Abstract
In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of characteristics; (2) For every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules.
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References
Alchourrón C.E., Makinson D. (1982) The logic of theory change: Contraction functions and their associated revision function. Theoria 48, 14–37
Anscombe F.J., Aumann R. (1963) A definition of subjective probability. Annals of Mathematical Statistics 34: 199–205
Epstein, L.G. (2005), An Axiomatic Model of non-Bayesian Updating, University of Rochester.
Epstein L.G., Schneider M. (2003) Recursive multiple-priors. Journal of Economic Theory 113: 1–31
Gärdenfors P. (1988) Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press, Cambridge, MA
Ghirardato P. (2002) Revisiting Savage in a conditional world. Economic Theory 20: 83–92
Gul F., Pesendorfer W. (2001) Temptation and self-control. Econometrica 69: 1403–1435
Hendon E., Jacobsen J., Sloth B. (1996) The one-shot deviation principle for sequential rationality. Games and Economic Behavior 12: 274–282
Lehmann D., Magidor M., Schlechta K. (2001) Distance semantics for belief revision. Journal of Symbolic Logic 66: 295–317
Lewis D.K. (1973) Counterfactuals. Blackwell, Oxford
Lewis D.K. (1976) Probabilities of conditionals and conditional probabilities. Philosophical Review 85: 297–315
Katsuno, H. and Mendelzon, A.O. (1992), On the difference between updating a knowledge base and revising it, in Gärdenfors, P. (ed.), Belief Revision, Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, pp. 183–203.
Majumdar D. (2004) An axiomatic characterization of Bayes’ rule. Mathematical Social Sciences 47: 261–273
Perea A. (2002) A note on the one-deviation property in extensive form games. Games and Economic Behavior 40: 322–338
Savage L.J. (1954) The Foundations of Statistics. Wiley, New York
Schulte O. (2002) Minimal belief change, Pareto-optimality and logical consequence. Economic Theory 19: 105–144
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Perea, A. A Model of Minimal Probabilistic Belief Revision. Theory Decis 67, 163–222 (2009). https://doi.org/10.1007/s11238-007-9073-z
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DOI: https://doi.org/10.1007/s11238-007-9073-z