From prejudice to racial profiling and back: A naïve intuitive statistician's curse

A designer conducts random searches to detect criminals, and may condition the search probability on individuals' appearance. She updates her belief about the distribution of criminals across appearances using her search results, but incorrectly takes her sample distribution for the population distribution. In equilibrium she employs optimal search probabilities given her belief, and her belief is consistent with her findings. We show that she will be discriminating an appearance if and only if she overestimates the probability of this appearance's being criminal. Moreover, in a linear model, tightening her budget will worsen the situation of those most discriminated against.