# Rawlsian many-to-one matching with non-linear utility

arXiv: https://arxiv.org/abs/2511.02533 · HTML: https://mlsanity.com/paper/2511.02533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Maxmin-Fair Ranking: Individual Fairness under Group-Fairness Constraints](https://mlsanity.com/paper/2106.08652/) (2021)
- [Fair-by-design matching](https://mlsanity.com/paper/1802.02562/) (2018)
- [Groupwise Maximin Fair Allocation of Indivisible Goods](https://mlsanity.com/paper/1711.07621/) (2017)
- [Guarantees of Stochastic Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraint](https://mlsanity.com/paper/1908.06242/) (2019)
- [Bandit Learning in Matching Markets: Utilitarian and Rawlsian Perspectives](https://mlsanity.com/paper/2412.00301/) (2024)

## Abstract (arXiv)

We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture diversity between them. In this setting, we show that classical stable matchings may fail to exist. To address this, we propose alternative solution concepts based on Rawlsian fairness, aiming to maximize the minimum utility across colleges. We design both deterministic and stochastic algorithms that iteratively improve the outcome of the worst-off college, offering a practical approach to fair allocation when stability cannot be guaranteed.