# The Condorcet Principle for Multiwinner Elections: From Shortlisting to Proportionality

arXiv: https://arxiv.org/abs/1701.08023 · HTML: https://mlsanity.com/paper/1701.08023/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2017.

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

- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [What Voting Rules Actually Do: A Data-Driven Analysis of Multi-Winner Voting](https://mlsanity.com/paper/2508.06454/) (2025)
- [Proportional Representation in Temporal Voting with Ranked Preferences](https://mlsanity.com/paper/2609.30555/) (2026)

## Abstract (arXiv)

We study two notions of stability in multiwinner elections that are based on the Condorcet criterion. The first notion was introduced by Gehrlein: A committee is stable if each committee member is preferred to each non-member by a (possibly weak) majority of voters. The second notion is called local stability (introduced in this paper): A size-k committee is locally stable in an election with n voters if there is no candidate c and no group of more than fracnk+1 voters such that each voter in this group prefers c to each committee member. We argue that Gehrlein-stable committees are appropriate for shortlisting tasks, and that locally stable committees are better suited for applications that require proportional representation. The goal of this paper is to analyze these notions in detail, explore their compatibility with notions of proportionality, and investigate the computational complexity of related algorithmic tasks.