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There has been a flurry of research in recent years on notions of fairness inranking and recommender systems, particularly on how to evaluate if arecommender allocates exposure equally across groups of relevant items (alsoknown as provider fairness). While this research has laid an importantfoundation, it gave rise to different approaches depending on whether relevantitems are compared per-user/per-query or aggregated across users. Despite bothbeing established and intuitive, we discover that these two notions can lead toopposite conclusions, a form of Simpson's Paradox. We reconcile these notionsand show that the tension is due to differences in distributions of users whereitems are relevant, and break down the important factors of the user'srecommendations. Based on this new understanding, practitioners might beinterested in either notions, but might face challenges with the per-usermetric due to partial observability of the relevance and user satisfaction,typical in real-world recommenders. We describe a technique based ondistribution matching to estimate it in such a scenario. We demonstrate onsimulated and real-world recommender data the effectiveness and usefulness ofsuch an approach.

Simpson's Paradox in Recommender Fairness: Reconciling differences between per-user and aggregated evaluations