少数能为多数做决定吗？抽签的度量失真
Can a Few Decide for Many? The Metric Distortion of Sortition
AI总结：
本文利用计算社会选择中的度量失真概念，证明了均匀选择仅需对数级别智能体即可实现近乎最优失真，且Fair Greedy Capture算法兼具近乎最优失真与常数级事后失真，肯定回答了抽签面板能否反映全体民意的问题。
摘要：
近期的研究探讨了用于选择代表性抽签面板的算法设计。然而，最核心的问题仍未解决：这些面板是否反映了全体民众的意见？我们通过采用计算社会选择中的度量失真概念给出了肯定回答，该概念旨在量化当偏好和智能体位于度量空间时，面板的决策与全体民众理想决策的契合程度。我们证明，就候选替代方案的数量而言，均匀选择仅需对数级别的智能体数量即可实现近乎最优的失真。我们还表明，由 Ebadian & Micha (2024) 最近提出的 Fair Greedy Capture 算法，不仅匹配了均匀选择近乎最优失真的保证，还实现了常数级的事后失真，从而确保了“两全其美”的性能表现。
英文摘要：
Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population's opinion? We present a positive answer by adopting the concept of metric distortion from computational social choice, which aims to quantify how much a panel's decision aligns with the ideal decision of the population when preferences and agents lie on a metric space. We show that uniform selection needs only logarithmically many agents in terms of the number of alternatives to achieve almost optimal distortion. We also show that Fair Greedy Capture, a selection algorithm introduced recently by Ebadian & Micha (2024), matches uniform selection's guarantees of almost optimal distortion and also achieves constant ex-post distortion, ensuring a "best of both worlds" performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
