Title: Pretending Fair Decisions via Stealthily Biased Sampling,
Abstract: 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.