Joint fairness for multiple sensitive traits reveals hidden disparities
Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation
Machine Learning
Summary
Fairness checks in algorithms often look at one sensitive trait at a time, like race or gender, but miss how combined traits might cause unfairness. The authors study a way to measure fairness across multiple traits together by comparing score distributions using a math tool called Wasserstein distance. They develop methods to break down overall unfairness into parts attributed fairly to each sensitive trait, even when traits interact or depend on each other. Their approach also provides tools to test fairness more accurately, and they demonstrate it on examples including income data.
What this means in practice
- •For machine learning fairness teams: Assess and attribute fairness impacts of multiple sensitive attributes jointly in predictive models to detect intersectional disparities.
- •For data auditing services: Develop statistical auditing tools that provide exact decompositions of fairness disparities across combined sensitive traits to improve audit accuracy.
Tested on one dataset.
Authors
Agathe Fernandes Machado, Charlotte Jamotton, Arthur Charpentier
Abstract
Fairness audits with several sensitive attributes are often performed one coordinate at a time. This can miss purely intersectional disparities: a score may be independent of each sensitive coordinate while depending on their joint profile. We study distributional demographic parity for a real-valued score using one-dimensional Wasserstein geometry. We distinguish two complementary constructions. Conditional and sequential audits characterize joint parity through their zero sets, but their positive values do not generally decompose a fixed joint Wasserstein disparity. By contrast, full-cell conditional quantile functions define a Hilbert-valued random variable whose variance is the joint disparity. Conditional expectations of this quantile process induce a monotone information game: every reveal order yields an exact martingale decomposition of the same joint disparity, while Shapley values provide an order-free attribution across sensitive attributes. Under independent sensitive attributes, the game reduces to a Hoeffding-ANOVA decomposition and Shapley splits each interaction energy equally among its members; under dependence, orthogonality is lost and explicit formulas reveal suppression and redundancy effects that marginal audits can hide. We give fixed-grid estimators and permutation calibration, and illustrate the framework on synthetic examples and ACSIncome. The resulting framework separates three questions that are often conflated: whether joint distributional parity holds, how a fixed joint disparity decomposes along an information path, and how that disparity can be attributed across sensitive coordinates without privileging an ordering.