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Preference orderings represented by coherent upper and lower conditional previsions

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  • Serena Doria

    (University G. D’Annunzio)

Abstract

Preference orderings assigned by coherent lower and upper conditional previsions are defined and they are considered to define maximal random variables and Bayes random variables. Sufficient conditions are given such that a random variable is maximal if and only if it is a Bayes random variable. In a metric space preference orderings represented by coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are given.

Suggested Citation

  • Serena Doria, 2019. "Preference orderings represented by coherent upper and lower conditional previsions," Theory and Decision, Springer, vol. 87(2), pages 233-252, September.
    • Handle: RePEc:kap:theord:v:87:y:2019:i:2:d:10.1007_s11238-019-09699-3
    DOI: 10.1007/s11238-019-09699-3
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    References listed on IDEAS

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    1. Serena Doria, 2017. "On the disintegration property of coherent upper conditional prevision defined by the Choquet integral with respect to its associated Hausdorff outer measure," Annals of Operations Research, Springer, vol. 256(2), pages 253-269, September.
    2. Serena Doria, 2012. "Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure," Annals of Operations Research, Springer, vol. 195(1), pages 33-48, May.
    3. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    4. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. Serena Doria, 2015. "Symmetric coherent upper conditional prevision defined by the Choquet integral with respect to Hausdorff outer measure," Annals of Operations Research, Springer, vol. 229(1), pages 377-396, June.
    7. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    Cited by:

    1. Serena Doria, 2022. "Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    2. Serena Doria & Radko Mesiar & Adam Šeliga, 2020. "Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions," Mathematics, MDPI, vol. 9(1), pages 1-12, December.

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