Counterfactual AUC Fairness: Learning Fair Bipartite Ranking under Intervention

Causal fairness and AUC fairness have largely developed separately: the former studies how predictions respond to interventions on sensitive attributes, whereas the latter compares ranking performance across observed groups. We bridge these perspectives by introducing counterfactual AUC fairness (CF-AUC), which asks whether ranking accuracy within each positive–negative pair population remains stable when both individuals' sensitive attributes are counterfactually intervened. By fixing the pair population, CF-AUC isolates intervention-induced ranking changes from changes in population composition. We decompose observational AUC disparities into causal and population components and show that observational parity can be achieved by introducing counterfactual ranking changes while leaving factual AUC unchanged. We further characterize CF-AUC's relation to its pairwise and population variants and distinguish it from fixed-threshold decision invariance and score invariance. We then formulate fair ranking as maximizing factual AUC subject to groupwise CF-AUC constraints, providing a differentiable surrogate formulation, and bound the discrepancy between true and estimated CF-AUC gaps in terms of counterfactual-generation error, scorer sensitivity, and pairwise margin concentration near the ranking boundary. Experiments on synthetic and real data demonstrate favorable fairness–utility trade-offs.