(with Paula Onuchic), October 2019.
A sender is about to come into possession of an object of heterogeneous quality. Prior to knowing that quality, she commits to a categorization. That is, she partitions the set of qualities into subsets — some possibly singletons — and verifiably commits to reveal the element in which the quality belongs. The categories must be monotone. Our main results fully describe the profit-maximizing categorization for any pair of priors over object quality held by sender and receiver. We apply these results to the design of educational grades.