Rationality, the Bayesian standpoint, and the Monty-Hall problem

The Monty-Hall Problem (MHP) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view MHP and its two-player extension (MHP(2)) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that MHP(2) (studied here) be described in different terms than usually applied and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge.