Is Complexity the Problem? Testing Random Choice with Heterogeneity

Economic choices are often stochastic: the same person may make a different choice when facing the same alternatives repeatedly. Standard models assume that the degree of randomness reflects the size of utility differences, but choice inconsistencies could also reflect difficulty comparing alternatives. Recent studies estimate such comparison difficulty (or "complexity") by fitting functional forms to aggregate choice data under a representative agent assumption. However, aggregate data could violate standard models of random choice simply because of heterogeneity in preferences, even in the absence of variation in comparison difficulty. This paper develops a revealed preference framework, collective rationalizability, that tests for variation in comparison difficulty from aggregate data while explicitly accounting for heterogeneity. The framework characterizes whether violations of standard models can be explained by comparison difficulty alone, heterogeneity alone, or require both. I provide a statistical test with finite-sample inference and apply the method to two existing experiments. In both cases, heterogeneity alone explains observed failures of stochastic transitivity well, demonstrating that comparison difficulty can be not only theoretically but also empirically confused with heterogeneity in aggregate data.