  Fair Machine Learning endeavors to prevent unfairness arising in the context
of machine learning applications embedded in society. Despite the variety of
definitions of fairness and proposed "fair algorithms", there remain unresolved
conceptual problems regarding fairness. In this paper, we dissect the role of
statistical independence in fairness and randomness notions regularly used in
machine learning. Thereby, we are led to a suprising hypothesis: randomness and
fairness can be considered equivalent concepts in machine learning.
  In particular, we obtain a relativized notion of randomness expressed as
statistical independence by appealing to Von Mises' century-old foundations for
probability. This notion turns out to be "orthogonal" in an abstract sense to
the commonly used i.i.d.-randomness. Using standard fairness notions in machine
learning, which are defined via statistical independence, we then link the ex
ante randomness assumptions about the data to the ex post requirements for fair
predictions. This connection proves fruitful: we use it to argue that
randomness and fairness are essentially relative and that both concepts should
reflect their nature as modeling assumptions in machine learning.
