# Group Fairness in Committee Selection

arXiv: https://arxiv.org/abs/1905.04438 · HTML: https://mlsanity.com/paper/1905.04438/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2019.

## Built on by (most cited first, 10 of 10)

- [Proportional Fairness in Clustering: A Social Choice Perspective](https://mlsanity.com/paper/2310.18162/) (2023)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Proportional Representation in Metric Spaces and Low-Distortion Committee Selection](https://mlsanity.com/paper/2312.10369/) (2023)
- [Optimized Distortion in Linear Social Choice](https://mlsanity.com/paper/2510.20020/) (2025)
- [A Computational Approach to Improving Fairness in K-means Clustering](https://mlsanity.com/paper/2505.22984/) (2025)
- [Fairly Allocating Utility in Constrained Multiwinner Elections](https://mlsanity.com/paper/2211.12820/) (2022)
- [On the Complexity of Finding a Diverse and Representative Committee using a Monotone, Separable Positional Multiwinner Voting Rule](https://mlsanity.com/paper/2211.13217/) (2022)
- [Asymptotic Universal Alignment: A New Alignment Framework via Test-Time Scaling](https://mlsanity.com/paper/2601.08777/) (2026)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [Improving Randomized Metric Distortion to 2.1441](https://mlsanity.com/paper/2608.29308/) (2026)

## Abstract (arXiv)

In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is stable if no coalition of voters can deviate and choose a committee of proportional size, so that all these voters strictly prefer the new committee to the existing one. Our main contribution is to extend this definition to stability of a distribution (or lottery) over committees. We consider two canonical voter preference models: the Approval Set setting where each voter approves a set of candidates and prefers committees with larger intersection with this set; and the Ranking setting where each voter ranks committees based on how much she likes her favorite candidate in a committee. Our main result is to show that stable lotteries always exist for these canonical preference models. Interestingly, given preferences of voters over committees, the procedure for computing an approximately stable lottery is the same for both models and therefore extends to the setting where some voters have the former preference structure and others have the latter. Our existence proof uses the probabilistic method and a new large deviation inequality that may be of independent interest.