A Omitted Proofs

We start with describing the pseudocode of our algorithm.Algorithm 1: Algorithm to compute closest weak fair ranking under Kendall tauInput: Input ranking π S Initialize a set P . Iterate over ranking σ, and count the fraction of elements in the top-k from each group. We first provide the pseudocode of our algorithm.Algorithm 2: Algorithm to compute closest fair ranking under Kendall tauInput: Input ranking π S If not, return "No fair ranking exists"; else continue. The claim now follows.Claim 3.9. From Claim 3.7 we know that Algorithm 1 and the optimal solution have the same set of elements.