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A geometric proof of Gibbard's random dictatorship theorem (*)

Author

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  • John Duggan

    (Division of the Humanities and Social Sciences, Caltech, Pasadena, CA 91125, USA)

Abstract

Gibbard has shown that a social choice function is strategy-proof if and only if it is a convex combination of dictatorships and pair-wise social choice functions. I use geometric techniques to prove the corollary that every strategy-proof and sovereign social choice function is a random dictatorship.

Suggested Citation

  • John Duggan, 1996. "A geometric proof of Gibbard's random dictatorship theorem (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 365-369.
    • Handle: RePEc:spr:joecth:v:7:y:1996:i:2:p:365-369
    Note: Received: November 26, 1993; revised version June 20, 1994
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    Cited by:

    1. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    2. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    3. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    4. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
    5. 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.
    6. 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.
    7. Arunava Sen, 2011. "The Gibbard random dictatorship theorem: a generalization and a new proof," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 515-527, December.

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