arXiv:2605.20069cs.LGcs.GT2026-05

提出平滑抽奖机制,让评分微调不引发选中概率大波动。

Smooth Partial Lotteries for Stable Randomized Selection

  • 设计基于评分的线性截断抽奖,高低分区固定接受或拒绝。
  • 理论证明其最坏后悔值逼近平滑规则下最优边界。
  • 实测现有抽奖在微小评分变动时极不稳定,新方法更稳且高效。

竞争性选拔如科研资助、招生和招聘常依赖评分选出候选者。近年来许多机构采用部分抽奖机制,根据评分随机决定人选。但现有设计存在固有不稳定性:单个候选者评分的微小变化可能引发其入选概率大幅波动。这削弱了抽奖的核心目标——降低决策边界附近精细评分差异的影响。本文提出以平滑性为设计原则,形式化为评分到入选概率映射的Lipschitz条件。引入截断线性抽奖(Clipped Linear Lottery),其入选概率在上下阈值间线性增长,高于上限则必选,低于下限则必弃。证明该机制最坏后悔值在任意平滑规则中仅差因子(1 - k/n),其中k/n为录取率。与个体公平性和差分隐私等稳定性概念对比,表明其在平滑性与性能间权衡更优。基于ICLR 2025、NeurIPS 2024及瑞士国家科学基金会的真实同行评审数据实验显示,现有抽奖机制在单个评分扰动下仍高度不稳定。实验也验证了理论分析的紧致性,并表明所提方法在实践中优于其他方案。

原文摘要 · Abstract (English)

Competitive selection processes, from scientific funding to admissions and hiring, use evaluations to score candidates, and eventually choose a subset of them based on those scores. Recently, many organizations have adopted partial lotteries, which randomize selection based on evaluation scores. However, existing lottery designs are inherently unstable, as a small change to a single candidate's score can cause large shifts in their selection probabilities. This instability undermines a key goal of lotteries: reducing the influence of fine-grained score distinctions near the decision boundary. We propose smoothness as a design principle for partial lotteries, formalizing it as a Lipschitz condition on the mapping from review scores over candidates to selection probabilities. We introduce the Clipped Linear Lottery, a simple mechanism in which selection probabilities scale linearly with estimated quality between an upper threshold, above which we always accept, and a lower threshold, below which we always reject. We prove that the Clipped Linear Lottery's worst-case regret matches a lower bound for any smooth selection rule up to a factor of $(1 - k/n)$, where $k/n$ is the acceptance rate. We compare smooth selection to other stability notions like Individual Fairness and Differential Privacy, showing that the Clipped Linear Lottery achieves a better smoothness-regret tradeoff than alternatives. Experiments on real peer review data from ICLR 2025, NeurIPS 2024, and the Swiss National Science Foundation demonstrate that existing lottery designs are highly unstable in practice even under perturbations to a single score. Our experiments also confirm the tightness of our theoretical analysis and show that our proposed Clipped Linear Lottery achieves a better smoothness-utility tradeoff than alternatives in practice.

抽奖机制平滑性稳定性评分系统

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。