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Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice

  • Machina Mark J.
  • Schmeidler David

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 67 (1995)
Issue (Month): 1 (October)
Pages: 106-128

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Handle: RePEc:eee:jetheo:v:67:y:1995:i:1:p:106-128
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  2. 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.
  3. 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.
  4. 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.
  5. Munier, Bertrand, 1989. "New models of decision under uncertainty: An interpretative essay," European Journal of Operational Research, Elsevier, vol. 38(3), pages 307-317, February.
  6. 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.
  7. 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.
  8. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
  10. 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.
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