# Your Recourse, My Loss? Algorithmic Recourse under Shared Constraints

arXiv: https://arxiv.org/abs/2508.11070 · HTML: https://mlsanity.com/paper/2508.11070/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Fairness in Machine Learning: Lessons from Political Philosophy](https://mlsanity.com/paper/1712.03586/) (2017)
- [Achieving Fairness in the Stochastic Multi-armed Bandit Problem](https://mlsanity.com/paper/1907.10516/) (2019)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making](https://mlsanity.com/paper/1806.04959/) (2018)
- [Fair Algorithms for Multi-Agent Multi-Armed Bandits](https://mlsanity.com/paper/2007.06699/) (2020)
- [Fair Classification and Social Welfare](https://mlsanity.com/paper/1905.00147/) (2019)
- [Setting the Right Expectations: Algorithmic Recourse Over Time](https://mlsanity.com/paper/2309.06969/) (2023)
- [Fairness in Algorithmic Recourse Through the Lens of Substantive Equality of Opportunity](https://mlsanity.com/paper/2401.16088/) (2024)
- [The Good, the Bad and the Submodular: Fairly Allocating Mixed Manna Under Order-Neutral Submodular Preferences](https://mlsanity.com/paper/2307.12516/) (2023)

## Built on by (most cited first, 1 of 1)

- [Algorithmic Recourse Under Competition](https://mlsanity.com/paper/2609.39877/) (2026)

## Abstract (arXiv)

Decision makers are increasingly relying on machine learning in sensitive situations. Algorithmic recourse aims to provide individuals with actionable and minimally costly steps to reverse unfavorable AI-driven decisions. While existing research focuses on single-individual (i.e., seeker) and single-model (i.e., provider) scenarios, real-world applications involve multiple stakeholders. Optimizing outcomes for seekers under an individual welfare approach overlooks the multi-agent nature of real-world systems, with competition for limited resources. Accordingly, we extend algorithmic recourse to a many-to-many setting with capacity constraints, where individually computed recourse recommendations no longer compose independently and stakeholder interactions affect recourse validity. We model this multi-agent algorithimc recourse as a capacitated weighted bipartite matching problem, based on recourse cost and provider capacity. Edge weights, reflecting recourse costs, are optimized for social welfare while quantifying the welfare gap between individual welfare and this collectively feasible outcome. We propose three optimization layers: capacitated matching, optimal capacity redistribution, and cost-aware optimization. We further model inequality-averse objectives through a concave social-welfare formulation that prioritizes the most disadvantaged seekers. Experiments demonstrate that our framework enables the many-to-many algorithmic recourse to achieve near-optimal welfare with minimum modification in system settings. Our results also show how recourse systems can be designed to balance aggregate welfare with distributive considerations. We extend algorithmic recourse from individual recommendations to system-level design, providing a tractable path toward higher social welfare while maintaining individual actionability.