  A challenge in fair algorithm design is that, while there are compelling
notions of individual fairness, these notions typically do not satisfy
desirable composition properties, and downstream applications based on fair
classifiers might not preserve fairness. To study fairness under composition,
Dwork and Ilvento introduced an archetypal problem called fair-cohort-selection
problem, where a single fair classifier is composed with itself to select a
group of candidates of a given size, and proposed a solution to this problem.
In this work we design algorithms for selecting cohorts that not only preserve
fairness, but also maximize the utility of the selected cohort under two
notions of utility that we introduce and motivate. We give optimal (or
approximately optimal) polynomial-time algorithms for this problem in both an
offline setting, and an online setting where candidates arrive one at a time
and are classified as they arrive.
