  Data-driven decision-making has drawn scrutiny from policy makers due to
fears of potential discrimination, and a growing literature has begun to
develop fair statistical techniques. However, these techniques are often
specialized to one model context and based on ad-hoc arguments, which makes it
difficult to perform theoretical analysis. This paper develops an optimization
hierarchy, which is a sequence of optimization problems with an increasing
number of constraints, for fair statistical decision problems. Because our
hierarchy is based on the framework of statistical decision problems, this
means it provides a systematic approach for developing and studying fair
versions of hypothesis testing, decision-making, estimation, regression, and
classification. We use the insight that qualitative definitions of fairness are
equivalent to statistical independence between the output of a statistical
technique and a random variable that measures attributes for which fairness is
desired. We use this insight to construct an optimization hierarchy that lends
itself to numerical computation, and we use tools from variational analysis and
random set theory to prove that higher levels of this hierarchy lead to
consistency in the sense that it asymptotically imposes this independence as a
constraint in corresponding statistical decision problems. We demonstrate
numerical effectiveness of our hierarchy using several data sets, and we use
our hierarchy to fairly perform automated dosing of morphine.
