  A crucial but often neglected aspect of algorithmic fairness is the question
of how we justify enforcing a certain fairness metric from a moral perspective.
When fairness metrics are proposed, they are typically argued for by
highlighting their mathematical properties. Rarely are the moral assumptions
beneath the metric explained. Our aim in this paper is to consider the moral
aspects associated with the statistical fairness criterion of independence
(statistical parity). To this end, we consider previous work, which discusses
the two worldviews "What You See Is What You Get" (WYSIWYG) and "We're All
Equal" (WAE) and by doing so provides some guidance for clarifying the possible
assumptions in the design of algorithms. We present an extension of this work,
which centers on morality. The most natural moral extension is that
independence needs to be fulfilled if and only if differences in predictive
features (e.g. high school grades and standardized test scores are predictive
of performance at university) between socio-demographic groups are caused by
unjust social disparities or measurement errors. Through two counterexamples,
we demonstrate that this extension is not universally true. This means that the
question of whether independence should be used or not cannot be satisfactorily
answered by only considering the justness of differences in the predictive
features.
