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A topological proof of Terao's generalized Arrow's Impossibility Theorem

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  • Takuma Okura

Abstract

In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using combinatorial arguments. This paper provides another proof of this generalized Arrow's Impossibility Theorem, using the idea of algebraic topology.

Suggested Citation

  • Takuma Okura, 2024. "A topological proof of Terao's generalized Arrow's Impossibility Theorem," Papers 2408.14263, arXiv.org.
    • Handle: RePEc:arx:papers:2408.14263
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    References listed on IDEAS

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    1. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    2. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    3. Baryshnikov, Yuliy & Root, Joseph, 2024. "A topological proof of the Gibbard–Satterthwaite theorem," Economics Letters, Elsevier, vol. 234(C).
    4. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    5. Tanaka, Yasuhito, 2009. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 241-249, March.
    6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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