Abstract
A well-known result by Diaconis and Zabell examines when a shift from a prior to a posterior can be represented by conditionalization. This paper extends their result and connects it to the reflection principle and common priors. A shift from a prior to a set of posteriors can be represented within a conditioning model if and only if the prior and the posteriors are satisfy a form of the reflection principle. Common priors can be characterized by principles that require distinct sets of posteriors to cohere. These results have implications for updating, game theory, and time-slice epistemology.
