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On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem (forthcoming in ``Applied Mathematics and Computation''(Elsevier))

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  • Yasuhito Tanaka

    (Doshisha University)

Abstract

We will show that in the case where there are two individuals and three alternatives (or under the assumption of free-triple property) the Arrow impossibility theorem for social welfare functions that there exists no social welfare function which satisfies transitivity, Pareto principle, independence of irrelevant alternatives, and has no dictator is equivalent to the Brouwer fixed point theorem on a 2-dimensional ball (circle).

Suggested Citation

  • Yasuhito Tanaka, 2005. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem (forthcoming in ``Applied Mathematics and Computation''(Elsevier))," Public Economics 0506012, University Library of Munich, Germany, revised 17 Jun 2005.
    • Handle: RePEc:wpa:wuwppe:0506012
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    References listed on IDEAS

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    1. Yuliy M. Baryshnikov, 1997. "Topological and discrete social choice: in a search of a theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 199-209.
    2. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
    3. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    4. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    5. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    6. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 295-302.
    7. Luc Lauwers, 2004. "Topological manipulators form an ultrafilter," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 437-445, June.
    8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    9. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 233-243.
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    Cited by:

    1. Yasuhito Tanaka, 2009. "The Hex Game Theorem And The Arrow Impossibility Theorem: The Case Of Weak Orders," Metroeconomica, Wiley Blackwell, vol. 60(1), pages 77-90, February.
    2. Alessio Faccia & Leonardo José Mataruna-Dos-Santos & Hussein Munoz Helù & Daniel Range, 2020. "Measuring and Monitoring Sustainability in Listed European Football Clubs: A Value-Added Reporting Perspective," Sustainability, MDPI, vol. 12(23), pages 1-13, November.

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    More about this item

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • H - Public Economics

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