Alcantud, José Carlos R. and Bosi, Gianni and Zuanon, Magalì (2009): A selection of maximal elements under non-transitive indifferences.
Download (146Kb) | Preview
In this work we are concerned with maximality issues under intransitivity of the indifference. Our approach relies on the analysis of "undominated maximals" (cf., Peris and Subiza, J Math Psychology 2002). Provided that an agent's binary relation is acyclic, this is a selection of its maximal elements that can always be done when the set of alternatives is finite. In the case of semiorders, proceeding in this way is the same as using Luce's selected maximals.
We put forward a sufficient condition for the existence of undominated maximals for interval orders without any cardinality restriction. Its application to certain type of continuous semiorders is very intuitive and accommodates the well-known "sugar example" by Luce.
|Item Type:||MPRA Paper|
|Original Title:||A selection of maximal elements under non-transitive indifferences|
|Keywords:||Maximal element; Selection of maximals; Acyclicity; Interval order; Semiorder|
|Subjects:||D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory|
|Depositing User:||Jose Carlos R. Alcantud|
|Date Deposited:||10. Aug 2009 08:03|
|Last Modified:||13. Feb 2013 01:26|
Alcantud, J.C.R. (2002). Characterization of the existence of maximal elements of acyclic relations. Economic Theory, 19, 407-416.
Bosi, G., Candeal, J.C., Indurain, E., Oloriz, E., Zudaire, M. (2001). Numerical representations of interval orders. Order, 18, 171-190.
Bridges, D. S. (1985). Representing interval orders by a single real-valued function. Journal of Economic Theory, 36, 149-155.
Campion, M.J., Candeal, J.C., Indurain, E., Zudaire, M. (2008). Continuous representability of semiorders. Journal of Mathematical Psychology, 52, 48-54.
Fishburn, P. C. (1985). Interval Orders and Interval Graphs. John Wiley & Sons.
Luce, R. D. (1956). Semiorders and a theory of utility discrimination. Econometrica, 24, 178-191.
Peris, J. P. and Subiza, B. (2002). Choosing among maximals. Journal of Mathematical Psychology, 46, 1-11.
Willard, S. (1970). General Topology. Addison-Wesley.