# Fair Division with Two-Sided Preferences

arXiv: https://arxiv.org/abs/2206.05879 · HTML: https://mlsanity.com/paper/2206.05879/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2022.

## Built on by (most cited first, 4 of 4)

- [Fairness in Matching under Uncertainty](https://mlsanity.com/paper/2302.03810/) (2023)
- [Automating Food Drop: The Power of Two Choices for Dynamic and Fair Food Allocation](https://mlsanity.com/paper/2406.06363/) (2024)
- [Fair Division with Market Values](https://mlsanity.com/paper/2410.23137/) (2024)
- [Stable Matching with Ties: Approximation Ratios and Learning](https://mlsanity.com/paper/2411.03270/) (2024)

## Abstract (arXiv)

We study a fair division setting in which participants are to be fairly distributed among teams, where not only do the teams have preferences over the participants as in the canonical fair division setting, but the participants also have preferences over the teams. We focus on guaranteeing envy-freeness up to one participant (EF1) for the teams together with a stability condition for both sides. We show that an allocation satisfying EF1, swap stability, and individual stability always exists and can be computed in polynomial time, even when teams may have positive or negative values for participants. When teams have nonnegative values for participants, we prove that an EF1 and Pareto optimal allocation exists and, if the valuations are binary, can be found in polynomial time. We also show that an EF1 and justified envy-free allocation does not necessarily exist, and deciding whether such an allocation exists is computationally difficult.