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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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    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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