Removing algorithmic discrimination (with minimal individual error)

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analytically in the case of two populations, with a uniform bonus-malus on the zones where each population is a majority. We then address the general case of n populations, where the entanglement of populations does not allow a similar analytical solution. We show that an approximate solution with an arbitrarily high level of precision can be computed with linear programming. Finally, we address the reverse problem where the error should not go beyond a certain value and we seek to minimize the discrimination.