Quasi-transitive and Suzumura consistent relations (original) (raw)

Abstract

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, in conjunction with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is weaker than transitivity but in the case of collective choice rules that satisfy further properties, this conjunction 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, and standard social choice axioms are satisfied.

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References

• Arrow KJ (1951/1963) Social choice and individual values. Wiley, New York
• Blair DH, Bordes G, Kelly JS, Suzumura K (1976) Impossibility theorems without collective rationality. J Econ Theory 13: 361–379
  Article Google Scholar
• Bossert W, Suzumura K (2008) A characterization of consistent collective choice rules. J Econ Theory 138:311–320. Erratum in 140:355
  Google Scholar
• Bossert W, Suzumura K (2010a) Consistency, choice, and rationality. Harvard University Press, Cambridge, MA
  Google Scholar
• Bossert W, Suzumura K (2010b) Product filters, acyclicity and Suzumura consistency. Discussion paper 20-2010. CIREQ, University of Montreal
• Hansson B (1976) The existence of group preference functions. Public Choice 38: 89–98
  Article Google Scholar
• Kirman AP, Sondermann D (1972) Arrow’s theorem, many agents, and invisible dictators. J Econ Theory 5: 267–277
  Article Google Scholar
• Mas-Colell A, Sonnenschein H (1972) General possibility theorems for group decisions. Rev Econ Stud 39: 185–192
  Article Google Scholar
• Plott CR (1973) Path independence, rationality, and social choice. Econometrica 41: 1075–1091
  Article Google Scholar
• Sen AK (1969) Quasi-transitivity, rational choice and collective decisions. Rev Econ Stud 36: 381–393
  Article Google Scholar
• Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco
  Google Scholar
• Suzumura K (1976) Remarks on the theory of collective choice. Economica 43: 381–390
  Article Google Scholar
• Weymark JA (1984) Arrow’s theorem with social quasi-orderings. Public Choice 42: 235–246
  Article Google Scholar

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Authors and Affiliations

1. Department of Economics and CIREQ, University of Montreal, P.O. Box 6128, Station Downtown, Montreal, QC, H3C 3J7, Canada
   Walter Bossert
2. School of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan
   Kotaro Suzumura

Authors

1. Walter Bossert
2. Kotaro Suzumura

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Correspondence toWalter Bossert.

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This article is dedicated to Maurice Salles in appreciation of his invaluable contribution and commitment to the academic community in general and the Society for Social Choice and Welfare in particular.

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Bossert, W., Suzumura, K. Quasi-transitive and Suzumura consistent relations.Soc Choice Welf 39, 323–334 (2012). https://doi.org/10.1007/s00355-011-0600-z

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• Received: 07 September 2011
• Accepted: 14 September 2011
• Published: 07 October 2011
• Issue date: July 2012
• DOI: https://doi.org/10.1007/s00355-011-0600-z

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