It is often assumed (for analytical convenience, but also in accordance with common intuition) that consumer preferences are convex. In this paper, we consider circumstances under which such preferences are (or are not) optimal. In particular, we investigate a setting in which goods possess
some hidden quality with known distribution, and the consumer chooses a bundle of goods that
maximizes the probability that he receives some threshold level of this quality. We show that if the
threshold is small relative to consumption levels, preferences will tend to be convex; whereas the
opposite holds if the threshold is large. Our theory helps explain a broad spectrum of economic behavior (including, in particular, certain common commercial advertising strategies), suggesting
that sensitivity to information about thresholds is deeply rooted in human psychology
