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Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof

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  • H. Reiju Mihara

    (Kagawa University)

Abstract

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is "describable". The "describable" coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones.

Suggested Citation

  • H. Reiju Mihara, 1996. "Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof," Public Economics 9604002, University Library of Munich, Germany, revised 01 Jun 2004.
    • Handle: RePEc:wpa:wuwppe:9604002
    Note: Social Choice and Welfare (2001) 18: 543-553
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    References listed on IDEAS

    as
    1. 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.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    3. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
    4. Mihara, H. Reiju, 1999. "Arrow's theorem, countably many agents, and more visible invisible dictators1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 267-287, November.
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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. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, University Library of Munich, Germany, revised 01 Jun 2004.
    5. Cato, Susumu, 2021. "Preference aggregation and atoms in measures," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    6. Surekha Rao & Achille Basile & K. P. S. Bhaskara Rao, 2018. "On the ultrafilter representation of coalitionally strategy-proof social choice functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 1-13, April.
    7. 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.
    8. Torres, Ricard, 2005. "Limiting Dictatorial rules," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 913-935, November.
    9. 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.
    10. Mihara, H. Reiju, 1999. "Arrow's theorem, countably many agents, and more visible invisible dictators1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 267-287, November.

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    More about this item

    Keywords

    Gibbard-Satterthwaite theorem; cheatproofness; dominant strategy implementation; strategy-proof social choice functions; plurality rule; infinitely large societies; countable Boolean algebras of coalitions; free ultrafilters; models of knowledge; partitional information functions.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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