Dietrich, Franz and List, Christian and Bradley, Richard (2012): A Joint Characterization of Belief Revision Rules.

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Abstract
This paper characterizes different belief revision rules in a unified framework: Bayesian revision upon learning some event, Jeffrey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and `dualJeffrey' revision upon learning an entire new conditional probability function. Though seemingly different, these revision rules follow from the same two principles: responsiveness, which requires that revised beliefs be consistent with the learning experience, and conservativeness, which requires that those beliefs of the agent on which the learning experience is `silent' (in a technical sense) do not change. So, the four revision rules apply the same revision policy, yet to different kinds of learning experience.
Item Type:  MPRA Paper 

Original Title:  A Joint Characterization of Belief Revision Rules 
Language:  English 
Keywords:  Subjective probability, Bayes's rule, Jeffrey's rule, axiomatic foundations, unawareness 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C00  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search; Learning; Information and Knowledge; Communication; Belief D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General D  Microeconomics > D0  General > D00  General 
Item ID:  41240 
Depositing User:  Franz Dietrich 
Date Deposited:  12. Sep 2012 12:50 
Last Modified:  20. Feb 2013 08:19 
References:  Bradley, R. (2005) Radical Probabilism and Bayesian Conditioning, Philosophy of Science 72: 342364 Bradley, R. (2007) The Kinematics of Belief and Desire, Synthese 56(3): 513535 Csiszar, I. (1967) Information type 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: 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. (2010) Bayesian group belief, Social Choice and Welfare 35(4): 595626 Dietrich, F. (2012) Modelling change in individual characteristics: an axiomatic approach, Games and Economic Behavior, in press Douven, I., Romeijn, J. W. (2012) A new resolution of the Judy Benjamin Problem, Mind, in press Fagin, R., Halpern, J. Y. (1991a) A new approach to updating beliefs, Uncertainty in Artificial Intelligence 6 (Bonissone et al. (eds.), Elsevier Science Publishers) Fagin, R., Halpern, J. Y. (1991b), Uncertainty, belief, and probability, Computational Intelligence 7: 160173 Genest, C., McConway, K. J., Schervish, M. J. (1986) Characterization of externally Bayesian pooling operators, Annals of Statistics 14, 487501 Genest, C., Zidek, J. V. (1986) Combining probability distributions: a critique and an annotated bibliography, Statist. Sci. 1: 114148 Gilboa, I., Schmeidler, D. (1989) Maximin expected utility with a nonunique prior, Journal of Mathematical Economics 18: 14153 Gilboa, I., Schmeidler, D. (2001) A Theory of CaseBased Decisions, Cambridge University Press Grove, A., Halpern, J. (1998) Updating Sets of Probabilities. In: D. Poole et al. (eds.) Proceedings of the 14th Conference on Uncertainty in AI, Morgan Kaufmann, Madison, WI, USA, 173182 Grunwald, P., Halpern, J. (2003) Updating probabilities, Journal of AI Research 19: 24378 Halpern, J. (2003) Reasoning About Uncertainty, MIT Press, Cambridge, MA, USA Heifetz, A., Meier, M. and B. C. Schipper (2006). Interactive unawareness, Journal of Economic Theory, 130, 7894. Hylland, A., Zeckhauser, R. (1979) The impossibility of group decision making with separate aggregation of beliefs and values, Econometrica 47: 132136 Jeffrey, R. (1957) Contributions to the theory of inductive probability, PhD Thesis, Princeton University McConway, K. (1981) Marginalization and linear opinion pools, Journal of the American Statistical Association 76: 410414 Modica, S., Rustichini, A. (1999) Unawareness and partitional information structures, Games and Economic Behavior 27: 265298 Sarin, R., Wakker, P. (1994) A General Result for Quantifying Beliefs, Econometrica 62, 683685 Schmeidler, D. (1989) Subjective probability and expected utility without additivity, Econometrica 57: 57187 Shafer, G. (1976) A Mathematical Theory of Evidence, Princeton University Press Shafer, G. (1981) Jeffrey's rule of conditioning, Philosophy of Science 48: 33762 van Fraassen, B. C. (1981) A Problem for Relative Information Minimizers in Probability Kinematics, British Journal for the Philosophy of Science 32: 375379 Wakker, P. (1989) Continuous Subjective Expected Utility with Nonadditive Probabilities, Journal of Mathematical Economics 18: 127 Wakker, P. (2001) Testing and Characterizing Properties of Nonadditive Measures through Violations of the SureThing Principle, Econometrica 69: 103959 Wakker, P. (2010) Prospect Theory: For Risk and Ambiguity, Cambridge University Press 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/41240 