From fair decision making to social equality

Hussein Mozannar, Nathan Srebro, Mesrob I Ohannessian

Abstract:

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.