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A Topological Proof of The Gibbard-Satterthwaite Theorem

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  • Yuliy Baryshnikov
  • Joseph Root

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

  • Yuliy Baryshnikov & Joseph Root, 2023. "A Topological Proof of The Gibbard-Satterthwaite Theorem," Papers 2309.03123, arXiv.org.
    • Handle: RePEc:arx:papers:2309.03123
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    File URL: http://arxiv.org/pdf/2309.03123
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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. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    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. Isaac Lara & Sergio Rajsbaum & Armajac Ravent'os-Pujol, 2024. "A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology," Papers 2402.06024, arXiv.org, revised Jul 2024.

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