Abstract

When can a shift from a prior to a posterior be represented by conditionalization? A well-known result, known as “superconditioning” and going back to work by Diaconis and Zabell, gives a sharp answer. This paper extends the result and connects it to the reflection principle and common priors. I show that 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 connected via a general form of the reflection principle. Common priors can be characterized by principles that require a certain kind of coherence between distinct sets of posteriors. I discuss the implications these results have for diachronic and synchronic modes of updating, learning experiences, the common prior assumption of game theory, and time-slice epistemology.