Many fairness goals are defined at a population level that misaligns with siloed data collection, which remains unsharable due to privacy regulations. Horizontal federated learning (FL) enables collaborative modeling across clients with aligned features without sharing raw data. We study federated auditing of demographic parity through score distributions, measuring disparity as a Wasserstein--Frechet variance between sensitive-group score laws, and expressing the population metric in federated form that makes explicit how silo-specific selection drives local-global mismatch. For the squared Wasserstein distance, we prove an ANOVA-style decomposition that separates (i) selection-induced mixture effects from (ii) cross-silo heterogeneity, yielding tight bounds linking local and global metrics. We then propose a one-shot, communication-efficient protocol in which each silo shares only group counts and a quantile summary of its local score distributions, enabling the server to estimate global disparity and its decomposition, with $O(1/k)$ discretization bias ($k$ quantiles) and finite-sample guarantees. Experiments on synthetic data and COMPAS show that a few dozen quantiles suffice to recover global disparity and diagnose its sources.

翻译：许多公平性目标定义在群体层面，这与分散化的数据收集模式存在错位，且因隐私法规限制而无法共享数据。横向联邦学习（FL）使得具有对齐特征的客户端能够在不共享原始数据的情况下进行协作建模。本研究通过评分分布探讨联邦化的人口统计均等性审计，将差异度量定义为敏感群体评分分布之间的Wasserstein--Frechet方差，并以联邦化形式表达群体度量，从而明确揭示特定数据孤岛的选择机制如何导致局部与全局度量的不匹配。针对平方Wasserstein距离，我们证明了一种方差分析式分解，将（i）选择诱导的混合效应与（ii）跨孤岛异质性分离，由此得到连接局部与全局度量的紧致边界。随后提出一种单轮通信高效协议：每个数据孤岛仅需共享其组别计数和局部评分分布的分位数摘要，服务器即可据此估计全局差异及其分解，该协议具有$O(1/k)$离散化偏差（$k$分位数）和有限样本保证。在合成数据和COMPAS数据集上的实验表明，仅需数十个分位数即可准确还原全局差异并诊断其来源。