IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1484.html
   My bibliography  Save this paper

Rationality of Belief. Or: Why Bayesianism is Neither Necessary nor Sufficient for Rationality

Author

Listed:
  • Itzhak Gilboa

    (School of Economics, Tel Aviv University)

  • Andrew Postlewaite

    (Economics, University of Pennsylvania)

  • David Schmeidler

    (School of Mathematical Sciences, Tel Aviv Univ.)

Abstract

Economic theory reduces the concept of rationality to internal consistency. The practice of economics, however, distinguishes between rational and irrational beliefs. There is therefore an interest in a theory of rational beliefs, and of the process by which beliefs are generated and justified. We argue that the Bayesian approach is unsatisfactory for this purpose, for several reasons. First, the Bayesian approach begins with a prior, and models only a very limited form of learning, namely, Bayesian updating. Thus, it is inherently incapable of describing the formation of prior beliefs. Second, there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. Third, this lack of information is even more acute when we address the beliefs that can be attributed to a society. We hold that one needs to explore other approaches to the representation of information and of beliefs, which may be helpful in describing the formation of Bayesian as well as non-Bayesian beliefs.

Suggested Citation

  • Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief. Or: Why Bayesianism is Neither Necessary nor Sufficient for Rationality," Cowles Foundation Discussion Papers 1484, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1484
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d14/d1484.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    3. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    4. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2012. "Fact-Free Learning," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 8, pages 185-210, World Scientific Publishing Co. Pte. Ltd..
    5. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    9. 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. Tigran Melkonyan & Mark Pingle, 2010. "Ambiguity, pessimism, and rational religious choice," Theory and Decision, Springer, vol. 69(3), pages 417-438, September.
    2. Ani Guerdjikova & John Quiggin, 2018. "Heuristic Modes of Decision Making and Survival in Financial Markets," Post-Print hal-02086267, HAL.
    3. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," PIER Working Paper Archive 07-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Luigi Guiso & Paola Sapienza & Luigi Zingales, 2009. "Cultural Biases in Economic Exchange?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(3), pages 1095-1131.
    5. Luigi Guiso & Paola Sapienza & Luigi Zingales, 2010. "Civic Capital as the Missing Link," NBER Working Papers 15845, National Bureau of Economic Research, Inc.
    6. Giocoli, Nicola, 2011. "From Wald to Savage: homo economicus becomes a Bayesian statistician," MPRA Paper 34117, University Library of Munich, Germany.
    7. Scott Condie & Jayant V. Ganguli, 2011. "Ambiguity and Rational Expectations Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(3), pages 821-845.
    8. Ani Guerdjikova & John Quiggin, 2018. "Intertemporal Portfolio Choice with Incorrect Beliefs and Aversion to Surprise," Post-Print hal-02086151, HAL.
    9. Avdagic, Sabina, 2006. "One Path or Several? Understanding the Varied Development of Tripartism in New European Capitalisms," MPIfG Discussion Paper 06/5, Max Planck Institute for the Study of Societies.
    10. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    11. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," PIER Working Paper Archive 07-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    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. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version," PIER Working Paper Archive 07-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Jan 2007.
    2. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version," PIER Working Paper Archive 07-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Jan 2007.
    3. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    4. Lo, Kin Chung, 2009. "Correlated Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 144(2), pages 722-743, March.
    5. Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Sonderforschungsbereich 504 Publications 07-50, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
      • Eichberger, Jürgen & Kelsey, David, 2007. "Ambiguity," Papers 07-50, Sonderforschungsbreich 504.
    6. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    7. repec:awi:wpaper:0448 is not listed on IDEAS
    8. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier L'Haridon & Author-Name: Chen Li, 2013. "Learning under ambiguity: An experiment using initial public offerings on a stock market," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201331, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    9. 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.
    10. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    11. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    12. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," Working Papers halshs-00797631, HAL.
    13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    14. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    15. Yoram Halevy & Vincent Feltkamp, 2005. "A Bayesian Approach to Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 449-466.
    16. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    17. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 483-505, May.
    18. Riddel, Mary C. & Shaw, W. Douglass, 2006. "A Theoretically-Consistent Empirical Non-Expected Utility Model of Ambiguity: Nuclear Waste Mortality Risk and Yucca Mountain," Pre-Prints 23964, Texas A&M University, Department of Agricultural Economics.
    19. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    20. Jian Yang, 2015. "Game-theoretic Modeling of Players' Ambiguities on External Factors," Papers 1510.06812, arXiv.org, revised Apr 2017.
    21. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.

    More about this item

    Keywords

    Bayesianism; rationality; savage axioms;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    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:cwl:cwldpp:1484. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.