In this work, we tackle the problem of intersectional group fairness in the classification setting, where the objective is to learn discrimination-free models in the presence of several intersecting sensitive groups. First, we illustrate various shortcomings of existing fairness measures commonly used to capture intersectional fairness. Then, we propose a new framework called the $\alpha$ Intersectional Fairness framework, which combines the absolute and the relative performances between sensitive groups. Finally, we provide various analyses of our proposed framework, including the min-max and efficiency analysis. Our experiments using the proposed framework show that several in-processing fairness approaches show no improvement over a simple unconstrained approach. Moreover, we show that these approaches minimize existing fairness measures by degrading the performance of the best of the group instead of improving the worst.

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