  Adequate uncertainty representation and quantification have become imperative
in various scientific disciplines, especially in machine learning and
artificial intelligence. As an alternative to representing uncertainty via one
single probability measure, we consider credal sets (convex sets of probability
measures). The geometric representation of credal sets as $d$-dimensional
polytopes implies a geometric intuition about (epistemic) uncertainty. In this
paper, we show that the volume of the geometric representation of a credal set
is a meaningful measure of epistemic uncertainty in the case of binary
classification, but less so for multi-class classification. Our theoretical
findings highlight the crucial role of specifying and employing uncertainty
measures in machine learning in an appropriate way, and for being aware of
possible pitfalls.

Machine Learning;Artificial Intelligence;Machine Learning