  As algorithmic prediction systems have become widespread, fears that these
systems may inadvertently discriminate against members of underrepresented
populations have grown. With the goal of understanding fundamental principles
that underpin the growing number of approaches to mitigating algorithmic
discrimination, we investigate the role of information in fair prediction. A
common strategy for decision-making uses a predictor to assign individuals a
risk score; then, individuals are selected or rejected on the basis of this
score. In this work, we study a formal framework for measuring the information
content of predictors. Central to this framework is the notion of a refinement,
first studied by Degroot and Fienberg. Intuitively, a refinement of a predictor
$z$ increases the overall informativeness of the predictions without losing the
information already contained in $z$. We show that increasing information
content through refinements improves the downstream selection rules across a
wide range of fairness measures (e.g. true positive rates, false positive
rates, selection rates). In turn, refinements provide a simple but effective
tool for reducing disparity in treatment and impact without sacrificing the
utility of the predictions. Our results suggest that in many applications, the
perceived "cost of fairness" results from an information disparity across
populations, and thus, may be avoided with improved information.
