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Quasi-transitive and Suzumura consistent relations

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  • BOSSERT, Walter
  • SUZUMURA, Kotaro

Abstract

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules that satisfy further properties, the conjunction of quasi-transitivity and Suzumura consistency implies transitivity of the social relation. We prove this observation by characterizing the Pareto rule as the only collective choice rule such that collective preference relations are quasi-transitive and Suzumura consistent but not necessarily complete.

Suggested Citation

  • BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Quasi-transitive and Suzumura consistent relations," Cahiers de recherche 2009-05, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2009-05
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    File URL: http://hdl.handle.net/1866/2742
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    1. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 185-192.
    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. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive Coalitions and Coherence Properties," Cahiers de recherche 05-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
    5. 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.
    6. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 381-393.
    7. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    8. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
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    Cited by:

    1. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    2. 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.
    3. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    4. 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

    Transitivity; Suzumura Consistency; Quasi-Transitivity; Pareto Rule;
    All these keywords.

    JEL classification:

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

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