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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.

Suggested Citation

  • 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.
    • 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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    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. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    3. Susumu Cato, 2022. "Stable preference aggregation with infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 287-304, August.
    4. Bossert, Walter & Cato, Susumu, 2021. "Superset-robust collective choice rules," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 126-136.
    5. Susumu Cato, 2019. "The possibility of Paretian anonymous decision-making with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 587-601, December.
    6. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 329-341, November.
    7. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    8. Cato Susumu, 2018. "Hybrid Invariance and Oligarchic Structures," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-12, January.
    9. Andrei Gomberg & César 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.
    10. 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.
    11. Torres, Ricard, 2005. "Limiting Dictatorial rules," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 913-935, November.
    12. 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.
    13. Andrew Mackenzie, 2020. "An axiomatic analysis of the papal conclave," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 713-743, April.
    14. Mackenzie, Andrew, 2018. "A Game of the Throne of Saint Peter," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    15. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    16. Susumu Cato, 2020. "Quasi-stationary social welfare functions," Theory and Decision, Springer, vol. 89(1), pages 85-106, July.
    17. Ricard Torres, 2002. "Smallness of Invisible Dictators," Working Papers 0213, Centro de Investigacion Economica, ITAM, revised Sep 2003.

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    JEL classification:

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

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