A selection of maximal elements under non-transitive indifferences

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 &; Subiza, 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 present a sufficient condition for the existence of undominated maximals for interval orders without any cardinality restriction. Its application to certain types of continuous semiorders is very intuitive and accommodates the well-known “sugar example” by Luce.     

Revealed Indifference and Models of Choice Behavior

This paper introduces an approach to the study of rational choice behavior which is based on the concept of subjective indifference, as well as its relationships with both the classical preference-based approach and the choice behavior approach. With regard to the first relationship (which has already been studied in Alcantud, 2001, as a purely topological and order-theoretical problem) new considerations are now put forward in the decision theory context. In short, if a decisionmaker has some indifference classes defined on a choice set, then we know the conditions under which his/her tastes can be modeled by a continuous preference yielding these indifference classes. The second problem is posed and tackled here and gives place to a theory of revealed indifference, where both the decisive, and indecisive cases will be considered.