TEL  Vol.4 No.6 , June 2014
Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference

We present different conditions for the existence of a pair of upper semicontinuous functions representing an interval order on a topological space without imposing any restrictive assumptions neither on the topological space nor on the representing functions. The particular case of second countable topological spaces, which is particularly interesting and frequent in economics, is carefully considered. Some final considerations concerning semiorders finish the paper.

Cite this paper
Bosi, G. and Zuanon, M. (2014) Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference. Theoretical Economics Letters, 4, 371-377. doi: 10.4236/tel.2014.46048.
[1]   Fishburn, P.C. (1970) Intransitive Indifference with Unequal Indifference Intervals. Journal of Mathematical Psychology, 7, 144-149.

[2]   Fishburn, P.C. (1985) Interval Orders and Interval Graphs. Wiley, New York.

[3]   Bosi, G., Candeal, J.C., Induráin, E., Oloriz, E. and Zudaire, M. (2001) Numerical Representations of Interval Orders. Order, 18, 171-190.

[4]   Doignon, J.-P., Ducamp, A. and Falmagne, J.-C. (1984) On Realizable Biorders and the Border Dimension of a Relation. Journal of Mathematical Psychology, 28, 73-109.

[5]   Bosi, G., Candeal, J.C. and Indurain, E. (2007) Continuous Representability of Interval Orders and Biorders. Journal of Mathematical Psychology, 51, 122-125.

[6]   Bosi, G., Campion, M., Candeal, J.C. and Indurain, E. (2007) Interval-Valued Representability of Qualitative Data: The Continuous Case. International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems, 15, 299-319.

[7]   Chateauneuf, A. (1987) Continuous Representation of a Preference Relation on a Connected Topological Space. Journal of Mathematical Economics, 16, 139-146.

[8]   Candeal, J.C. and Indurain, E. (2010) Semiorders and Thresholds of Utility Discrimination: Solving the Scott-Suppes Representability Problem. Journal of Mathematical Psychology, 54, 485-490.

[9]   Candeal, J.C., Estevan, A., Gutiérrez García, J. and Induráin, E. (2012) Semiorders with Separability Properties. Journal of Mathematical Psychology, 56, 445-451.

[10]   Alcantud, J.C.R., Bosi, G. and Zuanon, M. (2010) A Selection of Maximal Elements under Non-Transitive Indifferences. Journal of Mathematical Psychology, 54, 481-484.

[11]   Bridges, D.S. (1986) Numerical Representation of Interval Orders on a Topological Space. Journal of Economic Theory, 38, 160-166.

[12]   Bosi, G. and Zuanon, M. (2011) Representation of an Interval Order by Means of Two Upper Semicontinuous Functions. International Mathematical Forum, 6, 2067-2071.

[13]   Bosi, G. and Zuanon, M. (2014) Upper Semicontinuous Representations of Interval Orders. Mathematical Social Sciences, 60, 60-63.

[14]   Alcantud, J.C.R., Bosi, G., Rodriguez-Palmero, C. and Zuanon, M. (2006) Mathematical Utility Theory and the Re-presentability of Demand by Continuous Homogeneous Functions. Portuguese Economic Journal, 5, 195-205.

[15]   Bosi, G., Campión, M.J., Candeal, J.C., Induráin, E. and Zuanon, M. (2007) Isotonies on Ordered Cones through the Concept of a Decreasing Scale. Mathematical Social Sciences, 54, 115-127.

[16]   Alcantud, J.C.R. and Rodríguez-Palmero, C. (1999) Characterization of the Existence of Semicontinuous Weak Utilities. Journal of Mathematical Economics, 32, 503-509.

[17]   Bosi, G. and Herden, G. (2005) On a Strong Continuous Analogue of the Szpilrajn Theorem and Its Strengthening by Dushnik and Miller. Order, 22, 329-342.

[18]   Burgess, D.C.J. and Fitzpatrick, M. (1977) On Separation Axioms for Certain Types of Ordered Topological Space. Mathematical Proceedings of the Cambridge Philosophical Society, 82, 59-65.

[19]   Bosi, G. and Isler, R. (1995) Representing Preferences with Nontransitive Indifference by a Single Real-Valued Function. Journal of Mathematical Economics, 24, 621-631.