Evaluating ambiguous random variables from Choquet to maxmin expected utility

We introduce a new theory of belief revision under ambiguity. It is recursive (random variables are evaluated by backward induction) and consequentialist (the conditional expectation of any random variable depends only on the values the random variable attains on the conditioning event). Agents experience no change in preferences but are sensitive to the timing of resolution of uncertainty. We provide three main theorems: the first characterizes our rule and relates it to standard Bayesian updating; the others show that the dynamic behavior of an agent who adopts our rule is maxmin expected utility with an arbitrary set of priors.