A Model of Minimal Probabilistic Belief Revision
Abstract
A probabilistic belief revision function assigns to every initial probabilistic belief and every observable event some revised probabilistic belief that only attaches positive probability to states in this event. We propose three axioms for belief revision functions: (1) linearity, meaning that if the decision maker observes that the true state is in {a,b}, and hence state c is impossible, then the proportions of c''s initial probability that are shifted to a and b, respectively, should be independent of c''s initial probability; (2) transitivity, stating that if the decision maker deems belief β equally similar to states a and b, and deems β equally similar to states b and c, then he should deem β equally similar to states a and c; (3) information-order independence, stating that the way in which information is received should not matter for the eventual revised belief. We show that a belief revision function satisfies the three axioms above if and only if there is some linear one-to-one function ϕ, transforming the belief simplex into a polytope that is closed under orthogonal projections, such that the belief revision function satisfies minimal belief revision with respect to ϕ. By the latter, we mean that the decision maker, when having initial belief β₁ and observing the event E, always chooses the revised belief β₂ that attaches positive probability only to states in E and for which ϕ(β₂) has minimal Euclidean distance to ϕ(β₁).Download Info
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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 034.Length:
Date of creation: 2005
Date of revision:
Handle: RePEc:dgr:umamet:2005034
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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
Related research
Keywords: microeconomics ;Other versions of this item:
- Andrés Perea, 2009. "A Model of Minimal Probabilistic Belief Revision," Theory and Decision, Springer, vol. 67(2), pages 163-222, August.
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-04 (All new papers)
References
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- De Marco, Giuseppe & Romaniello, Maria, 2008. "Evolution of Coalition Structures under Uncertainty," MPRA Paper 14725, University Library of Munich, Germany, revised 16 Apr 2009.
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