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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).

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File URL: http://128.118.178.162/eps/pe/papers/0506/0506012.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Public Economics with number 0506012.

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Date of creation: 16 Jun 2005
Date of revision: 16 Jun 2005
Handle: RePEc:wpa:wuwppe:0506012

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  1. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer, vol. 14(2), pages 233-243.
  2. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer, vol. 14(2), pages 295-302.
  3. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
  4. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  5. Luc Lauwers, 2004. "Topological manipulators form an ultrafilter," Social Choice and Welfare, Springer, vol. 22(3), pages 437-445, 06.
  6. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
  7. Yuliy M. Baryshnikov, 1997. "Topological and discrete social choice: in a search of a theory," Social Choice and Welfare, Springer, vol. 14(2), pages 199-209.
  8. 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.
  9. 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.
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