  Ranking and scoring are ubiquitous. We consider the setting in which an
institution, called a ranker, evaluates a set of individuals based on
demographic, behavioral or other characteristics. The final output is a ranking
that represents the relative quality of the individuals. While automatic and
therefore seemingly objective, rankers can, and often do, discriminate against
individuals and systematically disadvantage members of protected groups. This
warrants a careful study of the fairness of a ranking scheme.
  In this paper we propose fairness measures for ranked outputs. We develop a
data generation procedure that allows us to systematically control the degree
of unfairness in the output, and study the behavior of our measures on these
datasets. We then apply our proposed measures to several real datasets, and
demonstrate cases of unfairness. Finally, we show preliminary results of
incorporating our ranked fairness measures into an optimization framework, and
show potential for improving fairness of ranked outputs while maintaining
accuracy.
