Revealed Convex Preference

Convexity of preferences is a pervasive assumption in economic analysis, so it is important to understand how this property is revealed in data. In this paper, we develop a method to test for convexity given partial preference information in the form of weak and strict incomplete orders. We characterize the pairs that can be extended to convex preferences and provide an efficient algorithm to verify this property. Requiring the convex preference to align with an order that satisfies independence, such as the Euclidean order or stochastic dominance, does not complicate the test. We apply our results to consumer demand, choice under risk and uncertainty, and preferences over information, and establish conditions under which upper semicontinuity or continuity can also be obtained. We identify environments in which convexity imposes no additional restrictions beyond rationality, extending Afriat-type results to infinite data and co-convex budgets and establishing a convex version of exact rationalization.