Fair Top-k Ranking with multiple protected groups. Issue 1 (January 2022) - Zehlike, Meike; Sühr, Tom; Baeza-Yates, Ricardo; Bonchi, Francesco; Castillo, Carlos; Hajian, Sara
Abstract: Ranking items or people is a fundamental operation at the basis of several processes and services, not all of them happening online. Ranking is required for different tasks, including search, personalization, recommendation, and filtering. While traditionally ranking has been aimed solely at maximizing some global utility function, recently the awareness of potential discrimination for some of the elements to rank, has captured the attention of researchers, which have thus started devising ranking systems which are non-discriminatory or fair for the items being ranked. So far, researchers have mostly focused on group fairness, which is usually expressed in the form of constraints on the fraction of elements from some protected groups that should be included in the top- k positions, for any relevant k . These constraints are needed in order to correct implicit societal biases existing in the input data and reflected in the relevance or fitness score computed. In this article, we tackle the problem of selecting a subset of k individuals from a pool of n ≫ k candidates, maximizing global utility ( i.e., selecting the "best" candidates) while respecting given group-fairness criteria. In particular, to tackle this Fair Top- k Ranking problem, we adopt a ranked group-fairness definition which extends the standard notion of group fairness based on protected groups, by ensuring that the proportion of protected candidates in every prefix of the top- k ranking remains statistically above, or indistinguishable from, a given minimum threshold. Our notion of utility requires, intuitively, that every individual included in the top- k should be more qualified than every candidate not included; and that for every pair of candidates in the top- k, the more qualified candidate should be ranked above. The main contribution of this paper is an algorithm for producing a fair top- k ranking that can be used when more than one protected group is present, which means that a statistical test based on a multinomial distribution needs to be used instead of one for a binomial distribution, as the original FA*IR algorithms does. This poses important technical challenges and increases both the space and time complexity of the re-ranking algorithm. Our experimental assessment on real-world datasets shows that our approach yields small distortions with respect to rankings that maximize utility without considering our fairness criteria.