Bayesian updating rules and AGM belief revision

We interpret the problem of updating beliefs as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after observing zero probability events and investigate two classes of updating rules for probabilities : 1) ”minimum distance” updating rules which select the posterior closest to the prior by some metric. 2) ”lexicographic” updating rules where posteriors are given by a lexicographic probability system. For the former, we show Bayesian updating as a special case and for specific AGM belief revisions, provide necessary and sufficient conditions for a minimumdistance representation. For the latter, we show that an updating rule is lexicographic if and only if it is Bayesian, AGM-consistent and satisfies a weak form of path independence. Lastly, we study a sub-class of lexicographic updating rules, which we call ”support-dependent” rules. We show that such updating rules have a minimum distance representation.