In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and tools to solve this task, which work well in many practical applications. However, the applicability and effectivity of these tools and definitions becomes less straightfoward in the case of multiple sensitive attributes. To tackle this issue, we propose a sequential framework, which allows to progressively achieve fairness across a set of sensitive features. We accomplish this by leveraging multi-marginal Wasserstein barycenters, which extends the standard notion of Strong Demographic Parity to the case with multiple sensitive characteristics. This method also provides a closed-form solution for the optimal, sequentially fair predictor, permitting a clear interpretation of inter-sensitive feature correlations. Our approach seamlessly extends to approximate fairness, enveloping a framework accommodating the trade-off between risk and unfairness. This extension permits a targeted prioritization of fairness improvements for a specific attribute within a set of sensitive attributes, allowing for a case specific adaptation. A data-driven estimation procedure for the derived solution is developed, and comprehensive numerical experiments are conducted on both synthetic and real datasets. Our empirical findings decisively underscore the practical efficacy of our post-processing approach in fostering fair decision-making.

翻译：在算法公平性的标准应用场景中，目标在于消除敏感变量与相应评分之间的关联。近年来，学界已发展出诸多定义与工具以解决该任务，并在许多实际应用中表现良好。然而，当涉及多个敏感属性时，这些工具与定义的适用性和有效性变得不再直观。针对此问题，我们提出一种序列化框架，可逐步实现跨敏感特征集的公平性。我们通过利用多边际Wasserstein重心来实现这一目标，该方法将标准强人口均等概念扩展至多个敏感特征的情形。该框架还提供了最优序列公平预测器的闭式解，使得对敏感特征间相关性的解释更为清晰。我们的方法可无缝扩展至近似公平性，构建了一个兼顾风险与不公平性权衡的泛化框架。该扩展允许在敏感属性集中针对特定属性进行定向公平性优化，实现案例自适应调整。我们推导了基于数据驱动的解估计方法，并在合成数据集与真实数据集上开展了全面的数值实验。实证结果充分证实了所提出的后处理方法在促进公平决策中的实际有效性。