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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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    1. 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.
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    3. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    4. Baryshnikov, Yuliy & Root, Joseph, 2024. "A topological proof of the Gibbard–Satterthwaite theorem," Economics Letters, Elsevier, vol. 234(C).
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    6. 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.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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