  We propose a framework for descriptively analyzing sets of partial orders
based on the concept of depth functions. Despite intensive studies of depth
functions in linear and metric spaces, there is very little discussion on depth
functions for non-standard data types such as partial orders. We introduce an
adaptation of the well-known simplicial depth to the set of all partial orders,
the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a
comparison of machine learning algorithms based on multidimensional performance
measures. Concretely, we analyze the distribution of different classifier
performances over a sample of standard benchmark data sets. Our results
promisingly demonstrate that our approach differs substantially from existing
benchmarking approaches and, therefore, adds a new perspective to the vivid
debate on the comparison of classifiers.
