A Note on the Significance Adjustment for FA*IR with Two Protected Groups

Abstract

In this report we provide an improvement of the significance adjustment from the FA*IR algorithm in Zehlike et al. [2], which did not work for very short rankings in combination with a low minimum proportion 𝑝 for the protected group. We show how the minimum number of protected candidates per ranking position can be calculated exactly and provide a mapping from the continuous space of significance levels (𝛼) to a discrete space of tables, which allows us to find 𝛼 corr using a binary search heuristic.