A unifying and general account of fairness measurement in recommender systems

Fairness is fundamental to all information access systems, including recommender systems. However, the landscape of fairness definition and measurement is quite scattered with many competing definitions that are partial and often incompatible. There is much work focusing on specific - and different - notions of fairness and there exist dozens of metrics of fairness in the literature, many of them redundant and most of them incompatible. In contrast, to our knowledge, there is no formal framework that covers all possible variants of fairness and allows developers to choose the most appropriate variant depending on the particular scenario. In this paper, we aim to define a general, flexible, and parameterizable framework that covers a whole range of fairness evaluation possibilities. Instead of modeling the metrics based on an abstract definition of fairness, the distinctive feature of this study compared to the current state of the art is that we start from the metrics applied in the literature to obtain a unified model by generalization. The framework is grounded on a general work hypothesis: interpreting the space of users and items as a probabilistic sample space, two fundamental measures in information theory (Kullback-Leibler Divergence and Mutual Information) can capture the majority of possible scenarios for measuring fairness on recommender system outputs. In addition, earlier research on fairness in recommender systems could be viewed as single-sided, trying to optimize some form of equity across either user groups or provider/procurer groups, without considering the user/item space in conjunction, thereby overlooking/disregarding the interplay between user and item groups. Instead, our framework includes the notion of statistical independence between user and item groups. We finally validate our approach experimentally on both synthetic and real data according to a wide range of state-of-the-art recommendation algorithms and real-world data sets, showing that with our framework we can measure fairness in a general, uniform, and meaningful way.