Abstract In accordance with Plott’s Discovered Preference Hypothesis, we model a decision-maker (DM) who starts life as indecisive, and—over time and through experience—gradually resolves their indecisiveness, until they fully discover their preferences. On the basis of two well-documented behavioural regularities, we provide an axiomatization of the evolution of the DM’s preferences that results in a model of decreasing indecisiveness. In the resulting axiomatization, the DM’s preferences at period t are given by a semiorder with threshold parameter σ(t), where σ(t) is a strictly decreasing function over time periods. We next study how two firms compete in a market consisting of a single indecisive consumer, thereby illustrating how preference discovery may be shaped by strategic interactions between firms.