  Following related work in law and policy, two notions of disparity have come
to shape the study of fairness in algorithmic decision-making. Algorithms
exhibit treatment disparity if they formally treat members of protected
subgroups differently; algorithms exhibit impact disparity when outcomes differ
across subgroups, even if the correlation arises unintentionally. Naturally, we
can achieve impact parity through purposeful treatment disparity. In one thread
of technical work, papers aim to reconcile the two forms of parity proposing
disparate learning processes (DLPs). Here, the learning algorithm can see group
membership during training but produce a classifier that is group-blind at test
time. In this paper, we show theoretically that: (i) When other features
correlate to group membership, DLPs will (indirectly) implement treatment
disparity, undermining the policy desiderata they are designed to address; (ii)
When group membership is partly revealed by other features, DLPs induce
within-class discrimination; and (iii) In general, DLPs provide a suboptimal
trade-off between accuracy and impact parity. Based on our technical analysis,
we argue that transparent treatment disparity is preferable to occluded methods
for achieving impact parity. Experimental results on several real-world
datasets highlight the practical consequences of applying DLPs vs. per-group
thresholds.
