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Continuity and completeness under risk

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  • Dubra, Juan

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.

Suggested Citation

  • Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    • Handle: RePEc:eee:matsoc:v:61:y:2011:i:1:p:80-81
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    References listed on IDEAS

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    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.
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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. 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.

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