0 such that if pPq, then ap+(1-a)rPq. Complete: for all p,q, either pRq or qRp.
(This abstract was borrowed from another version of this item.)"> 0 such that if pPq, then ap+(1-a)rPq. Complete: for all p,q, either pRq or qRp.
(This abstract was borrowed from another version of this item.)">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/mnt/wpaper/1004.html
   My bibliography  Save this paper

Continuity and Completeness under Risk

Author

Listed:
  • Juan Dubra

    (Universidad de Montevideo)

Abstract
Suppose some non-degenerate preferences R, with strict part P, over risky outcomes satisfy Independence. Then, when they satisfy any two of the following axioms, they satisfy the third. Herstein-Milnor: for all lotteries p,q,r, the set of a's for which ap+(1-a)qRr is closed. Archimedean: for all p,q,r there exists a>0 such that if pPq, then ap+(1-a)rPq. Complete: for all p,q, either pRq or qRp.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Juan Dubra, 2010. "Continuity and Completeness under Risk," Documentos de Trabajo/Working Papers 1004, Facultad de Ciencias Empresariales y Economia. Universidad de Montevideo..
    • Handle: RePEc:mnt:wpaper:1004
    as

    Download full text from publisher

    File URL: https://www2.um.edu.uy/fcee_papers/2010/working_paper_um_cee_2010_04.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    2. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    3. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    4. Karni, Edi, 2007. "Archimedean and continuity," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 332-334, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    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. Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
    5. 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.
    6. Karni, Edi, 2011. "Continuity, completeness and the definition of weak preferences," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 123-125, September.
    7. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    8. Leandro Gorno, 2018. "The structure of incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 159-185, July.
    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. Karni, Edi & Safra, Zvi, 2015. "Continuity, completeness, betweenness and cone-monotonicity," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 68-72.
    11. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    12. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    13. Galaabaatar, Tsogbadral, 2020. "On expected utility theorems on mixture sets," Economics Letters, Elsevier, vol. 197(C).
    14. 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.
    15. Uyanık, Metin & Khan, M. Ali, 2019. "On the consistency and the decisiveness of the double-minded decision-maker," Economics Letters, Elsevier, vol. 185(C).
    16. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    17. 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).
    18. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    19. Tsogbadral Galaabaatar & Edi Karni, 2010. "Objective and Subjective Expected Utility with Incomplete Preferences," Economics Working Paper Archive 572, The Johns Hopkins University,Department of Economics.
    20. 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.
    21. 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.
    22. Gerasimou, Georgios, 2015. "(Hemi)continuity of additive preference preorders," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 79-81.
    23. Georgios Gerasimou, 2013. "On continuity of incomplete preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 157-167, June.
    24. Diecidue, Enrico & Somasundaram, Jeeva, 2017. "Regret theory: A new foundation," Journal of Economic Theory, Elsevier, vol. 172(C), pages 88-119.
    25. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.

    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. 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.
    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. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    4. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    5. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    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. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    8. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.
    9. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    10. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    11. Karni, Edi & Vierø, Marie-Louise, 2023. "Comparative incompleteness: Measurement, behavioral manifestations and elicitation," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 423-442.
    12. Leandro Nascimento, 2011. "Remarks on the consumer problem under incomplete preferences," Theory and Decision, Springer, vol. 70(1), pages 95-110, January.
    13. Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. 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.
    15. 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).
    16. repec:san:wpecon:1305 is not listed on IDEAS
    17. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2013. "Representations of preorders by strong multi-objective functions," MPRA Paper 52329, University Library of Munich, Germany.
    18. Georgios Gerasimou, 2013. "On continuity of incomplete preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 157-167, June.
    19. Karni, Edi, 2011. "Continuity, completeness and the definition of weak preferences," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 123-125, September.
    20. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    21. Leandro Gorno, 2018. "The structure of incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 159-185, July.

    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:mnt:wpaper:1004. 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: Mathias Ribeiro (email available below). General contact details of provider: https://edirc.repec.org/data/fceumuy.html .

    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.