  In selection processes such as hiring, promotion, and college admissions,
implicit bias toward socially-salient attributes such as race, gender, or
sexual orientation of candidates is known to produce persistent inequality and
reduce aggregate utility for the decision maker. Interventions such as the
Rooney Rule and its generalizations, which require the decision maker to select
at least a specified number of individuals from each affected group, have been
proposed to mitigate the adverse effects of implicit bias in selection. Recent
works have established that such lower-bound constraints can be very effective
in improving aggregate utility in the case when each individual belongs to at
most one affected group. However, in several settings, individuals may belong
to multiple affected groups and, consequently, face more extreme implicit bias
due to this intersectionality. We consider independently drawn utilities and
show that, in the intersectional case, the aforementioned non-intersectional
constraints can only recover part of the total utility achievable in the
absence of implicit bias. On the other hand, we show that if one includes
appropriate lower-bound constraints on the intersections, almost all the
utility achievable in the absence of implicit bias can be recovered. Thus,
intersectional constraints can offer a significant advantage over a
reductionist dimension-by-dimension non-intersectional approach to reducing
inequality.
