Global Fairness: Learning Fair Score Functions Across Acceptance Rates

Fair learning methods typically optimize the accuracy–fairness trade-off of a binary classifier at a particular decision threshold. In many applications, however, the deployment threshold is determined by a desired acceptance rate, which may be unknown during training and vary with downstream requirements. This motivates learning a score function that remains both fair and predictive across a range of acceptance rates. Existing score-level fairness measures move beyond a single threshold, but do not explicitly account for the range of acceptance rates over which group disparity persists. We introduce *global fairness*, a score-function fairness measure that aggregates threshold-wise group disparity according to the population score density. Our key observation is that the location of disparity relative to this density determines its acceptance-rate coverage: the same disparity in a high-density score region spans a wider range of acceptance rates than in a low-density region. We show that this density-weighted formulation is equivalent to averaging group disparity uniformly over population acceptance rates. Consequently, global fairness can distinguish score functions whose threshold-wise disparities have the same magnitude and shape but substantially different acceptance-rate coverage, including cases not distinguished by Kolmogorov–Smirnov or Wasserstein-1 measures. To jointly account for fairness and predictive utility, we introduce *global accuracy*, which aggregates predictive performance across acceptance rates, and formulate learning as maximizing global accuracy subject to a global fairness constraint. We establish consistency of the empirical global fairness estimator and characterize global accuracy over the full acceptance-rate range through its relationship with AUC. Experiments on three fairness benchmarks demonstrate favorable global accuracy–fairness trade-offs and more stable fairness across acceptance rates, while remaining competitive under conventional single-threshold evaluation.