Individual Fairness Under Composition

Much of the literature on fairness in classification considers the case of a single classifier used once, in isolation. However, fairness is not a property of isolated classifiers alone, it is also a property of classifiers composed into systems, and systems must handle repeated use and interaction with other fair (or unfair) systems. We initiate the study of composition of individually fair classifiers proposed in [Dwork, Hardt, Pitassi, Reingold, Zemel, 2011]. We find that fairness does not behave well under composition and propose directions to remedy the situation.