The Gibbard random dictatorship theorem: a generalization and a new proofReport as inadecuate

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, Volume 2, Issue 4, pp 515–527

First Online: 01 March 2011Received: 24 November 2010Accepted: 10 January 2011


This paper proves stronger versions of the Gibbard random dictatorship theorem using induction on the number of voters. It shows that when there are at least three voters, every random social choice function defined on a domain satisfying a Free Triple at the Top property and satisfying a weak form of strategy-proofness called Limited-Comparison Strategy-proofness and Unanimity, is a random dictatorship provided that there are at least three alternatives. The weaker notion of strategy-proofness requires truth-telling to maximize a voter’s expected utility only for a limited class of von Neumann–Morgenstern utility representations of the voter’s true preference ordering. In the case of two voters, an even weaker condition on the domain and a weaker notion of strategy-proofness are sufficient for the random dictatorship result.

KeywordsGibbard’s random dictatorship theorem Free Triple at the Top Limited comparison strategy-proofness Salvador Barberà is one of the pioneers in probabilistic mechanism design theory. He introduced me to the subject when I visited the Economics Department of the Universitat Autònoma de Barcelona in 1987. My own ideas in this area and on the theory of strategy-proofness in general have been strongly shaped by his work and by numerous discussions I have had with him over the years. It is a particular pleasure to be able to contribute to a volume celebrating his 65th birthday. I would also like to thank Debasis Mishra, Souvik Roy and two anonymous referees of the journal for their comments on the paper.

JEL ClassificationD71  Download to read the full article text

Author: Arunava Sen


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