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A topological proof of the Gibbard–Satterthwaite theorem

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  • Baryshnikov, Yuliy
  • Root, Joseph

Abstract

We give a new proof of the Gibbard–Satterthwaite Theorem. We construct two topological spaces: one for the space of preference profiles and another for the space of outcomes. We show that social choice functions induce continuous mappings between the two spaces. By studying the properties of this mapping, we prove the theorem.

Suggested Citation

  • Baryshnikov, Yuliy & Root, Joseph, 2024. "A topological proof of the Gibbard–Satterthwaite theorem," Economics Letters, Elsevier, vol. 234(C).
    • Handle: RePEc:eee:ecolet:v:234:y:2024:i:c:s0165176523004731
    DOI: 10.1016/j.econlet.2023.111447
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    References listed on IDEAS

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    1. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    2. 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.
    3. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    4. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Takuma Okura, 2024. "A topological proof of Terao's generalized Arrow's Impossibility Theorem," Papers 2408.14263, arXiv.org.

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    More about this item

    Keywords

    Social choice; Topological social choice; Mechanism design;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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