How Do the Score Distributions of Subpopulations Influence Fairness Notions?

Automated decisions based on trained algorithms influence human life in an increasingly far-reaching way. In recent years, it has become clear that these decisions are often accompanied by bias and unfair treatment of different subpopulations.Meanwhile, several notions of fairness circulate in the scientific literature, with trade-offs between profit and fairness and between fairness metrics among themselves. Based on both analytical calculations and numerical simulations, we show in this study that some profit-fairness trade-offs and fairness-fairness trade-offs depend substantially on the underlying score distributions given to subpopulations and we present two complementary perspectives to visualize this influence. We further show that higher symmetry in scores of subpopulations can significantly reduce the trade-offs between fairness notions within a given acceptable strictness, even when sacrificing expressiveness. Our exploratory study may help to understand how to overcome the strict mathematical statements about the statistical incompatibility of certain fairness notions.