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A selection of maximal elements under non-transitive indifferences

Author

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  • Alcantud, José Carlos R.
  • Bosi, Gianni
  • Zuanon, Magalì

Abstract

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.

Suggested Citation

  • Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2009. "A selection of maximal elements under non-transitive indifferences," MPRA Paper 16601, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16601
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    File URL: https://mpra.ub.uni-muenchen.de/16601/1/MPRA_paper_16601.pdf
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    References listed on IDEAS

    as
    1. 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).
    2. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 407-416.
    3. 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.
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    Cited by:

    1. Gianni Bosi & Magalì E. Zuanon, 2017. "Maximal elements of quasi upper semicontinuous preorders on compact spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-117, April.
    2. Bosi, Gianni & Zuanon, Magalì, 2014. "Upper semicontinuous representations of interval orders," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 60-63.
    3. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.

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    More about this item

    Keywords

    Maximal element; Selection of maximals; Acyclicity; Interval order; Semiorder;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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