  In this paper, we provide a moral analysis of two criteria of statistical
fairness debated in the machine learning literature: 1) calibration between
groups and 2) equality of false positive and false negative rates between
groups. In our paper, we focus on moral arguments in support of either measure.
The conflict between group calibration vs. false positive and false negative
rate equality is one of the core issues in the debate about group fairness
definitions among practitioners. For any thorough moral analysis, the meaning
of the term fairness has to be made explicit and defined properly. For our
paper, we equate fairness with (non-)discrimination, which is a legitimate
understanding in the discussion about group fairness. More specifically, we
equate it with prima facie wrongful discrimination in the sense this is used in
Prof. Lippert-Rasmussen's treatment of this definition. In this paper, we argue
that a violation of group calibration may be unfair in some cases, but not
unfair in others. This is in line with claims already advanced in the
literature, that algorithmic fairness should be defined in a way that is
sensitive to context. The most important practical implication is that
arguments based on examples in which fairness requires between-group
calibration, or equality in the false-positive/false-negative rates, do no
generalize. For it may be that group calibration is a fairness requirement in
one case, but not in another.
