IDEAS home Printed from https://ideas.repec.org/p/aue/wpaper/2307.html
   My bibliography  Save this paper

Counterfactual Priors: A Bayesian Response to Ellsberg's Paradox

Author

Listed:
  • Phoebe Koundouri
  • Nikitas Pittis

    (University of Piraeus, Greece)

  • Panagiotis Samartzis

Abstract

This paper analyzes the root cause of Ellsberg-type choices. This class of problems shares the feature that at the time of the decision, t=m, the decision maker (DM) possesses partial information about the events/propositions of interest: DM knows the objective probabilities of some sub-class only, whereas she is uninformed about the probabilities of the complement of this subclass. As a result, DM may slip into the state of 'comparative ignorance' (see Heath and Tversky 1991 and Fox and Tversky 1995). Under this state, DM is likely to exhibit 'ambiguity aversion' (AA) for the events for which she does not have any information relative to those for which she does. AA, in turn, results in DM having non-coherent beliefs, that is, her prior probability function is not additive. A possible way to mitigate AA is to motivate DM to form her prior in a state of 'uniform ignorance'. This may be accomplished by inviting DM to bring herself to the hypothetical time t=0, in the context of which the information was still a contingency, and trace her "counterfactual prior back then". Under uniform ignorance, DM may adhere to the 'Principle of Indifference', thus identifying the prior counterfactual probability with the uniform distribution. Once this probability is elicited, DM can embody the existing information into her current, actual set of beliefs by means of Bayesian Conditionalization. In this case, we show that this set of beliefs is additive.

Suggested Citation

  • Phoebe Koundouri & Nikitas Pittis & Panagiotis Samartzis, 2023. "Counterfactual Priors: A Bayesian Response to Ellsberg's Paradox," DEOS Working Papers 2307, Athens University of Economics and Business.
    • Handle: RePEc:aue:wpaper:2307
    as

    Download full text from publisher

    File URL: http://wpa.deos.aueb.gr/docs/2023.Ellsberg.EL4.pdf
    File Function: First version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Chow, Clare Chua & Sarin, Rakesh K, 2001. "Comparative Ignorance and the Ellsberg Paradox," Journal of Risk and Uncertainty, Springer, vol. 22(2), pages 129-139, March.
    3. 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.
    4. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    7. Heath, Chip & Tversky, Amos, 1991. "Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
    8. Al-Najjar, Nabil I. & Weinstein, Jonathan, 2009. "The Ambiguity Aversion Literature: A Critical Assessment," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 249-284, November.
    9. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    10. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    11. Curley, Shawn P. & Yates, J. Frank & Abrams, Richard A., 1986. "Psychological sources of ambiguity avoidance," Organizational Behavior and Human Decision Processes, Elsevier, vol. 38(2), pages 230-256, October.
    12. Al-Najjar, Nabil I. & Weinstein, Jonathan, 2009. "Rejoinder: The €Œambiguity Aversion Literature: A Critical Assessmentâ€," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 357-369, November.
    13. 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)

    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. Phoebe Koundouri & Nikitas Pittis & Panagiotis Samartzis, 2024. "Comparative Ignorance as an Explanation of Ambiguity Aversion and Ellsberg Choices: A Survey with a New Proposal for Bayesian Training," DEOS Working Papers 2408, Athens University of Economics and Business.
    2. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    3. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    4. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    5. Olga Metzger & Thomas Spengler, 2019. "Modeling rational decisions in ambiguous situations: a multi-valued logic approach," Business Research, Springer;German Academic Association for Business Research, vol. 12(1), pages 271-290, April.
    6. Christoph Bühren & Fabian Meier & Marco Pleßner, 2023. "Ambiguity aversion: bibliometric analysis and literature review of the last 60 years," Management Review Quarterly, Springer, vol. 73(2), pages 495-525, June.
    7. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    8. Laure Cabantous & Denis Hilton, 2006. "De l'aversion à l'ambiguïté aux attitudes face à l'ambiguïté. Les apports d'une perspective psychologique en économie," Revue économique, Presses de Sciences-Po, vol. 57(2), pages 259-280.
    9. Craig S. Webb, 2017. "Purely subjective variational preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 121-137, June.
    10. Daniel Heyen, 2018. "Ambiguity aversion under maximum-likelihood updating," Theory and Decision, Springer, vol. 84(3), pages 373-386, May.
    11. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    12. Keiran Sharpe, 2023. "On the Ellsberg and Machina paradoxes," Theory and Decision, Springer, vol. 95(4), pages 539-573, November.
    13. Mercè Roca & Robin Hogarth & A. Maule, 2006. "Ambiguity seeking as a result of the status quo bias," Journal of Risk and Uncertainty, Springer, vol. 32(3), pages 175-194, May.
    14. Jean Desrochers & J. Francois Outreville, 2013. "Uncertainty, Ambiguity and Risk Taking: an experimental investigation of consumer behavior and demand for insurance," ICER Working Papers 10-2013, ICER - International Centre for Economic Research.
    15. Loïc Berger, 2011. "Smooth Ambiguity Aversion in the Small and in the Large," Working Papers ECARES ECARES 2011-020, ULB -- Universite Libre de Bruxelles.
    16. Casaca, Paulo & Chateauneuf, Alain & Faro, José Heleno, 2014. "Ignorance and competence in choices under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 143-150.
    17. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    18. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    19. Milos Borozan & Loreta Cannito & Barbara Luppi, 2022. "A tale of two ambiguities: A conceptual overview of findings from economics and psychology," Journal of Behavioral Economics for Policy, Society for the Advancement of Behavioral Economics (SABE), vol. 6(S1), pages 11-21, July.
    20. Douglas Norton & R. Isaac, 2012. "Experts with a conflict of interest: a source of ambiguity?," Experimental Economics, Springer;Economic Science Association, vol. 15(2), pages 260-277, June.

    More about this item

    Keywords

    counterfactual priors; ambiguity; ellsberg paradox;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aue:wpaper:2307. 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: Ekaterini Glynou (email available below). General contact details of provider: https://edirc.repec.org/data/diauegr.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.