A Unied Characterization of Belief-Revision Rules

This paper characterizes several belief-revision rules in a uni…ed framework: Bayesian revision upon learning some event, Je¤rey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and ‘dual-Je¤rey’revision upon learning a new conditional probability function. Despite their di¤erences, 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 di¤erent learnt inputs. To illustrate that there is room for non-Bayesian belief revision in economic theory, we also sketch a simple decision-theoretic application. Keywords: Subjective probability, Bayes’s rule, Je¤rey’s rule, axiomatic foundations, …ne-grained versus coarse-grained beliefs, unawareness