Algorithmic fairness, and in particular the fairness of scoring and
classification algorithms, has become a topic of increasing social concern and
has recently witnessed an explosion of research in theoretical computer
science, machine learning, statistics, the social sciences, and law. Much of
the literature considers the case of a single classifier (or scoring function)
used once, in isolation. In this work, we initiate the study of the fairness
properties of systems composed of algorithms that are fair in isolation; that
is, we study fairness under composition. We identify pitfalls of naive
composition and give general constructions for fair composition, demonstrating
both that classifiers that are fair in isolation do not necessarily compose
into fair systems and also that seemingly unfair components may be carefully
combined to construct fair systems. We focus primarily on the individual
fairness setting proposed in [Dwork, Hardt, Pitassi, Reingold, Zemel, 2011],
but also extend our results to a large class of group fairness definitions
popular in the recent literature, exhibiting several cases in which group
fairness definitions give misleading signals under composition.Comment: Fixed two word omission