IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v99y2019icp49-62.html

Completeness and transitivity of preferences on mixture sets

Author

Listed:
  • Galaabaatar, Tsogbadral
  • Khan, M. Ali
  • Uyanık, Metin

Abstract

This paper contributes to the interplay of the behavioral assumptions on a binary relation and the structure of the choice space on which it is defined: the (ES) research program of Eilenberg (1941) and Sonnenschein (1965) to which Schmeidler (1971) is an especially influential contribution. We show that the presence of the Archimedean and mixture-continuity properties, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without decisiveness (completeness), or decisiveness without consistency, or in the presence of a weak consistency condition, both indecisiveness and inconsistency altogether. Second, we delineate how semi-transitivity of a relation is already hidden in linearity assumptions; and third, offer sufficient conditions that yield an isomorphism theorem that reduces a general setting to the usual order on an interval, and thereby yields the classic theorem of Herstein–Milnor (1953). We remark on extensions to a generalized mixture set of Chipman–Fishburn.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:99:y:2019:i:c:p:49-62
    DOI: 10.1016/j.mathsocsci.2019.03.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489619300277
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2019.03.004?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 look for a different version below or

    for a different version of it.

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. Galaabaatar, Tsogbadral, 2020. "On expected utility theorems on mixture sets," Economics Letters, Elsevier, vol. 197(C).
    4. Uyanık, Metin & Khan, M. Ali, 2019. "On the consistency and the decisiveness of the double-minded decision-maker," Economics Letters, Elsevier, vol. 185(C).
    5. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    6. 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).
    7. M. Ali Khan & Metin Uyanik, 2020. "Binary Relations in Mathematical Economics: On the Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot," Papers 2007.01952, arXiv.org.
    8. 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.
    9. 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.

    More about this item

    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:matsoc:v:99:y:2019:i:c:p:49-62. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/inca/505565 .

    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.