arXiv:2609.29646 · v3

Sequential Phragmén Guarantees 2-Approximate Core Stability

首次提交 2026-09-11 12:18

版本更新 2026-11-11 01:38

雷达观测 2026-11-11 13:07

摘要

We study approximately stable committee selection under approval preferences, following Cheng et al.~[EC~2019] and Jiang, Munagala, and Wang~[STOC~2020]. In an approval-based committee election, $n$ voters each approve a subset of the candidates, and a committee of size $k$ is selected. A size-$k$ committee is $λ$-stable if, for every nonempty subset $T$ of candidates, the number of voters who strictly prefer $T$ is less than $λ$ times the proportional share $\frac{n|T|}{k}$. We consider sequential Phragmén, a classical polynomial-time voting rule, and prove that it always returns a $2$-stable committee. This implies that the $2$-core is always nonempty and improves upon the $3.651$-stability guarantee of Gao, Sun, and Vondrák~[EC~2026]. The guarantee also extends to weighted voters and is tight even for unweighted elections: for every $1\leλ<2$, sequential Phragmén can return a committee that is not $λ$-stable. Compared with the exact-core algorithm developed in concurrent work by Becker, Greger, and Peters~[arXiv~2026], sequential Phragmén is simpler to implement, and our proof of its $2$-stability is elementary.