Consider the problem of allocating a scarce resource to people. A fair decision procedure is one where each person has an equal chance of receiving the resource. An unfair decision procedure is one where the chances are not equal. Normally we think that, in an unfair decision procedure, that the correct way to redress the injustice is by rerunning the allocation using a fair decision procedure. In this paper, I show that this actually creates an overall bias favouring one person, (...) and solutions to this problem are counterintuitive, in that they typically involve introducing additional unfair elements into the situation. (shrink)