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A Model of Minimal Probabilistic Belief Revision

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  • Perea,Andrés

    (METEOR)

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).

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Bibliographic Info

Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 034.

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Date of creation: 2005
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Handle: RePEc:dgr:umamet:2005034

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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm

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Keywords: microeconomics ;

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  1. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  2. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  3. Larry Epstein, 2005. "An Axiomatic Model of Non-Bayesian Updating," RCER Working Papers 521, University of Rochester - Center for Economic Research (RCER).
  4. Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
  5. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
  6. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
  7. Majumdar, Dipjyoti, 2004. "An axiomatic characterization of Bayes' Rule," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 261-273, May.
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Cited by:
  1. 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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