Entropy steered Kendall's tau measure for a fair Rank Aggregation

Abstract

Rank Aggregation, in layman's term, is a technique of inferring a consensus ranking when multiple ranked lists of a set objects are given. Rank Aggregation has importance in a wide spectrum of fields including spam reduction in meta search, social choice theory of welfare economics, microarray analysis in bioinformatics etc. Unfortunately an ample Rank Aggregation is computationally a hard task to do even for a small set of objects. Till the date several heuristic algorithms have been devised towards its improvement. Almost all these heuristics rely on certain notion of disagreement between two ranked lists. Kendall's tau distance is undoubtedly quite popular among them, for its various desirable features. Kendall's tau distance is often used by different heuristics for approximating the consensus list. We in this article point out an important drawback of the Kendall's tau distance and propose a modified measure by using Shanon's Entropy formula. We also explain its benefit through some artificial and real data.