A supervised learning approach to rankability

The rankability of data is a novel problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have been proposed, based on comparisons to a complete dominance graph via combinatorial and linear algebraic methods. Interest in this field has been steadily expanding, with a growing appreciation for the significance of evaluating rankability across diverse applications. Consequently, the validation of these rankability methodologies in different scenarios holds paramount importance. In this paper, we review existing measures of rankability and highlight some questions to which they give rise. We go on to introduce a new framework designed to evaluate rankability with a tailored approach, one that allows for efficient estimation in specific problem domains. Finally, we present a comparative analysis of these metrics by applying them to both synthetic and real-life sports data.