  This work facilitates ensuring fairness of machine learning in the real world
by decoupling fairness considerations in compound decisions. In particular,
this work studies how fairness propagates through a compound decision-making
processes, which we call a pipeline. Prior work in algorithmic fairness only
focuses on fairness with respect to one decision. However, many decision-making
processes require more than one decision. For instance, hiring is at least a
two stage model: deciding who to interview from the applicant pool and then
deciding who to hire from the interview pool. Perhaps surprisingly, we show
that the composition of fair components may not guarantee a fair pipeline under
a $(1+\varepsilon)$-equal opportunity definition of fair. However, we identify
circumstances that do provide that guarantee. We also propose numerous
directions for future work on more general compound machine learning decisions.
