Parameterized Fair Resource Allocation under Diversity Constraints

In many resource allocation scenarios—such as public housing, course enrollment, or job recommendations—systems must balance efficiency with diversity constraints to ensure fairness across different agent groups. Traditional approaches often enforce these diversity requirements as hard constraints, which can lead to suboptimal utility and overly restrictive solutions. This paper asks: can we develop a more flexible, parameterized framework that achieves fairness-optimal allocations while maintaining efficiency and accommodating diverse, application-specific constraints?

Inspired by risk-aversion models in economics, the authors propose PRA (Parameterized Resource Allocation). Instead of using hard thresholds, PRA introduces a set of inequality-aversion parameters that regulate group-level diversity. By adjusting these parameters, the system can prioritize different fairness objectives, such as the Atkinson inequality, statistical parity, or Nash welfare. The authors also introduce an adaptive variant, APRA, to handle additional, application-specific constraints. The framework uses a greedy algorithm based on marginal welfare gains to efficiently compute allocations, and the authors provide theoretical proofs that this approach achieves optimal welfare and fairness regardless of the specific metric chosen.

This work provides a robust, generalizable solution for real-world resource allocation problems where fairness is a primary concern. By moving away from rigid constraints, the PRA framework allows policymakers and system designers to tune the trade-off between efficiency and equity dynamically. The authors demonstrate that their approach outperforms existing baselines in both effectiveness and robustness across three real-world applications, making it a highly practical tool for complex, multi-group allocation tasks.