalized single-peaked domains. It is shown that a strategy-proof voting mechanism on such a domain is efficient if and only if it satisfies a weak neutrality condition and is either almost dictatorial, or defined on a median space of dimension less than or equal to two. In more than two dimensions, weakly neutral voting mechanisms are still “locally” efficient.

[1]  Ken-Ichi Shimomura,et al.  Partially efficient voting by committees , 1996 .

[2]  Fred W. Roush,et al.  Nonmanipulability in two dimensions , 1984 .

[3]  S. Brams,et al.  The paradox of multiple elections , 1998 .

[4]  C. List,et al.  Aggregating Sets of Judgments: An Impossibility Result , 2002, Economics and Philosophy.

[5]  Jerry R. Green,et al.  Incentives in public decision-making , 1979 .

[6]  Hans Peters,et al.  Generalized median solutions, strategy-proofness and strictly convex norms , 1993, ZOR Methods Model. Oper. Res..

[7]  Rakesh V. Vohra,et al.  Strategy-proof Location on a Network , 2002, J. Econ. Theory.

[8]  Hugo Sonnenschein,et al.  Voting By Quota And Committee , 1988 .

[9]  Salvador Barberà,et al.  Voting by Committees , 1991 .

[10]  Klaus Nehring,et al.  The structure of strategy-proof social choice - Part I: General characterization and possibility results on median spaces , 2007, J. Econ. Theory.

[11]  Gabrielle Demange,et al.  Single-peaked orders on a tree , 1982, Math. Soc. Sci..

[12]  Lawrence G. Sager,et al.  Unpacking the Court , 1986 .

[13]  S. Barberà,et al.  Voting under Constraints , 1997 .

[14]  Faruk Gul,et al.  Generalized Median Voter Schemes and Committees , 1993 .

[15]  M. Satterthwaite,et al.  Strategy-proofness and single-peakedness , 1976 .

[16]  Klaus Nehring,et al.  Diversity and the Geometry of Similarity , 1999 .

[17]  H. Peters,et al.  Pareto optimality, anonymity, and strategy-proofness in location problems , 1992 .

[18]  Kim C. Border,et al.  Straightforward Elections, Unanimity, and Phantom Voters , 1983 .

[19]  Van de M. L. J. Vel.  Theory of convex structures , 1993 .

[20]  Klaus Nehring,et al.  On the Possibility of Strategy-Proof Social Choice: Non-Dictatorship, Anonymity and Neutrality * , 2005 .

[21]  Christian List,et al.  STRATEGY-PROOF JUDGMENT AGGREGATION* , 2005, Economics and Philosophy.