  We study the impact of pre and post processing for reducing discrimination in
data-driven decision makers. We first analyze the fundamental trade-off between
fairness and accuracy in a pre-processing approach, and propose a design for a
pre-processing module based on a convex optimization program, which can be
added before the original classifier. This leads to a fundamental lower bound
on attainable discrimination, given any acceptable distortion in the outcome.
Furthermore, we reformulate an existing post-processing method in terms of our
accuracy and fairness measures, which allows comparing post-processing and
pre-processing approaches. We show that under some mild conditions,
pre-processing outperforms post-processing. Finally, we show that by
appropriate choice of the discrimination measure, the optimization problem for
both pre and post processing approaches will reduce to a linear program and
hence can be solved efficiently.
