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Real-life tools for decision-making in many critical domains are based onranking results. With the increasing awareness of algorithmic fairness, recentworks have presented measures for fairness in ranking. Many of thosedefinitions consider the representation of different ``protected groups'', inthe top-$k$ ranked items, for any reasonable $k$. Given the protected groups,confirming algorithmic fairness is a simple task. However, the groups'definitions may be unknown in advance. In this paper, we study the problem ofdetecting groups with biased representation in the top-$k$ ranked items,eliminating the need to pre-define protected groups. The number of such groupspossible can be exponential, making the problem hard. We propose efficientsearch algorithms for two different fairness measures: global representationbounds, and proportional representation. Then we propose a method to explainthe bias in the representations of groups utilizing the notion of Shapleyvalues. We conclude with an experimental study, showing the scalability of ourapproach and demonstrating the usefulness of the proposed algorithms.

Detection of Groups with Biased Representation in Ranking