Abstract
We give sufficient conditions for the existence of a numerical representation which is equivalent to consistency as defined by Suzumura (Economica 43:381–390).
Similar content being viewed by others
References
Alcantud J, Rodriguez-Palmero C (1999) Characterization of the existence of semicontinuous weak utilities. J Math Econ 32:503–509
Bossert W, Sprumont Y, Suzumura K (2002) Upper semicontinuous extensions of binary relations. J Math Econ 37:231–246
Bridges D (1983) Numerical representation of intransitive preference on a countable set. J Econ Theory 30:213–217
Chateauneuf A (1987) Continuous representations of a preference relation on a connected topological space. J Math Econ 16:139–146
Debreu G (1954) Representation of a preference ordering by a numerical function. In: Thrall R, Coombs C, Davis R(eds) Decision processes. Wiley, New York 159–166
Debreu G (1964) Continuity properties of Paretian Utility. Int Econ Rev 5:285–293
Doignon J, Ducamp A, Flamagne JC (1984) On realizable biorders and the biorder dimension of a relation. J Math Psychol 28:29–62
Doitchinov D (1991) A concept of completeness of quasi-uniform spaces. Topol Appl 38:205–217
Duggan J (1999) A general extension theorem for binary relations. J Econ Theory 86:1–16
Eilenberg S (1941) Ordered topological spaces. Am J Math 63:39–45
Fisburn P (1970) Intransitive indifference with unequal indifference intervals. J Math Psychol 7:144–149
Fishburn P (1999) Preference structures and their numerical representations. Theoretical Comput Sci 217:359–383
Rader T (1963) The existence of a utility function to represent preferences. Rev Econ Stud 30:229–232
Rodríguez-Palmero C (1997) A representation of acyclic preferences. Econ Lett 54:143–146
Schwartz T (1986) The logic of collective choice. University Press, New York
Suzumura K (1976) Remarks on the theory of collective. Economica 43:381–390
Suzumura K (1999) Paretian welfare judgements and Bergsonian social choice. Econ J 109:204–220
Suzumura K, Xu Y (2003) Recoverability of choice function and binary relations: some duality results. Soc Choice Welf 21:21–37
Suzumura K, Xu Y (2003) On constrained dual recoverability theorems. Math Soc Sci 45:143–154
Van Deemen MA (1997) Coalition formation and social choice. Academic Publishers, Dordrecht
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Andrikopoulos, A. A representation of consistent binary relations. SpanEconRev 9, 299–307 (2007). https://doi.org/10.1007/s10108-007-9024-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10108-007-9024-4