Belief revision generalized: A joint characterization of Bayes' and Jeffrey's rules

We present a general framework for representing belief-revision rules and use it to characterize Bayes’s rule as a classical example and Je¤rey’s rule as a non-classical one. In Je¤rey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’s rule, but a new assignment of probabilities to some events. Despite their di¤erences, Bayes’s and Je¤rey’s rules can be characterized in terms of the same 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. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. Keywords: Belief revision, subjective probability, Bayes’s rule, Je¤rey’s rule, axiomatic foundations, …ne-grained versus coarse-grained beliefs, unawareness