发表机构
Rensselaer Polytechnic Institute; Beijing Normal University-Zhuhai; Beijing Normal-Hong Kong Baptist University（伦斯勒理工学院; 北京师范大学珠海校区; 北京师范-香港联合大学深圳分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对基于批准的委员会选举，证明加权顺序Phragmén规则总能返回2-稳定委员会，从而保证2核心非空，改进了先前3.651-稳定的最佳结果。
AI 中文摘要
在基于批准的委员会选举中，从一组候选人中选出规模为$k$的委员会，以代表总权重为$n$的选民，每位选民具有正权重并批准一部分候选人。若对于每个非空候选人子集$T$，严格偏好$T$的选民总权重小于$\n$乘以比例份额$n|T|/k$，则规模为$k$的委员会是$\n$稳定的。是否存在恰好稳定（即$\n=1$）的委员会，仍是基于批准的委员会投票中的一个重大开放问题。因此，一个自然的目标是找出较小的$\n>1$值，使得$\n$稳定性总能得到保证。我们证明了加权顺序Phragmén规则——一种经典且自然的规则——总能返回规模为$k$的2-稳定委员会。由于$\n$核心是所有$\n$稳定委员会的集合，我们的结果意味着2核心总是非空的。这改进了先前由Gao、Sun和Vondrák [EC 2026]给出的最佳已知保证，即3.651-稳定委员会总是存在。
英文摘要
In an approval-based committee election, a committee of size $k$ is selected from a set of candidates to represent voters of total weight $n$, each of whom has positive weight and approves a subset of the candidates. A size-$k$ committee is $λ$-stable if, for every nonempty subset $T$ of candidates, the total weight of voters who strictly prefer $T$ is less than $λ$ times the proportional share $n|T|/k$. Whether there exists a committee that is exactly stable, corresponding to $λ=1$, remains a major open problem in approval-based committee voting. Thus, a natural objective is to identify small values of $λ>1$ for which $λ$-stability can always be guaranteed. We prove that weighted sequential Phragmén, a classical and natural rule, always returns a $2$-stable committee of size $k$. Since the $λ$-core is the set of all $λ$-stable committees, our result implies that the $2$-core is always nonempty. This improves upon the previously best-known guarantee, due to Gao, Sun, and Vondrák~[EC~2026], that a $3.651$-stable committee always exists.
CommentsThis work is submitted on Aug 29th, 2026, independent with the exact core work of 2609.11912
