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On expected utility theorems on mixture sets

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  • Galaabaatar, Tsogbadral

Abstract

This note discusses expected utility theorems on mixture sets by Herstein and Milnor (1953) and Fishburn (1970). We show that the Archimedean axiom in Fishburn’s expected utility theorem can be weakened to a one-sided Archimedean axiom. We also show that the mixture continuity and transitivity axioms in Herstein–Milnor expected utility theorem can be further weakened under the strong independence axiom.

Suggested Citation

  • Galaabaatar, Tsogbadral, 2020. "On expected utility theorems on mixture sets," Economics Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:ecolet:v:197:y:2020:i:c:s0165176520303682
    DOI: 10.1016/j.econlet.2020.109608
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    References listed on IDEAS

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    1. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    2. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    3. Galaabaatar, Tsogbadral & Khan, M. Ali & Uyanık, Metin, 2019. "Completeness and transitivity of preferences on mixture sets," Mathematical Social Sciences, Elsevier, vol. 99(C), pages 49-62.
    4. Philippe Mongin, 2001. "A note on mixture sets in decision theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(1), pages 59-69, May.
    5. Nakamura, Yutaka, 2002. "Lexicographic quasilinear utility," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 157-178, May.
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    More about this item

    Keywords

    Archimedean axiom; Mixture continuity; Expected utility; Mixture set;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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