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 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.
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- Bridges, Douglas S., 1985. "Representing interval orders by a single real-valued function," Journal of Economic Theory, Elsevier, vol. 36(1), pages 149-155, June.
- J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer, vol. 19(2), pages 407-416.
- Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1997. "Choosing among maximals," Working Papers. Serie AD 1997-19, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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