IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v146y2011i5p2117-2125.html
   My bibliography  Save this article

Probabilistic sophistication and variational preferences

Author

Listed:
  • Tomasz, Strzalecki

Abstract

This paper shows that in the class of variational preferences the notion of probabilistic sophistication is equivalent to expected utility as long as there exists at least one event such that the independence axiom holds for bets on that event. This extends the result of Marinacci (2002) [13] and provides a novel interpretation of his result.

Suggested Citation

  • Tomasz, Strzalecki, 2011. "Probabilistic sophistication and variational preferences," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2117-2125, September.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2117-2125
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000949
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    6. Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September.
    7. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    8. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
    9. Chew Soo Hong & Jacob S. Sagi, 2006. "Event Exchangeability: Probabilistic Sophistication Without Continuity or Monotonicity," Econometrica, Econometric Society, vol. 74(3), pages 771-786, May.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-189, January.
    12. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    15. 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.
    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. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    2. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    3. 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.
    4. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    5. Grant, Simon & Rich, Patricia & Stecher, Jack, 2022. "Bayes and Hurwicz without Bernoulli," Journal of Economic Theory, Elsevier, vol. 199(C).
    6. Claudia Ravanelli & Gregor Svindland, 2014. "Comonotone Pareto optimal allocations for law invariant robust utilities on L 1," Finance and Stochastics, Springer, vol. 18(1), pages 249-269, January.
    7. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    8. Liebrich, Felix-Benedikt & Svindland, Gregor, 2019. "Efficient allocations under law-invariance: A unifying approach," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 28-45.
    9. Laeven, Roger J.A. & Rosazza Gianin, Emanuela & Zullino, Marco, 2024. "Law-invariant return and star-shaped risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 140-153.
    10. Sergio Almeida & Marcos Rangel, 2016. "Probabilistic Sophistication, Sources Of Uncertainty, And Cognitive Ability: Experimental Evidence," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 131, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    11. Werner, Jan, 2011. "Risk aversion for variational and multiple-prior preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 382-390.

    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. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    2. Mucahit Aygun & Roger J. A. Laeven & Mitja Stadje, 2025. "Higher-Order Ambiguity Attitudes," Papers 2501.13143, arXiv.org.
    3. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic Information," Management Science, INFORMS, vol. 67(7), pages 4310-4326, July.
    4. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    5. Werner, Jan, 2011. "Risk aversion for variational and multiple-prior preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 382-390.
    6. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    8. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    9. Principi, Giulio & Wakker, Peter P. & Wang, Ruodu, 0. "Antimonotonicity for preference axioms: the natural counterpart to comonotonicity," Theoretical Economics, Econometric Society.
    10. Treich, Nicolas, 2010. "The value of a statistical life under ambiguity aversion," Journal of Environmental Economics and Management, Elsevier, vol. 59(1), pages 15-26, January.
    11. Ilke Aydogan & Loïc Berger & Valentina Bosetti & Ning Liu, 2023. "Three Layers of Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 21(5), pages 2209-2236.
    12. Peng Liu & Tiantian Mao & Ruodu Wang, 2024. "Quantiles under ambiguity and risk sharing," Papers 2412.19546, arXiv.org.
    13. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • 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.
    14. 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.
    15. Faro, José Heleno, 2015. "Variational Bewley preferences," Journal of Economic Theory, Elsevier, vol. 157(C), pages 699-729.
    16. Sadowski, Philipp & Sarver, Todd, 2024. "Adaptive preferences: An evolutionary model of non-expected utility and ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 218(C).
    17. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    18. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    19. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    20. repec:hal:journl:hal-03031751 is not listed on IDEAS
    21. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.

    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:jetheo:v:146:y:2011:i:5:p:2117-2125. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.