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

Author

Listed:
  • 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.

Suggested Citation

  • Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, University Library of Munich, Germany, revised 01 Jun 2004.
  • Handle: RePEc:wpa:wuwppe:9902001
    Note: Mathematical Logic Quarterly (2000) 46: 335-359
    as

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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/9902/9902001.pdf
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    References listed on IDEAS

    as
    1. H. Reiju Mihara, 1997. "Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(4), pages 503-512.
    2. 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.
    3. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 543-553.
    4. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 257-276.
    5. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
    6. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, University Library of Munich, Germany, revised 01 Jun 2004.
    7. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Adrian Miroiu, 2020. "Coalitions of concerned voters: a characterization of the majority rule," Economics Bulletin, AccessEcon, vol. 40(4), pages 2717-2722.
    2. Mihara, H. Reiju, 1999. "Arrow's theorem, countably many agents, and more visible invisible dictators1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 267-287, November.

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    More about this item

    Keywords

    Arrow impossibility theorem; anonymity; ecological welfare functions; axiomatic set theory; ultrafilters; Weglorz's models; permutation models;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines

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