Dietrich, Franz and List, Christian and Bradley, Richard (2014): Belief revision generalized: A joint characterization of Bayes's and Jeffrey's rules. Forthcoming in: Journal of Economic Theory
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Abstract
We present a general framework for representing beliefrevision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a nonclassical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: 'responsiveness', which requires that revised beliefs incorporate what has been learnt, and 'conservativeness', which requires that beliefs on which the learnt input is silent do not change. To illustrate the use of nonBayesian belief revision in economic theory, we sketch a simple decisiontheoretic application.
Item Type:  MPRA Paper 

Original Title:  Belief revision generalized: A joint characterization of Bayes's and Jeffrey's rules 
Language:  English 
Keywords:  Subjective probability, Bayes's rule, Jeffrey's rule, axiomatic foundations, finegrained versus coarsegrained beliefs, unawareness 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C00  General D  Microeconomics > D0  General > D00  General D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness 
Item ID:  71304 
Depositing User:  Franz Dietrich 
Date Deposited:  15 May 2016 07:43 
Last Modified:  15 May 2016 07:44 
References:  Adams, E. (1975) The Logic of Conditionals. Dordrecht and Boston: Reidel. Bradley, R. (2005) Radical Probabilism and Bayesian Conditioning, Philosophy of Science 72(2): 342364. Bradley, R. (2007) The Kinematics of Belief and Desire, Synthese 56(3): 513535. Csiszar, I. (1967) Informationtype measures of difference of probability distributions and indirect observations, Studia Scientiarum Mathematicarum Hungarica 2: 299318. Csiszar, I. (1977) Information Measures: A Critical Survey, Transactions of the Seventh Prague Conference on Information Theory: 7386. Dekel, E., Lipman, B., Rustichini, A. (1998) Standard statespace models preclude unawareness, Econometrica 66(1): 159174. Dempster, A. P. (1967) Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics 38: 325399 Diaconis, P., Zabell, S. (1982) Updating subjective probability, Journal of the American Statistical Association 77: 822830. Dietrich, F. (2012) Modelling change in individual characteristics: an axiomatic framework, Games and Economic Behavior 76(2): 471494. Douven, I., Romeijn, J. W. (2011) A new resolution of the Judy Benjamin Problem, Mind 120(479): 637670. Grünwald, P., Halpern, J. (2003) Updating probabilities, Journal of AI Research 19: 243278. Halpern, J. (2003) Reasoning About Uncertainty, MIT Press, Cambridge, MA. Heifetz, A., Meier, M. and B. C. Schipper (2006). Interactive unawareness, Journal of Economic Theory, 130: 7894. Jeffrey, R. (1957) Contributions to the theory of inductive probability, PhD Thesis, Princeton University. Modica, S., Rustichini, A. (1999) Unawareness and partitional information structures, Games and Economic Behavior 27: 265298. Shafer, G. (1981) Jeffrey's rule of conditioning, Philosophy of Science 48: 337362. van Fraassen, B. C. (1981) A Problem for Relative Information Minimizers in Probability Kinematics, British Journal for the Philosophy of Science 32: 375379. Vineberg, S. (2011) Dutch Book Arguments, Stanford Encyclopedia of Philosophy (Summer 2011 Edition). 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/71304 
Available Versions of this Item

A Joint Characterization of Belief Revision Rules. (deposited 12 Sep 2012 12:50)

A Unified Characterization of Belief Revision Rules. (deposited 24 Nov 2014 06:16)
 Belief revision generalized: A joint characterization of Bayes's and Jeffrey's rules. (deposited 15 May 2016 07:43) [Currently Displayed]

A Unified Characterization of Belief Revision Rules. (deposited 24 Nov 2014 06:16)