Running summarizing tools on a new article

Abstract: The problem of ranking a set of items is fundamental in today's data-driven world. Ranking algorithms lie at the core of applications such as search engines, news feeds, and recommendation systems. However, recent events have pointed to the fact that algorithmic bias in rankings, which results in decreased fairness or diversity in the type of content presented, can promote stereotypes and propagate injustices. Motivated by such applications, we initiate the study of the traditional ranking problem with additional fairness constraints. 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, race) of each item and 3) a collection of fairness constraints that upper 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 constraints. This problem encapsulates various well-studied problems related to matching as special cases and turns out to be hard to approximate even with simple constraints. Our main technical contributions are exact and approximation algorithms and hardness results that, together, come close to settling the approximability of the constrained ranking maximization problem. Technically, our main results rely on novel insights about the standard linear programming relaxation for the constrained matching problem when the objective function satisfies certain properties that appear in common ranking metrics such as DCG, Spearman's rho or Bradley-Terry, along with the structure of fairness constraints. Overall, our results contribute to the growing set of algorithms that can counter algorithmic bias, and the structural insights obtained may find use in other algorithmic contexts related to ranking problems.