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Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras

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H. Reiju Mihara (Kagawa University)

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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. {Keywords} Arrow impossibility theorem, informational simplicity, coalitions, Boolean algebras, ultrafilters.

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Paper provided by EconWPA in its series Public Economics with number 9411001.

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Date of creation: 20 Nov 1994
Date of revision: 22 Nov 1994
Handle: RePEc:wpa:wuwppe:9411001

Note: LaTeX2.09 file; Appeared in Social Choice and Welfare (1997) 14: 503--512
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Web page: http://129.3.20.41

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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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  1. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004. [Downloadable!]
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  2. Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, EconWPA, revised 01 Jun 2004. [Downloadable!]
  3. H. Reiju Mihara, 1994. "Arrow's Theorem and Turing Computability," Public Economics 9408001, EconWPA, revised 23 Aug 1994. [Downloadable!]
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  4. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM. [Downloadable!]
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