Ranking with Fairness Constraints

Authors L. Elisa Celis, Damian Straszak, Nisheeth K. Vishnoi

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L. Elisa Celis
  • École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Damian Straszak
  • École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Nisheeth K. Vishnoi
  • École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

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L. Elisa Celis, Damian Straszak, and Nisheeth K. Vishnoi. Ranking with Fairness Constraints. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can result in decreased diversity in the type of content presented, promote stereotypes, and polarize opinions. In order to address such issues, we study the following variant of the traditional ranking problem when, in addition, there are fairness or diversity constraints. Given a collection of items along with 1) the value of placing an item in a particular position in the ranking, 2) the collection of sensitive attributes (such as gender, race, political opinion) of each item and 3) a collection of fairness constraints that, for each k, bound the number of items with each attribute that are allowed to appear in the top k positions of the ranking, the goal is to output a ranking that maximizes the value with respect to the original rank quality metric while respecting the constraints. This problem encapsulates various well-studied problems related to bipartite and hypergraph matching as special cases and turns out to be hard to approximate even with simple constraints. Our main technical contributions are fast exact and approximation algorithms along with complementary hardness results that, together, come close to settling the approximability of this constrained ranking maximization problem. Unlike prior work on the approximability of constrained matching problems, our algorithm runs in linear time, even when the number of constraints is (polynomially) large, its approximation ratio does not depend on the number of constraints, and it produces solutions with small constraint violations. Our results rely on insights about the constrained matching problem when the objective function satisfies certain properties that appear in common ranking metrics such as discounted cumulative gain (DCG), Spearman's rho or Bradley-Terry, along with the nested structure of fairness constraints.

Subject Classification

ACM Subject Classification
  • Information systems → Retrieval models and ranking
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Discrete optimization
  • Ranking
  • Fairness
  • Optimization
  • Matching
  • Approximation Algorithms


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