Pretending Fair Decisions via Stealthily Biased Sampling

Fairness by decision-makers is believed to be auditable by third parties. In this study, we show that this is not always true. We consider the following scenario. Imagine a decision-maker who discloses a subset of his dataset with decisions to make his decisions auditable. If he is corrupt, and he deliberately selects a subset that looks fair even though the overall decision is unfair, can we identify this decision-maker's fraud? We answer this question negatively. We first propose a sampling method that produces a subset whose distribution is biased from the original (to pretend to be fair); however, its differentiation from uniform sampling is difficult. We call such a sampling method as stealthily biased sampling, which is formulated as a Wasserstein distance minimization problem, and is solved through a minimum-cost flow computation. We proved that the stealthily biased sampling minimizes an upper-bound of the indistinguishability. We conducted experiments to see that the stealthily biased sampling is, in fact, difficult to detect.