A Unified Characterization of Belief Revision Rules

Dietrich, Franz and List, Christian and Bradley, Richard (2014): A Unified Characterization of Belief Revision Rules.

Abstract

This paper characterizes several 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 a new conditional probability function. Despite their differences, these revision rules can be characterized in terms of the same two axioms: responsiveness, which requires that revised beliefs incorporate what has been learnt, and conservativeness, which requires that beliefs on which the learnt input is `silent' do not change. So, the four revision rules apply the same principles, albeit to different learnt inputs. To illustrate that there is room for non-Bayesian belief revision in economic theory, we also sketch a simple decision-theoretic application.

• Item Type: MPRA Paper
• Language: English
• Keywords: Subjective probability, Bayes's rule, Jeffrey's rule, axiomatic foundations, fine-grained versus coarse-grained beliefs, unawareness
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; D - Microeconomics > D0 - General > D00 - General; D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

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