# Core-Stable Committees under Restricted Domains

arXiv: https://arxiv.org/abs/2108.01987 · HTML: https://mlsanity.com/paper/2108.01987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 16 of 16)

- [Justified Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/1407.8269/) (2014)
- [Proportional Justified Representation](https://mlsanity.com/paper/1611.09928/) (2016)
- [Fair Allocation of Indivisible Public Goods](https://mlsanity.com/paper/1805.03164/) (2018)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [The Core of the Participatory Budgeting Problem](https://mlsanity.com/paper/1610.03474/) (2016)
- [Fair mixing: the case of dichotomous preferences](https://mlsanity.com/paper/1712.02542/) (2017)
- [Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation](https://mlsanity.com/paper/1402.3044/) (2014)
- [Proportional Rankings](https://mlsanity.com/paper/1612.01434/) (2016)
- [Group Fairness in Committee Selection](https://mlsanity.com/paper/1905.04438/) (2019)
- [Approval-Based Apportionment](https://mlsanity.com/paper/1911.08365/) (2019)
- [Structure in Dichotomous Preferences](https://mlsanity.com/paper/1505.00341/) (2015)
- [Approximately Stable Committee Selection](https://mlsanity.com/paper/1910.14008/) (2019)
- [A verifiably secure and proportional committee election rule](https://mlsanity.com/paper/2004.12990/) (2020)
- [The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality](https://mlsanity.com/paper/1701.08023/) (2017)
- [Overview of Polkadot and its Design Considerations](https://mlsanity.com/paper/2005.13456/) (2020)

## Built on by (most cited first, 3 of 3)

- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Fair Transit Stop Placement: A Clustering Perspective and Beyond](https://mlsanity.com/paper/2602.06776/) (2026)
- [Computing Thiele Rules on Interval Elections and their Generalizations](https://mlsanity.com/paper/2605.03067/) (2026)

## Abstract (arXiv)

We study the setting of committee elections, where a group of individuals needs to collectively select a given size subset of available objects. This model is relevant for a number of real-life scenarios including political elections, participatory budgeting, and facility-location. We focus on the core -- the classic notion of proportionality, stability and fairness. We show that for a number of restricted domains including voter-interval, candidate-interval, single-peaked, and single-crossing preferences the core is non-empty and can be found in polynomial time. We show that the core might be empty for strict top-monotonic preferences, yet we introduce a relaxation of this class, which guarantees non-emptiness of the core. Our algorithms work both in the randomized and discrete models. We also show that the classic known proportional rules do not return committees from the core even for the most restrictive domains among those we consider (in particular for 1D-Euclidean preferences). We additionally prove a number of structural results that give better insights into the nature of some of the restricted domains, and which in particular give a better intuitive understanding of the class of top-monotonic preferences.