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Arrow's theorem, Weglorz' models and the axiom of choice

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Author Info

  • Norbert Brunner

    (U. Bodenkultur)

  • H. Reiju Mihara

    (Kagawa University)

Abstract

Applying Weglorz' models of set theory without the axiom of choice, we investigate Arrow-type social welfare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying "finite discrimination", if and only if in Weglorz' model there is a free ultrafilter on a set representing the individuals.

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File URL: http://128.118.178.162/eps/pe/papers/9902/9902001.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Public Economics with number 9902001.

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Date of creation: 02 Feb 1999
Date of revision: 01 Jun 2004
Handle: RePEc:wpa:wuwppe:9902001

Note: Mathematical Logic Quarterly (2000) 46: 335-359
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Web page: http://128.118.178.162

Related research

Keywords: Arrow impossibility theorem; anonymity; ecological welfare functions; axiomatic set theory; ultrafilters; Weglorz's models; permutation models;

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  1. KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997.
  3. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer, vol. 18(3), pages 543-553.
  4. H. Reiju Mihara, 1994. "Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras," Public Economics 9411001, EconWPA, revised 22 Nov 1994.
  5. H. Reiju Mihara, 1994. "Arrow's Theorem and Turing Computability," Public Economics 9408001, EconWPA, revised 23 Aug 1994.
  6. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
  7. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, October.
  8. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
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