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An alternative direct proof of Gibbard’s random dictatorship theorem

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  • Yasuhito Tanaka

Abstract

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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    Citations

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    Cited by:

    1. Felix Brandt & Patrick Lederer & Ren'e Romen, 2022. "Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes," Papers 2201.10418, arXiv.org.
    2. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    3. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.

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