The rankability of weighted data from pairwise comparisons

Abstract

In prior work [ 4 ], Anderson et al. introduced a new problem, the rankability problem, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. Ranking is a fundamental data science task with numerous applications that include web search, data mining, cybersecurity, machine learning, and statistical learning theory. Yet little attention has been paid to the question of whether a dataset is suitable for ranking. As a result, when a ranking method is applied to a dataset with low rankability, the resulting ranking may not be reliable. Rankability paper [ 4 ] and its methods studied unweighted data for which the dominance relations are binary, i.e., an item either dominates or is dominated by another item. In this paper, we extend rankability methods to weighted data for which an item may dominate another by any finite amount. We present combinatorial approaches to a weighted rankability measure and apply our new measure to several weighted datasets.