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.

什么时候可以用条件化来表示从先验到后验的转变？ Diaconis 和 Zabell 的一项被称为“超级调节”并返回工作的著名结果给出了尖锐的答案。本文扩展了结果并将其与反射原理和共同先验联系起来。我证明，当且仅当先验和后验通过反射原理的一般形式连接时，才能在条件模型中表示从先验到后验集合的转变。共同先验的特征在于需要不同后验集之间具有某种一致性的原则。我讨论了这些结果对历时和共时更新模式、学习经验、博弈论的共同先验假设和时间片认识论的影响。