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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)

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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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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://129.3.20.41

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

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Find related papers by 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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  1. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276. [Downloadable!] (restricted)
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  2. H. Reiju Mihara, 1997. "Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras," Social Choice and Welfare, Springer, vol. 14(4), pages 503-512. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
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  7. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237. [Downloadable!] (restricted)
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