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Utility representation of an incomplete and nontransitive preference relation

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  • Nishimura, Hiroki
  • Ok, Efe A.

Abstract

The objective of this paper is to provide continuous utility representation theorems analogous to Debreu's classic utility representation theorem, albeit for preference relations that may fail to be complete and/or transitive. Specifically, we show that every (continuous and) reflexive binary relation on a (compact) metric space can be represented by means of the maxmin, or dually, minmax, of a (compact) set of (compact) sets of continuous utility functions. This notion of “maxmin multi-utility representation,” generalizes the recently proposed notions of “multi-utility representation” for preorders and “justifiable preferences” for complete and quasitransitive relations. As such, our main representation theorems lead to some new characterizations of these special cases as well.

Suggested Citation

  • Nishimura, Hiroki & Ok, Efe A., 2016. "Utility representation of an incomplete and nontransitive preference relation," Journal of Economic Theory, Elsevier, vol. 166(C), pages 164-185.
  • Handle: RePEc:eee:jetheo:v:166:y:2016:i:c:p:164-185
    DOI: 10.1016/j.jet.2016.07.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Nontransitive binary relations; Continuous utility; Debreu's theorem; Multi-utility representation;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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