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A note on mixture sets in decision theory

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  • Philippe Mongin

Abstract

Mixture sets were introduced by Herstein and Milnor (1953) into decision theory, where they are still widely used. This note clarifies the formal connection between mixture sets and convex sets. The results suggest that the former concept might be unnecessary for decision-theoretic purposes.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:24:y:2001:i:1:p:59-69
    DOI: 10.1007/s102030170010
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    Cited by:

    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    2. Danan, Eric & Gajdos, Thibault & Tallon, Jean-Marc, 2013. "Aggregating sets of von Neumann–Morgenstern utilities," Journal of Economic Theory, Elsevier, vol. 148(2), pages 663-688.
    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. Aniruddha Ghosh & Mohammed Ali Khan & Metin Uyanik, 2022. "The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation," Games, MDPI, vol. 13(4), pages 1-24, July.
    5. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    6. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    7. Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 139-147, November.
    8. Galaabaatar, Tsogbadral, 2020. "On expected utility theorems on mixture sets," Economics Letters, Elsevier, vol. 197(C).
    9. O’Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," The Warwick Economics Research Paper Series (TWERPS) 973, University of Warwick, Department of Economics.
    10. repec:hal:pseose:halshs-00788647 is not listed on IDEAS
    11. Alcantud, J. C. R., 2002. "Non-binary choice in a non-deterministic model," Economics Letters, Elsevier, vol. 77(1), pages 117-123, September.
    12. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    13. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.

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