Measuring and Mitigating Group Inequalities In Resource Allocation

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Resource allocation, an integral part of socio-economic governance, profoundly influences individual prosperity and has the potential to mitigate or exacerbate socioeconomic disparities. This paper addresses the challenge of equitably allocating finite resources among individuals by answering two fundamental questions: (1) how to accurately measure and test group disparities and (2) how to optimally distribute resources while ensuring group fairness. We propose the Group Beneficiary Disparity (GBD) metric – an evaluation tool engineered to systematically gauge inequalities in a binary beneficiary/non-beneficiary context. The GBD provides decision-makers and planners with a powerful tool to audit social programs and optimize policies from a lens of group equality. We argue that utilitarian decision-makers cannot fully eliminate group disparities even when operating under social welfare constraints. To address this issue, we propose a new resource allocation optimization model, called A-FARM (Asymptotically Fair Allocation of Resources Model), with asymptotic group fairness guarantees. A-FARM partitions individuals into distinct, non-overlapping units and distributes resources among these units based on a utility-based allocation mechanism. Finally, we evaluate the performance of our proposed algorithm using both simulated and real-world data. Our results demonstrate that, A-FARM enables decision-makers to (1) achieve maximum efficiency under group fairness constraints and (2) perform a fairness-efficiency trade-off.