Ranking with Fairness Constraints

The problem of ranking a set of items is a fundamental algorithmic task in today’s datadriven world. Ranking algorithms lie at the core of applications such as search engines, news feeds, and recommendation systems. However, recent events and studies show that bias exists in the output of such applications. This results in unfairness or decreased diversity in the presentation of the content and can exacerbate stereotypes and manipulate perceptions. Motivated by these concerns, in this paper we introduce a framework for incorporating fairness in ranking problems. In our model, we are given a collection of items along with 1) the value of placing an item at a particular position, 2) the collection of possibly non-disjoint attributes (e.g., gender and ethnicity or genre and price point depending on the context) of each item and 3) a collection of fairness constraints that bound the number of items with each attribute that are allowed to appear in the top positions of the ranking. The goal is to output a ranking that maximizes value while respecting the fairness constraints. We present algorithms along with complementary hardness results which, together, come close to settling the complexity of this constrained ranking maximization problem. 1 ar X iv :1 70 4. 06 84 0v 2 [ cs .D S] 2 0 N ov 2 01 7