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.

翻译：现实生活许多关键领域的决策工具基于排名结果。随着对算法公平性意识的日益增强，近期研究提出了排名公平性的度量方法。其中许多定义考虑了任意合理k值下，受保护群体在top-k排名项中的代表性。给定受保护群体后，验证算法公平性是一项简单任务。然而，群体定义可能事先未知。本文研究检测top-k排名项中存在代表性偏见群体的问题，无需预定义受保护群体。此类群体的可能数量呈指数级增长，使得问题变得困难。针对两种不同的公平性度量标准——全局代表性界限与比例代表性——我们提出了高效的搜索算法。随后利用夏普利值（Shapley value）概念，提出解释群体代表性偏差的方法。最后通过实验研究，展示了我们方法的可扩展性及所提算法的有效性。