Group fairness is achieved by equalising prediction distributions between protected sub-populations; individual fairness requires treating similar individuals alike. These two objectives, however, are incompatible when a scoring model is calibrated through discontinuous probability functions, where individuals can be randomly assigned an outcome determined by a fixed probability. This procedure may provide two similar individuals from the same protected group with classification odds that are disparately different -- a clear violation of individual fairness. Assigning unique odds to each protected sub-population may also prevent members of one sub-population from ever receiving equal chances of a positive outcome to another, which we argue is another type of unfairness called individual odds. We reconcile all this by constructing continuous probability functions between group thresholds that are constrained by their Lipschitz constant. Our solution preserves the model's predictive power, individual fairness and robustness while ensuring group fairness.

翻译：群体公平通过均衡受保护子群体间的预测分布实现；个体公平要求相似个体获得一致对待。然而，当评分模型通过不连续概率函数进行校准（此时个体可能依据固定概率被随机分配结果）时，这两个目标存在不相容性。该过程可能导致同一受保护群体中两个相似个体获得显著不同的分类几率——这明显违背个体公平原则。为每个受保护子群体分配唯一种类几率，还可能使某个子群体成员永远无法获得与其他子群体同等的正向结果机会，我们将此类不公平称为"个体几率不公"。通过构建受Lipschitz常数约束的群体阈值间连续概率函数，我们调和了上述矛盾。该解决方案在保障群体公平的同时，保持了模型的预测能力、个体公平性与鲁棒性。