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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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
Bossert W, Suzumura K (2008) A characterization of consistent collective choice rules. J Econ Theory 138:311–320. Erratum in 140:355
Bossert W, Suzumura K (2010a) Consistency, choice, and rationality. Harvard University Press, Cambridge, MA
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
Kirman AP, Sondermann D (1972) Arrow’s theorem, many agents, and invisible dictators. J Econ Theory 5: 267–277
Mas-Colell A, Sonnenschein H (1972) General possibility theorems for group decisions. Rev Econ Stud 39: 185–192
Plott CR (1973) Path independence, rationality, and social choice. Econometrica 41: 1075–1091
Sen AK (1969) Quasi-transitivity, rational choice and collective decisions. Rev Econ Stud 36: 381–393
Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco
Suzumura K (1976) Remarks on the theory of collective choice. Economica 43: 381–390
Weymark JA (1984) Arrow’s theorem with social quasi-orderings. Public Choice 42: 235–246
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-011-0600-z