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.

翻译：本研究探讨一种双机构稳定匹配模型，其中来自两个不同群体的候选人通过具有群体偏向性的部分相关信号进行评估。该模型将先前研究（假设机构以相同方式评估候选人）扩展至更现实的场景，即机构依赖重叠但独立处理的评估标准。这些评估可包含多种信息工具，如标准化测试、共享推荐系统或带有局部噪声的基于人工智能的评估。评估过程由两个关键参数控制：偏差参数$\beta \in (0,1]$（用于建模某一群体面临的系统性劣势）和相关性参数$\gamma \in [0,1]$（用于刻画机构排名间的一致性）。我们重点研究表征比率，即在此设定下匹配过程所选劣势候选人与优势候选人的数量之比。聚焦于所有候选人偏好同一机构的情形，我们刻画了大市场均衡并推导出表征比率的闭合表达式。先前研究表明当$\gamma = 1$时，该比率随$\beta$线性变化。与之相反，我们证明表征比率随$\gamma$呈非线性增长，即使相关性轻微下降也可能导致表征比率急剧降低。我们的分析识别出机构选择行为发生离散转变的关键$\gamma$阈值，并揭示了评估者一致性或偏差缓解最有效的结构性条件。最后，我们展示了该框架与结果如何为去中心化选拔系统中实现公平感知设计提供干预路径。