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Arrow's Theorem Through a Fixpoint Argument

Author

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  • Frank M. V. Feys

    (Delft University of Technology)

  • Helle Hvid Hansen

    (Delft University of Technology)

Abstract

We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our approach shows that dictatorships can be seen as fixpoints of a certain process.

Suggested Citation

  • Frank M. V. Feys & Helle Hvid Hansen, 2019. "Arrow's Theorem Through a Fixpoint Argument," Papers 1907.10381, arXiv.org.
    • Handle: RePEc:arx:papers:1907.10381
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    References listed on IDEAS

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    1. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
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    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    4. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
    5. Blau, Julian H, 1972. "A Direct Proof of Arrow's Theorem," Econometrica, Econometric Society, vol. 40(1), pages 61-67, January.
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