  Fairness is a concept of justice. Various definitions exist, some of them
conflicting with each other. In the absence of an uniformly accepted notion of
fairness, choosing the right kind for a specific situation has always been a
central issue in human history. When it comes to implementing sustainable
fairness in artificial intelligence systems, this old question plays a key role
once again: How to identify the most appropriate fairness metric for a
particular application? The answer is often a matter of context, and the best
choice depends on ethical standards and legal requirements. Since ethics
guidelines on this topic are kept rather general for now, we aim to provide
more hands-on guidance with this document. Therefore, we first structure the
complex landscape of existing fairness metrics and explain the different
options by example. Furthermore, we propose the "Fairness Compass", a tool
which formalises the selection process and makes identifying the most
appropriate fairness definition for a given system a simple, straightforward
procedure. Because this process also allows to document the reasoning behind
the respective decisions, we argue that this approach can help to build trust
from the user through explaining and justifying the implemented fairness.
