Dietrich, Franz and List, Christian and Bradley, Richard (2012): A Joint Characterization of Belief Revision Rules.
Preview |
PDF
MPRA_paper_41240.pdf Download (361kB) | Preview |
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 `dual-Jeffrey' 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 ; Unawareness 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: | 02 Oct 2019 17:20 |
References: | Bradley, R. (2005) Radical Probabilism and Bayesian Conditioning, Philosophy of Science 72: 342-364 Bradley, R. (2007) The Kinematics of Belief and Desire, Synthese 56(3): 513-535 Csiszar, I. (1967) Information type measures of difference of probability distributions and indirect observations, Studia Scientiarum Mathematicarum Hungarica 2: 299-318 Csiszar, I. (1977) Information Measures: A Critical Survey, Transactions of the Seventh Prague Conference: 73-86 Dekel, E., Lipman, B., Rustichini, A. (1998) Standard state-space models preclude unawareness, Econometrica 66(1): 159-174 Dempster, A. P. (1967) Upper and lower probabilities induced by a multi-valued mapping, Annals of Mathematical Statistics 38: 325-399 Diaconis, P., Zabell, S. (1982) Updating subjective probability, Journal of the American Statistical Association 77: 822-830 Dietrich, F. (2010) Bayesian group belief, Social Choice and Welfare 35(4): 595-626 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: 160-173 Genest, C., McConway, K. J., Schervish, M. J. (1986) Characterization of externally Bayesian pooling operators, Annals of Statistics 14, 487-501 Genest, C., Zidek, J. V. (1986) Combining probability distributions: a critique and an annotated bibliography, Statist. Sci. 1: 114-148 Gilboa, I., Schmeidler, D. (1989) Maximin expected utility with a non-unique prior, Journal of Mathematical Economics 18: 141-53 Gilboa, I., Schmeidler, D. (2001) A Theory of Case-Based 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, 173-182 Grunwald, P., Halpern, J. (2003) Updating probabilities, Journal of AI Research 19: 243-78 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, 78-94. Hylland, A., Zeckhauser, R. (1979) The impossibility of group decision making with separate aggregation of beliefs and values, Econometrica 47: 1321-36 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: 410-414 Modica, S., Rustichini, A. (1999) Unawareness and partitional information structures, Games and Economic Behavior 27: 265-298 Sarin, R., Wakker, P. (1994) A General Result for Quantifying Beliefs, Econometrica 62, 683-685 Schmeidler, D. (1989) Subjective probability and expected utility without additivity, Econometrica 57: 571-87 Shafer, G. (1976) A Mathematical Theory of Evidence, Princeton University Press Shafer, G. (1981) Jeffrey's rule of conditioning, Philosophy of Science 48: 337-62 van Fraassen, B. C. (1981) A Problem for Relative Information Minimizers in Probability Kinematics, British Journal for the Philosophy of Science 32: 375--379 Wakker, P. (1989) Continuous Subjective Expected Utility with Nonadditive Probabilities, Journal of Mathematical Economics 18: 1-27 Wakker, P. (2001) Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle, Econometrica 69: 1039-59 Wakker, P. (2010) Prospect Theory: For Risk and Ambiguity, Cambridge University Press |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/41240 |
Available Versions of this Item
- A Joint Characterization of Belief Revision Rules. (deposited 12 Sep 2012 12:50) [Currently Displayed]