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Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras

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  • H. Reiju Mihara

    (Economics, Kagawa University, Takamatsu, Kagawa 760, Japan)

Abstract

In the very general setting of Armstrong (1980) for Arrow's Theorem, I show two results. First, in an infinite society, Anonymity is inconsistent with Unanimity and Independence if and only if a domain for social welfare functions satisfies a modest condition of richness. While Arrow's axioms can be satisfied, unequal treatment of individuals thus persists. Second, Neutrality is consistent with Unanimity (and Independence). However, there are both dictatorial and nondictatorial social welfare functions satisfying Unanimity and Independence but not Neutrality. In Armstrong's setting, one can naturally view Neutrality as a stronger condition of informational simplicity than Independence.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 14 (1997)
Issue (Month): 4 ()
Pages: 503-512

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Handle: RePEc:spr:sochwe:v:14:y:1997:i:4:p:503-512

Note: Received: 11 August 1994/Accepted: 1 April 1996
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Cited by:
  1. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276.
  2. Andrei Gomberg & C├ęsar Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer, vol. 25(1), pages 187-205, October.
  3. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 329-341, November.
  4. Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, EconWPA, revised 01 Jun 2004.

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