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Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice

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Author Info
Mark J. Machina
David Schmeidler

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Abstract

In 1963, Anscombe and Aumann demonstrated that the introduction of an objective randomizing device into the Savage setting of subjective uncertainty considerably simplified the derivation of subjective probability from a decision maker's preferences over uncertain bets. The purpose of this paper is to present a more general derivation of classical subjective probability in such a framework, which neither assumes nor implies that the individual's risk preferences necessarily conform to the expected utility principle. We argue that the essence of "Bayesian rationality" is the assignment, correct manipulation, and proper updating of subjective event probablities when evaluating and comparing uncertain prospects, regardless of whether attitudes toward risk satisfy the expected utility property.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1088.

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Date of creation: Apr 1994
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Handle: RePEc:nwu:cmsems:1088

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July. [Downloadable!] (restricted)
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  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  3. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
  4. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December. [Downloadable!] (restricted)
  5. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-54, Summer. [Downloadable!] (restricted)
  6. Grether, David M, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 537-57, November. [Downloadable!] (restricted)
  7. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June. [Downloadable!] (restricted)
  8. 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.
  9. Sugden, Robert, 1991. "Rational Choice: A Survey of Contributions from Economics and Philosophy," Economic Journal, Royal Economic Society, vol. 101(407), pages 751-85, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Halevy, Yoram & Ozdenoren, Emre, 2008. "Uncertainty and Compound Lotteries: Calibration," Micro Theory Working Papers yoram_halevy-2008-7, Microeconomics.ca Website, revised 17 Jun 2008. [Downloadable!]
  2. ALLARD, Marie & BRONSARD, Camille & GOURIÉROUX, Christian, 2003. "Aversion Analysis," Cahiers de recherche 04-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
    • ALLARD, Marie & BRONSARD, Camille & GOURIÉROUX Christian, 2003. "Aversion Analysis," Cahiers de recherche 2003-06, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  3. Andrea Capotorti & Giulianella Coletti & Barbara Vantaggi, 2008. "Preferences Representable by a Lower Expectation: Some Characterizations," Theory and Decision, Springer, vol. 64(2), pages 119-146, March. [Downloadable!] (restricted)
  4. Edi Karni, 2005. "A New Approach to Modeling Decision-Making under Uncertainty and Defining Subjective Probabilities," Economics Working Paper Archive 519, The Johns Hopkins University,Department of Economics. [Downloadable!]
  5. Marciano Siniscalchi, 2003. "A Behavioral Characterization of Plausible Priors," Discussion Papers 1365, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  6. Mark J. Machina, 2001. "Almost-Objective Uncertainty," University of California at San Diego, Economics Working Paper Series 2001-12, Department of Economics, UC San Diego. [Downloadable!]
  7. 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. [Downloadable!]
    Other versions:
  8. Marciano Siniscalchi, . "Vector-Adjusted Expected Utility," Working Papers 191, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
  9. Edi Karni, 2007. "A new approach to modeling decision-making under uncertainty," Economic Theory, Springer, vol. 33(2), pages 225-242, November. [Downloadable!] (restricted)
  10. Peter Klibanoff & Emre Ozdenoren, 2007. "Subjective recursive expected utility," Economic Theory, Springer, vol. 30(1), pages 49-87, January. [Downloadable!] (restricted)
  11. Sarin, R. & Wakker, P., 1996. "A single-stage approach to Anscombe and Aumann's expected utility," Discussion Paper 45, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  12. Edi Karni, 2009. "A Theory of Bayesian Decision Making," Economics Working Paper Archive 550, The Johns Hopkins University,Department of Economics. [Downloadable!]
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