IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v197y2020ics0165176520303682.html
   My bibliography  Save this article

On expected utility theorems on mixture sets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176520303682
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2020.109608?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    3. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    4. 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.
    5. Nakamura, Yutaka, 2002. "Lexicographic quasilinear utility," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 157-178, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Uyanik, Metin & Khan, M. Ali, 2022. "The continuity postulate in economic theory: A deconstruction and an integration," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    3. Uyanık, Metin & Khan, M. Ali, 2019. "On the consistency and the decisiveness of the double-minded decision-maker," Economics Letters, Elsevier, vol. 185(C).
    4. M. Ali Khan & Metin Uyanik, 2019. "On an Extension of a Theorem of Eilenberg and a Characterization of Topological Connectedness," Papers 1912.12787, arXiv.org.
    5. 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.
    6. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    7. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    8. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    9. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    10. 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).
    11. Metin Uyanik & Aniruddha Ghosh & M. Ali Khan, 2023. "Separately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer, and Bergstrom-Parks-Rader," Papers 2310.00531, arXiv.org.
    12. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.
    13. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Representation of strongly independent preorders by sets of scalar-valued functions," MPRA Paper 79284, University Library of Munich, Germany.
    14. Nakamura, Yutaka, 2015. "Mean-variance utility," Journal of Economic Theory, Elsevier, vol. 160(C), pages 536-556.
    15. Hauser, John R., 2014. "Consideration-set heuristics," Journal of Business Research, Elsevier, vol. 67(8), pages 1688-1699.
    16. repec:hal:pseose:halshs-00788647 is not listed on IDEAS
    17. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    18. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    19. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    20. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    21. Alcantud, J. C. R., 2002. "Non-binary choice in a non-deterministic model," Economics Letters, Elsevier, vol. 77(1), pages 117-123, September.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:197:y:2020:i:c:s0165176520303682. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.