Your Recourse, My Loss? Algorithmic Recourse under Shared Constraints

This research paper addresses the limitations of current algorithmic recourse systems, which typically focus on single-individual scenarios. In real-world applications involving multiple stakeholders and limited resources, optimizing for individual welfare often overlooks competition and capacity constraints. The authors extend algorithmic recourse to a many-to-many setting, modeling it as a capacitated weighted bipartite matching problem. This approach accounts for recourse costs and provider capacities, ensuring that recommendations are collectively feasible rather than just individually optimal. The study proposes three optimization layers: capacitated matching, optimal capacity redistribution, and cost-aware optimization. Additionally, it introduces inequality-averse objectives using a concave social-welfare formulation to prioritize disadvantaged seekers. Experimental results demonstrate that this framework achieves near-optimal social welfare with minimal system modifications. The findings highlight how recourse systems can balance aggregate welfare with distributive fairness, shifting the focus from individual recommendations to comprehensive system-level design. This work provides a tractable path for improving social welfare in AI-driven decision-making processes while maintaining actionable steps for individuals.