  Real-life tools for decision-making in many critical domains are based on
ranking results. With the increasing awareness of algorithmic fairness, recent
works have presented measures for fairness in ranking. Many of those
definitions consider the representation of different ``protected groups'', in
the 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 of
detecting groups with biased representation in the top-$k$ ranked items,
eliminating the need to pre-define protected groups. The number of such groups
possible can be exponential, making the problem hard. We propose efficient
search algorithms for two different fairness measures: global representation
bounds, and proportional representation. Then we propose a method to explain
the bias in the representations of groups utilizing the notion of Shapley
values. We conclude with an experimental study, showing the scalability of our
approach and demonstrating the usefulness of the proposed algorithms.
