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，目标是消除敏感变量与对应评分之间的关联。近年来，科学界已发展出众多定义和工具来解决该问题，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，这些工具和定义的适用性与有效性变得不再直接。为解决此问题，我们提出了一种序列框架，能够逐步在一组敏感特征上实现公平性。我们通过利用多边际Wasserstein重心来实现这一目标，该重心将标准强人口平价概念扩展至多敏感特征情形。该方法还为最优序列公平预测器提供了闭式解，从而清晰解释敏感特征间的相关性。我们的方法可无缝扩展至近似公平性，构建了一个容纳风险与不公平性权衡的框架。该扩展允许针对一组敏感属性中的特定属性进行定向公平性改进优先级排序，支持具体案例的自适应调整。我们为所求推导解开发了数据驱动估计流程，并在合成数据集与真实数据集上进行了全面的数值实验。实证结果明确表明，我们的后处理方法在促进公平决策方面具有显著的实际效能。