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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.

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File URL: http://hdl.handle.net/1866/2742
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2009-05.

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Length: 15 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:mtl:montde:2009-05

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Keywords: Transitivity; Suzumura Consistency; Quasi-Transitivity; Pareto Rule;

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References

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  1. 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.
  2. Bossert, Walter & Suzumura, Kotaro, 2009. "Decisive coalitions and coherence properties," PIE/CIS Discussion Paper 427, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  3. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
  4. Mas-Colell, Andreu & Sonnenschein, Hugo, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Wiley Blackwell, vol. 39(2), pages 185-92, April.
  5. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "A Characterization of Consistent Collective Choice Rules," Cahiers de recherche 2006-12, Universite de Montreal, Departement de sciences economiques.
  6. KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  8. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
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Cited by:
  1. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
  2. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer, vol. 34(4), pages 611-630, April.

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