Fairness in machine learning is predominantly evaluated through outcome-oriented metrics, such as Demographic parity, which measure whether predictions are statistically consistent across protected groups. However, these metrics cannot detect whether a model uses systematically different reasoning for different demographic groups, which violates procedural fairness principles. This problem is compounded by intersectionality, where models may appear fair on individual attributes (e.g., race) while exhibiting significant disparities for intersectional subgroups (e.g., race $\times$ gender), a phenomenon known as fairness gerrymandering. In this work, we introduce Multi-category Explanation Stability Disparity (MESD), a procedural fairness metric that quantifies disparities in explanation quality across intersectional subgroups formed by the Cartesian product of multiple protected attributes. MESD integrates three components, which are label-aware aggregation aligned with outcome-conditional fairness, empirical-Bayes shrinkage to stabilize estimates for small intersectional groups, and Conditional Value-at-Risk (CVaR) weighting to emphasize worst-case subgroup disparities. We integrate MESD within a multi-objective optimization framework (UEF) that jointly optimizes utility, outcome fairness, and procedural fairness using NSGA-II. We evaluated MESD and UEF on three benchmark datasets along with four state-of-the-art methods in several experiments, and we demonstrate that MESD reveals procedural disparities invisible to outcome metrics alone. We position our contribution within procedural justice theory and discuss implications for regulatory compliance and intersectional equity.

翻译：机器学习中的公平性主要通过结果导向性指标（如人口均等）进行评估，这些指标衡量预测结果在受保护群体间是否具有统计一致性。然而，此类指标无法检测模型是否对不同人口统计群体采用了系统性不同的推理过程，这违反了程序公平性原则。交叉性进一步加剧了该问题：模型可能在单一属性（如种族）上表现公平，而对交叉子群（如种族×性别）却显现显著差异——这种现象被称为公平杰利蝾螈。本文提出多类别可解释性稳定性差异（MESD），这是一种程序公平性度量指标，用于量化由多个受保护属性笛卡尔积所构成的交叉子群间可解释性质量的差异。MESD整合了三项组件：与结果条件公平性对齐的标签感知聚合、用于稳定小微交叉子群估计的经验贝叶斯收缩，以及强调最劣子群差异的条件风险价值（CVaR）加权。我们将MESD嵌入基于NSGA-II的多目标优化框架（UEF）中，该框架联合优化效用、结果公平性与程序公平性。我们在三个基准数据集上结合四种先进方法，通过多项实验评估了MESD与UEF，证明MESD能够揭示单纯结果指标无法观测到的程序性差异。我们将本研究贡献置于程序正义理论框架内，并探讨其对监管合规性与交叉性平等的启示。