A Unified Characterization of Belief Revision Rules

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.