Fairness Under Composition

Much of the literature on fair classifiers considers the case of a single classifier used once, in isolation. We initiate the study of composition of fair classifiers. In particular, we address the pitfalls of na{\i}ve composition and give general constructions for fair composition. Focusing on the individual fairness setting proposed in [Dwork, Hardt, Pitassi, Reingold, Zemel, 2011], we also extend our results to a large class of group fairness definitions popular in the recent literature. We exhibit several cases in which group fairness definitions give misleading signals under composition and conclude that additional context is needed to evaluate both group and individual fairness under composition.