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We consider social resource allocations that deliver an array of scarcesupports to a diverse population. Such allocations pervade social servicedelivery, such as provision of homeless services, assignment of refugees tocities, among others. At issue is whether allocations are fair acrosssociodemographic groups and intersectional identities. Our paper shows thatnecessary trade-offs exist for fairness in the context of scarcity; manyreasonable definitions of equitable outcomes cannot hold simultaneously exceptunder stringent conditions. For example, defining fairness in terms ofimprovement over a baseline inherently conflicts with defining fairness interms of loss compared with the best possible outcome. Moreover, we demonstratethat the fairness trade-offs stem from heterogeneity across groups inintervention responses. Administrative records on homeless service deliveryoffer a real-world example. Building on prior work, we measure utilities foreach household as the probability of reentry into homeless services if giventhree homeless services. Heterogeneity in utility distributions (conditional onreceived services) for several sociodemographic groups (e.g. single women withchildren versus without children) generates divergence across fairness metrics.We argue that such heterogeneity, and thus, fairness trade-offs pervade manysocial policy contexts.

Trade-offs between Group Fairness Metrics in Societal Resource Allocation