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An alternative direct proof of Gibbard’s random dictatorship theorem


  • Yasuhito Tanaka



We present an alternative proof of the Gibbard’s 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 Gibbard’s random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbard’s approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbard’s proof. Copyright Springer-Verlag Berlin/Heidelberg 2003

Suggested Citation

  • Yasuhito Tanaka, 2003. "An alternative direct proof of Gibbard’s random dictatorship theorem," Review of Economic Design, Springer;Society for Economic Design, vol. 8(3), pages 319-328, October.
  • Handle: RePEc:spr:reecde:v:8:y:2003:i:3:p:319-328 DOI: 10.1007/s10058-003-0102-2

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    References listed on IDEAS

    1. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    2. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    3. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1997. "The Loser's Curse and Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 65(6), pages 1247-1282, November.
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    Cited by:

    1. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.


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