Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice
AbstractIn 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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Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1088.
Date of creation: Apr 1994
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- Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
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.:
- 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.
- Mark J. Machina & David Schmeidler, 1990.
"A More Robust Definition of Subjective Probability,"
Discussion Paper Serie A
306, University of Bonn, Germany.
- Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
- Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
- Grether, David M., .
"Bayes Rule as a Descriptive Model: The Representativeness Heuristic,"
245, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- 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.
- Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
- 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.
- 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.
- 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.
- Edi Karni & Marie-Louise Vierø, 2013. "Probabilistic Sophistication and Reverse Bayesianism," Working Papers 1303, Queen's University, Department of Economics.
- Sarin, Rakesh & Wakker, Peter, 1997.
"A Single-Stage Approach to Anscombe and Aumann's Expected Utility,"
Review of Economic Studies,
Wiley Blackwell, vol. 64(3), pages 399-409, July.
- Sarin, R. & Wakker, P.P., 1996. "A Single-Stage Approach to Anscombe and Aumann's Expected Utility," Discussion Paper 1996-45, Tilburg University, Center for Economic Research.
- Marciano Siniscalchi, 2003.
"A Behavioral Characterization of Plausible Priors,"
234936000000000064, UCLA Department of Economics.
- Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012.
"Probabilistic sophistication, second order stochastic dominance and uncertainty aversion,"
Journal of Mathematical Economics,
Elsevier, vol. 48(5), pages 271-283.
- Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2010. "Probabilistic Sophistication, Second Order Stochastic Dominance, and Uncertainty Aversion," Carlo Alberto Notebooks 174, Collegio Carlo Alberto.
- Sarin, Rakesh & Wakker, Peter P., 2000. "Cumulative dominance and probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 191-196, September.
- Machina, Mark J, 2001. "Almost-Objective Uncertainty," University of California at San Diego, Economics Working Paper Series qt3ps1k85f, Department of Economics, UC San Diego.
- Edi Karni, 2011. "A theory of Bayesian decision making with action-dependent subjective probabilities," Economic Theory, Springer, vol. 48(1), pages 125-146, September.
- ALLARD, Marie & BRONSARD, Camille & GOURIÉROUX Christian, 2003.
Cahiers de recherche
2003-06, Universite de Montreal, Departement de sciences economiques.
- Marciano Siniscalchi, . "Vector-Adjusted Expected Utility," Working Papers 191, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- 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
08-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Dec 2008.
- 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.
- Ghossoub, Mario, 2011. "Towards a Purely Behavioral Definition of Loss Aversion," MPRA Paper 37628, University Library of Munich, Germany, revised 23 Mar 2012.
- 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.
- Peter Klibanoff & Emre Ozdenoren, 2007. "Subjective recursive expected utility," Economic Theory, Springer, vol. 30(1), pages 49-87, January.
- 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.
- Edi Karni, 2009. "A Theory of Bayesian Decision Making," Economics Working Paper Archive 550, The Johns Hopkins University,Department of Economics.
- repec:ebl:ecbull:v:4:y:2006:i:37:p:1-7 is not listed on IDEAS
- Edi Karni, 2007. "A new approach to modeling decision-making under uncertainty," Economic Theory, Springer, vol. 33(2), pages 225-242, November.
- Edi Karni, 2009. "A Theory of Bayesian Decision Making," EIEF Working Papers Series 0904, Einaudi Institute for Economics and Finance (EIEF), revised May 2009.
- Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
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