  In domains such as criminal justice, medicine, and social welfare, decision
makers increasingly have access to algorithmic Risk Assessment Instruments
(RAIs). RAIs estimate the risk of an adverse outcome such as recidivism or
child neglect, potentially informing high-stakes decisions such as whether to
release a defendant on bail or initiate a child welfare investigation. It is
important to ensure that RAIs are fair, so that the benefits and harms of such
decisions are equitably distributed.
  The most widely used algorithmic fairness criteria are formulated with
respect to observable outcomes, such as whether a person actually recidivates,
but these criteria are misleading when applied to RAIs. Since RAIs are intended
to inform interventions that can reduce risk, the prediction itself affects the
downstream outcome. Recent work has argued that fairness criteria for RAIs
should instead utilize potential outcomes, i.e. the outcomes that would occur
in the absence of an appropriate intervention. However, no methods currently
exist to satisfy such fairness criteria.
  In this paper, we target one such criterion, counterfactual equalized odds.
We develop a post-processed predictor that is estimated via doubly robust
estimators, extending and adapting previous post-processing approaches to the
counterfactual setting. We also provide doubly robust estimators of the risk
and fairness properties of arbitrary fixed post-processed predictors. Our
predictor converges to an optimal fair predictor at fast rates. We illustrate
properties of our method and show that it performs well on both simulated and
real data.
