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

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  • H. Reiju Mihara

    (Kagawa University)

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.

Suggested Citation

  • H. Reiju Mihara, 1994. "Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras," Public Economics 9411001, EconWPA, revised 07 Sep 1998.
  • Handle: RePEc:wpa:wuwppe:9411001
    Note: LaTeX2.09 file; Appeared in Social Choice and Welfare (1997) 14: 503--512
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    References listed on IDEAS

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    1. Kelly, Jerry S., 1978. "Arrow Impossibility Theorems," Elsevier Monographs, Elsevier, edition 1, number 9780124033504 edited by Shell, Karl.
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    Cited by:

    1. 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.
    2. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 329-341, November.
    3. Kari Saukkonen, 2007. "Continuity of social choice functions with restricted coalition algebras," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 637-647, June.
    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.
    5. repec:bpj:bejtec:v:18:y:2018:i:1:p:12:n:16 is not listed on IDEAS
    6. Andrei Gomberg & C├ęsar Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 187-205, October.
    7. repec:eee:mateco:v:71:y:2017:i:c:p:28-35 is not listed on IDEAS
    8. Ricard Torres, 2002. "Smallness of Invisible Dictators," Working Papers 0213, Centro de Investigacion Economica, ITAM, revised Sep 2003.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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