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The proof of the Gibbard–Satterthwaite theorem revisited

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  • Svensson, Lars-Gunnar
  • Reffgen, Alexander

Abstract

This paper provides three short proofs of the classical Gibbard–Satterthwaite theorem. The theorem is first proved in the case with only two voters. The general case follows then from an induction argument over the number of voters. The proof of the theorem is further simplified when the voting rule is neutral. The simple arguments in the proofs may be especially useful in classroom situations.

Suggested Citation

  • Svensson, Lars-Gunnar & Reffgen, Alexander, 2014. "The proof of the Gibbard–Satterthwaite theorem revisited," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 11-14.
    • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:11-14
    DOI: 10.1016/j.jmateco.2014.09.007
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    References listed on IDEAS

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    1. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    2. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    3. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    4. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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