Probability Update: Conditioning vs. Cross-Entropy
This work addresses a foundational issue in probability theory and philosophy for researchers, but it is incremental as it revisits and critiques existing approaches without introducing new methods.
The paper tackles the problem of updating probability distributions given uncertain information, specifically re-examining van Fraassen's Judy Benjamin problem, and argues that simple conditionalization can yield intuitive results, contrasting with cross-entropy methods that may be unsatisfactory.
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.