A vexing question in Bayesian epistemology is how an agent should update on evidence which she assigned zero prior credence. Some theorists have suggested that, in such cases, the agent should update by Kolmogorov conditionalization, a norm based on Kolmogorov’s theory of regular conditional distributions. However, it turns out that in some situations, a Kolmogorov conditionalizer will plan to always assign a posterior credence of zero to the evidence she learns. Intuitively, such a plan is irrational and easily Dutch bookable. In this paper, we propose a revised norm, Kolmogorov–Blackwell conditionalization, which avoids this problem. We prove a Dutch book theorem and converse Dutch book theorem for this revised norm, and relate our results to those of Rescorla (2018).

贝叶斯认识论中一个令人烦恼的问题是代理人应该如何更新她分配为零的先前可信度的证据。一些理论家建议，在这种情况下，代理应该通过 Kolmogorov 条件化进行更新，这是基于 Kolmogorov 规则条件分布理论的规范。然而，事实证明，在某些情况下，Kolmogorov 条件化器将计划始终为她学习的证据分配零后验可信度。直观地说，这样的计划是不合理的，而且很容易被荷兰人预订。在本文中，我们提出了一个修订的规范，Kolmogorov-Blackwell 条件化，它避免了这个问题。我们为这个修订后的规范证明了荷兰书定理和荷兰书定理，并将我们的结果与 Rescorla (2018) 的结果联系起来。