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Review of Economic Design
Publisher: Springer-Verlag GmbH
ISSN: 1434-4742 (Paper) 1434-4750 (Online)
DOI: 10.1007/s10058-003-0102-2
Issue: Volume 8, Number 3
Date:  October 2003
Pages: 319 - 328
An alternative direct proof of Gibbardrsquos random dictatorship theorem

Yasuhito TanakaContact Information

(1) Faculty of Economics, Doshisha University, Kamigyo-ku, 602-8580 Kyoto, Japan

Abstract.  We present an alternative proof of the Gibbardrsquos random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbardrsquos random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbardrsquos approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbardrsquos proof.

Keywords:  Decision scheme - ex post Pareto optimality - Gibbardrsquos random dictatorship theorem

Received: 15 October 2001, Accepted: 23 May 2003,
JEL Classification:   D71, D72
Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.

Contact InformationYasuhito Tanaka
Email: yatanaka@mail.doshisha.ac.jp

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