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Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice

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  • Mark J. Machina
  • David Schmeidler

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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  1. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  2. 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.
  3. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. 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.
  5. 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.
  6. Grether, David M., . "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," Working Papers 245, California Institute of Technology, Division of the Humanities and Social Sciences.
  7. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
  8. 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.
  9. 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.
  10. 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.
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