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.

通过多次敏感特征逐步实现公平性，利用多元 Wasserstein 几何中心将 Strong Demographic Parity 的标准推广到具有多个敏感特征的情况，并提供一种闭式解决方案，使得对不同敏感特征之间的相关性有明确的解释，进而实现了风险和不公平性之间的权衡。该方法适用于近似公平性，提供了对特定敏感特征的公平性改进的有针对性优先级，从而实现了针对案例的适应性，通过数据驱动的解决方案估计程序，并在合成和真实数据集上进行了全面的数值实验证明了我们的后处理方法在促进公平决策方面的实际有效性。