  The study of fairness in intelligent decision systems has mostly ignored
long-term influence on the underlying population. Yet fairness considerations
(e.g. affirmative action) have often the implicit goal of achieving balance
among groups within the population. The most basic notion of balance is
eventual equality between the qualifications of the groups. How can we
incorporate influence dynamics in decision making? How well do
dynamics-oblivious fairness policies fare in terms of reaching equality? In
this paper, we propose a simple yet revealing model that encompasses (1) a
selection process where an institution chooses from multiple groups according
to their qualifications so as to maximize an institutional utility and (2)
dynamics that govern the evolution of the groups' qualifications according to
the imposed policies. We focus on demographic parity as the formalism of
affirmative action.
  We then give conditions under which an unconstrained policy reaches equality
on its own. In this case, surprisingly, imposing demographic parity may break
equality. When it doesn't, one would expect the additional constraint to reduce
utility, however, we show that utility may in fact increase. In more realistic
scenarios, unconstrained policies do not lead to equality. In such cases, we
show that although imposing demographic parity may remedy it, there is a danger
that groups settle at a worse set of qualifications. As a silver lining, we
also identify when the constraint not only leads to equality, but also improves
all groups. This gives quantifiable insight into both sides of the mismatch
hypothesis. These cases and trade-offs are instrumental in determining when and
how imposing demographic parity can be beneficial in selection processes, both
for the institution and for society on the long run.
