Strategy-proofness on Euclidean spaces

T. Storcken, Hans Peters, H. v. d. Stel and W. Peremans
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T. Storcken: Department of Economics, Limburg University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
H. v. d. Stel: Department of Economics, Limburg University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
W. Peremans: Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Social Choice and Welfare, 1997, vol. 14, issue 3, 379-401

Abstract: In this paper we characterize strategy-proof voting schemes on Euclidean spaces. A voting scheme is strategy-proof whenever it is optimal for every agent to report his best alternative. Here the individual preferences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if () its range is a closed Cartesian subset of Euclidean space, () the outcomes are at a minimal distance to the outcome under a specific coordinatewise veto voting scheme, and () it satisfies some monotonicity properties. Neither continuity nor decomposability is implied by strategy-proofness, but these are satisfied if we additionally impose Pareto-optimality or unanimity.

Date: 1997
Note: Received: 18 October 1993/Accepted: 2 February 1996
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