Probability Update: Conditioning vs. Cross-Entropy

TL;DR

This paper re-examines probability updating methods, demonstrating that simple conditioning can handle certain uncertain information cases effectively, challenging the necessity of cross-entropy minimization.

Contribution

It shows that conditioning can be used in cases previously thought to require cross-entropy, providing clearer, more intuitive updates and discussing broader philosophical implications.

Findings

Conditionalization suffices for Judy Benjamin problem

Cross-entropy can give unsatisfactory answers in some cases

Simple conditioning aligns with intuition in probability updates

Abstract

Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem, which in essence asks how one might update given the value of a conditional probability. We argue that -- contrary to the suggestions in the literature -- it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update.