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A representation of consistent binary relations

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Spanish Economic Review

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).

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References

  • Alcantud J, Rodriguez-Palmero C (1999) Characterization of the existence of semicontinuous weak utilities. J Math Econ 32:503–509

    Article  Google Scholar 

  • Bossert W, Sprumont Y, Suzumura K (2002) Upper semicontinuous extensions of binary relations. J Math Econ 37:231–246

    Article  Google Scholar 

  • Bridges D (1983) Numerical representation of intransitive preference on a countable set. J Econ Theory 30:213–217

    Article  Google Scholar 

  • Chateauneuf A (1987) Continuous representations of a preference relation on a connected topological space. J Math Econ 16:139–146

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Doignon J, Ducamp A, Flamagne JC (1984) On realizable biorders and the biorder dimension of a relation. J Math Psychol 28:29–62

    Article  Google Scholar 

  • Doitchinov D (1991) A concept of completeness of quasi-uniform spaces. Topol Appl 38:205–217

    Article  Google Scholar 

  • Duggan J (1999) A general extension theorem for binary relations. J Econ Theory 86:1–16

    Article  Google Scholar 

  • Eilenberg S (1941) Ordered topological spaces. Am J Math 63:39–45

    Article  Google Scholar 

  • Fisburn P (1970) Intransitive indifference with unequal indifference intervals. J Math Psychol 7:144–149

    Article  Google Scholar 

  • Fishburn P (1999) Preference structures and their numerical representations. Theoretical Comput Sci 217:359–383

    Article  Google Scholar 

  • Rader T (1963) The existence of a utility function to represent preferences. Rev Econ Stud 30:229–232

    Article  Google Scholar 

  • Rodríguez-Palmero C (1997) A representation of acyclic preferences. Econ Lett 54:143–146

    Article  Google Scholar 

  • Schwartz T (1986) The logic of collective choice. University Press, New York

    Google Scholar 

  • Suzumura K (1976) Remarks on the theory of collective. Economica 43:381–390

    Article  Google Scholar 

  • Suzumura K (1999) Paretian welfare judgements and Bergsonian social choice. Econ J 109:204–220

    Article  Google Scholar 

  • Suzumura K, Xu Y (2003) Recoverability of choice function and binary relations: some duality results. Soc Choice Welf 21:21–37

    Article  Google Scholar 

  • Suzumura K, Xu Y (2003) On constrained dual recoverability theorems. Math Soc Sci 45:143–154

    Article  Google Scholar 

  • Van Deemen MA (1997) Coalition formation and social choice. Academic Publishers, Dordrecht

    Google Scholar 

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Correspondence to Athanasios Andrikopoulos.

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Andrikopoulos, A. A representation of consistent binary relations. SpanEconRev 9, 299–307 (2007). https://doi.org/10.1007/s10108-007-9024-4

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