A theory of subjective learning

We study an individual who faces a dynamic decision problem in which the process of information arrival is unobserved by the analyst. We derive two utility representations of preferences over menus of acts that capture the individual’s uncertainty about his future beliefs. The most general representation identi…es a unique probability distribution over the set of posteriors that the decision maker might face at the time of choosing from the menu. We use this representation to characterize a notion of “more preference for ‡exibility”via a subjective analogue of Blackwell’s (1951, 1953) comparisons of experiments. A more specialized representation uniquely identi…es information as a partition of the state space. This result allows us to compare individuals who expect to learn di¤erently, even if they do not agree on their prior beliefs. We conclude by extending the basic model to accommodate an individual who expects to learn gradually over time by means of a subjective …ltration. Key words: Subjective learning, partitional learning, preference for ‡exibility, resolution of uncertainty, valuing more binary bets, subjective …ltration.