标题： 有偏和相关评价下的匹配 显示英文标题

标题： Matchings Under Biased and Correlated Evaluations

摘要： 我们研究了一个两机构稳定匹配模型，其中来自两个不同群体的候选人使用部分相关且具有群体偏见的信号进行评估。 这扩展了先前的研究（该研究假设机构以相同的方式评估候选人）到一个更现实的场景，在此场景中，机构依赖于重叠但独立处理的标准。 这些评估可能包括各种信息性工具，如标准化考试、共享推荐系统或带有局部噪声的基于人工智能的评估。 两个关键参数决定了评估：偏差参数$\beta \in (0,1]$，它模拟一个群体所面临的系统性劣势；相关性参数$\gamma \in [0,1]$，它捕捉机构排名之间的对齐程度。 我们研究了代表性比率，即在此设置中匹配过程选择的劣势群体候选人与优势群体候选人之间的比率。 专注于所有候选人都偏好同一机构的情况，我们描述了大市场均衡，并推导出由此产生的代表性比率的显式表达式。 先前的研究表明，当$\gamma = 1$时，该比率与$\beta$成线性比例。 相比之下，我们表明，代表性比率随着$\gamma$非线性增加，甚至相关性的小幅下降也会导致代表性比率急剧下降。 我们的分析确定了关键的$\gamma$-阈值，在这些阈值上，机构选择行为会发生离散转变，并揭示了评估者对齐或偏差缓解最有效的结构性条件。 最后，我们展示了如何利用这个框架和结果来实现去中心化选择系统中的公平意识设计干预措施。 显示英文摘要

摘要： We study a two-institution stable matching model in which candidates from two distinct groups are evaluated using partially correlated signals that are group-biased. This extends prior work (which assumes institutions evaluate candidates in an identical manner) to a more realistic setting in which institutions rely on overlapping, but independently processed, criteria. These evaluations could consist of a variety of informative tools such as standardized tests, shared recommendation systems, or AI-based assessments with local noise. Two key parameters govern evaluations: the bias parameter $\beta \in (0,1]$, which models systematic disadvantage faced by one group, and the correlation parameter $\gamma \in [0,1]$, which captures the alignment between institutional rankings. We study the representation ratio, i.e., the ratio of disadvantaged to advantaged candidates selected by the matching process in this setting. Focusing on a regime in which all candidates prefer the same institution, we characterize the large-market equilibrium and derive a closed-form expression for the resulting representation ratio. Prior work shows that when $\gamma = 1$, this ratio scales linearly with $\beta$. In contrast, we show that the representation ratio increases nonlinearly with $\gamma$ and even modest losses in correlation can cause sharp drops in the representation ratio. Our analysis identifies critical $\gamma$-thresholds where institutional selection behavior undergoes discrete transitions, and reveals structural conditions under which evaluator alignment or bias mitigation are most effective. Finally, we show how this framework and results enable interventions for fairness-aware design in decentralized selection systems.