When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing robust optimization methods such as minimizing worst-group loss or regret correspond to classical bargaining solutions and embody different fairness principles. We propose relative improvement, the ratio of actual risk reduction to potential reduction from a baseline predictor, which recovers the Kalai-Smorodinsky solution. Unlike absolute-scale methods that may not be comparable when groups have different potential predictability, relative improvement provides axiomatic justification including scale invariance and individual monotonicity. We establish finite-sample convergence guarantees under mild conditions.

翻译：当在多个子群体中部署单一预测器时，我们提出了一种根本不同的方法：将群体公平性解释为子群体之间的讨价还价问题。这一博弈论视角揭示，现有的鲁棒优化方法（如最小化最差群体损失或遗憾）对应于经典的讨价还价解，并体现了不同的公平原则。我们提出相对改进——即实际风险降低与基线预测器潜在降低之比，该指标恢复了Kalai-Smorodinsky解。与绝对尺度方法（当群体具有不同潜在可预测性时可能无法比较）不同，相对改进提供了公理化论证，包括尺度不变性和个体单调性。我们在温和条件下建立了有限样本收敛保证。