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Decisive coalitions and coherence properties

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  • BOSSERT, Walter
  • SUZUMURA, Kotaro

Abstract

In a seminal contribution, Hansson has demonstrated that the family of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. If the population under consideration is infinite, his result implies the existence of nondictatorial social welfare functions. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine the structure of decisive coalitions and analogous concepts with alternative coherence properties, namely, acyclicity and Suzumura consistency, and without assuming that the social relation is complete.

Suggested Citation

  • BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive coalitions and coherence properties," Cahiers de recherche 2009-04, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2009-04
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    File URL: http://hdl.handle.net/1866/2741
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    References listed on IDEAS

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    1. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    2. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    3. Walter Bossert & Kotaro Suzumura, 2011. "Multi-profile intergenerational social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 493-509, September.
    4. Robert A. Pollak, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(1), pages 73-90.
    5. Samuelson, Paul A, 1977. "Reaffirming the Existence of "Reasonable" Bergson-Samuelson Social Welfare Functions," Economica, London School of Economics and Political Science, vol. 44(173), pages 81-88, February.
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    13. Prasanta K. Pattanaik & Koichi Tadenuma & Yongsheng Xu & Naoki Yoshihara (ed.), 2008. "Rational Choice and Social Welfare," Studies in Choice and Welfare, Springer, number 978-3-540-79832-3, December.
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    Cited by:

    1. Shino Takayama & Akira Yokotani, 2017. "Social choice correspondences with infinitely many agents: serial dictatorship," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 573-598, March.
    2. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    3. Walter Bossert & Kotaro Suzumura, 2012. "Quasi-transitive and Suzumura consistent relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 323-334, July.
    4. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    5. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.

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    More about this item

    Keywords

    Infinite-Population Social Choice; Decisiveness; Suzumura Consistency;
    All these keywords.

    JEL classification:

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

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