A Weighted Generalization of the Graham-Diaconis Inequality for Ranked List Similarity

Abstract

The Graham-Diaconis inequality shows the equivalence between two well-known methods of measuring the similarity of two given ranked lists of items: Spearman's footrule and Kendall's tau. The original inequality assumes unweighted items in input lists. In this paper, we first define versions of these methods for weighted items. We then prove a generalization of the inequality for the weighted versions.