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：将群体公平解释为子群体间的讨价还价问题。这一博弈论视角揭示了现有鲁棒优化方法（如最小化最差群体损失或遗憾）对应于经典讨价还价解，并体现了不同的公平原则。我们提出相对改进——即从基线预测器出发的实际风险降低与潜在风险降低之比——这恢复了Kalai-Smorodinsky解。与当不同群体具有不同潜在可预测性时可能无法比较的绝对尺度方法不同，相对改进提供了公理化依据，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。