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A Study of Lexicographic Expected Utility

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  • Peter C. Fishburn

    (Research Analysis Corporation)

Abstract

A relation L on a set of real vectors a, b, ... is a lexicographic order when a L b if and only if a \ne b and for every j such that b j j there is an i i i . A simple and direct derivation is given for a multidimensional utility function whose lexicographically-ordered expected utility vectors preserve an individual's preference order on a set of probability measures. All but one of Hausner's axioms yield an equivalence on the set of preference intervals, and the resulting bet of equivalence classes is shown to account for the hierarchy in the lexicographic structure. A lexicographic utility representation is noted for the finite-dimensional case. When Hausner's other axiom is added, his theorem for lexicographic linear utility is obtained. This theorem is applied to sets of simple and discrete probability measures.

Suggested Citation

  • Peter C. Fishburn, 1971. "A Study of Lexicographic Expected Utility," Management Science, INFORMS, vol. 17(11), pages 672-678, July.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:11:p:672-678
    DOI: 10.1287/mnsc.17.11.672
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    Cited by:

    1. Smeele, Nicholas V.R. & Chorus, Caspar G. & Schermer, Maartje H.N. & de Bekker-Grob, Esther W., 2023. "Towards machine learning for moral choice analysis in health economics: A literature review and research agenda," Social Science & Medicine, Elsevier, vol. 326(C).
    2. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    3. Lehmann, Daniel, 2001. "Expected Qualitative Utility Maximization," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 54-79, April.
    4. Petri, Henrik, 2020. "Lexicographic probabilities and robustness," Games and Economic Behavior, Elsevier, vol. 122(C), pages 426-439.
    5. Russell, Jeffrey Sanford, 2020. "Non-Archimedean preferences over countable lotteries," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 180-186.
    6. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    7. Ulrich Schmidt, 2001. "Lottery Dependent Utility: a Reexamination," Theory and Decision, Springer, vol. 50(1), pages 35-58, February.
    8. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.
    9. Nakamura, Yutaka, 2002. "Lexicographic quasilinear utility," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 157-178, May.

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