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Imprecise probabilistic beliefs as a context for decision-making under ambiguity

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  • Nehring, Klaus

Abstract

Coherent imprecise probabilistic beliefs are modeled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general "Likelihood Compatibility" axiom relating preferences and probabilistic beliefs and characterize its implications for the class of "invariant biseparable" preferences that includes the MEU and CEU models among others.

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  • Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:1054-1091
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    Cited by:

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    2. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Documents de travail du Centre d'Economie de la Sorbonne 20008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Panagiotis Andrikopoulos & Nick Webber, 2019. "Understanding time-inconsistent heterogeneous preferences in economics and finance: a practice theory approach," Annals of Operations Research, Springer, vol. 282(1), pages 3-26, November.
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      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Cerreia-Vioglio, Simone, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    7. Hill, Brian, 2011. "Deferral, incomplete preferences and confidence," HEC Research Papers Series 940, HEC Paris.
    8. Giraud, Raphaël, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    9. Alon, Shiri & Lehrer, Ehud, 2014. "Subjective multi-prior probability: A representation of a partial likelihood relation," Journal of Economic Theory, Elsevier, vol. 151(C), pages 476-492.
    10. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Post-Print halshs-02900497, HAL.
    11. Harrison-Trainor, Matthew & Holliday, Wesley H. & Icard, Thomas F., 2018. "Inferring probability comparisons," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 62-70.
    12. Gul, Faruk & Pesendorfer, Wolfgang, 2020. "Calibrated uncertainty," Journal of Economic Theory, Elsevier, vol. 188(C).
    13. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    14. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    15. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Working Papers halshs-02563318, HAL.
    16. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    17. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    18. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02563318, HAL.
    19. Yehuda Izhakian & Zur Izhakian, 2015. "Decision making in phantom spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 59-98, January.
    20. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2020. "Objective rationality foundations for (dynamic) alpha-MEU," Cowles Foundation Discussion Papers 2244R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2021.
    21. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02900497, HAL.

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