  Ensuring fairness of prediction-based decision making is based on statistical
group fairness criteria. Which one of these criteria is the morally most
appropriate one depends on the context, and its choice requires an ethical
analysis. In this paper, we present a step-by-step procedure integrating three
elements: (a) a framework for the moral assessment of what fairness means in a
given context, based on the recently proposed general principle of "Fair
equality of chances" (FEC) (b) a mapping of the assessment's results to
established statistical group fairness criteria, and (c) a method for
integrating the thus-defined fairness into optimal decision making. As a second
contribution, we show new applications of the FEC principle and show that, with
this extension, the FEC framework covers all types of group fairness criteria:
independence, separation, and sufficiency. Third, we introduce an extended
version of the FEC principle, which additionally allows accounting for morally
irrelevant elements of the fairness assessment and links to well-known
relaxations of the fairness criteria. This paper presents a framework to
develop fair decision systems in a conceptually sound way, combining the moral
and the computational elements of fair prediction-based decision-making in an
integrated approach. Data and code to reproduce our results are available at
https://github.com/joebaumann/fair-prediction-based-decision-making.
