RAWLS–SHAPLEY FAIRNESS: A NASH-BARGAINING APPROACH TO EQUITABLE MACHINE LEARNING

We propose Rawls–Shapley (RS) learning, a machine-learning fairness objective grounded in Yaari’s (1981) formal result that applying Rawls’ Difference Principle through Shapley’s utility-transfer framework uniquely recovers the Nash bargaining solution. Translating this result into a training objective, we define each group’s utility gain and aggregate these gains through a Nash-product formulation. This gives rise to the Rawls–Shapley objective, whose optimization automatically places greater emphasis on groups with lower utility gains, thereby incorporating Rawlsian priority into the learning process in a principled and differentiable manner. We instantiate RS in two settings: RS-Known, which uses observed group labels, and RS-Proxy, which trains a supervised proxy predictor on group labels to derive soft group memberships (a “limited demographics” regime, distinct from the fully label-free setting). We evaluate both variants on Adult income and COMPAS recidivism benchmarks alongside empirical risk minimization (ERM), Adversarially Reweighted Learning (ARL), Logistic Regression, and XGBoost, reporting accuracy, AUC, and equalized-odds gap across protected groups. Empirically, RS-Proxy achieves the lowest equalized-odds gap among the RS and non-parity neural objectives on Adult (0.145), while Equalized-Odds Regularization (EqOdds-Reg) achieves the best parity across both datasets. The two RS variants achieve broadly similar worst-group accuracy. On COMPAS, where group labels are noisy and less predictable, all methods converge to similar performance, consistent with our graceful-degradation analysis.