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On the Utility Function Representability of Lexicographic Preferences

Author

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  • Shi, Bowen
  • Wang, Gaowang
  • Zhang, Zhixiang

Abstract

The paper examines the utility function representability of the lexicographic preferences over multiple attributes. A sufficient and necessary condition is provided: a lexicographic preference is utility function representable if and only if there is at most one attribute with uncountable levels and when such an attribute exists, it is the least important one. An auxiliary result of independent interest for general rational preferences is proved stating that the class of utility function representable sets is closed in countable unions under some mild condition.

Suggested Citation

  • Shi, Bowen & Wang, Gaowang & Zhang, Zhixiang, 2020. "On the Utility Function Representability of Lexicographic Preferences," MPRA Paper 102561, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:102561
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    File URL: https://mpra.ub.uni-muenchen.de/102561/1/MPRA_paper_102561.pdf
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    References listed on IDEAS

    as
    1. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    2. Peter C. Fishburn, 1975. "Axioms for Lexicographic Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 415-419.
    3. Bridges, Douglas S., 1983. "Numerical representation of intransitive preferences on a countable set," Journal of Economic Theory, Elsevier, vol. 30(1), pages 213-217, June.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Bridges, Douglas S., 1983. "A numerical representation of preferences with intransitive indifference," Journal of Mathematical Economics, Elsevier, vol. 11(1), pages 25-42, January.
    6. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
    7. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Lexicographic Preference; Utility Function Representation; Representable Class; Pseudo-continuous Points;
    All these keywords.

    JEL classification:

    • D0 - Microeconomics - - General

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