  How can we build recommender systems to take into account fairness?
Real-world recommender systems are often composed of multiple models, built by
multiple teams. However, most research on fairness focuses on improving
fairness in a single model. Further, recent research on classification fairness
has shown that combining multiple "fair" classifiers can still result in an
"unfair" classification system. This presents a significant challenge: how do
we understand and improve fairness in recommender systems composed of multiple
components?
  In this paper, we study the compositionality of recommender fairness. We
consider two recently proposed fairness ranking metrics: equality of exposure
and pairwise ranking accuracy. While we show that fairness in recommendation is
not guaranteed to compose, we provide theory for a set of conditions under
which fairness of individual models does compose. We then present an analytical
framework for both understanding whether a real system's signals can achieve
compositional fairness, and improving which component would have the greatest
impact on the fairness of the overall system. In addition to the theoretical
results, we find on multiple datasets -- including a large-scale real-world
recommender system -- that the overall system's end-to-end fairness is largely
achievable by improving fairness in individual components.
