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A new rank correlation coefficient with application to the consensus ranking problem
Author(s) -
Emond Edward J.,
Mason David W.
Publication year - 2002
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.313
Subject(s) - ranking (information retrieval) , rank (graph theory) , metric (unit) , rank correlation , mathematics , correlation coefficient , distance correlation , statistics , correlation , measure (data warehouse) , combinatorics , computer science , data mining , artificial intelligence , economics , random variable , operations management , geometry
The consensus ranking problem has received much attention in the statistical literature. Given m rankings of n objects the objective is to determine a consensus ranking. The input rankings may contain ties, be incomplete, and may be weighted. Two solution concepts are discussed, the first maximizing the average weighted rank correlation of the solution ranking with the input rankings and the second minimizing the average weighted Kemeny–Snell distance. A new rank correlation coefficient called τ x is presented which is shown to be the unique rank correlation coefficient which is equivalent to the Kemeny‐Snell distance metric. The new rank correlation coefficient is closely related to Kendall's tau but differs from it in the way ties are handled. It will be demonstrated that Kendall's τ b is flawed as a measure of agreement between weak orderings and should no longer be used as a rank correlation coefficient. The use of τ x in the consensus ranking problem provides a more mathematically tractable solution than the Kemeny–Snell distance metric because all the ranking information can be summarized in a single matrix. The methods described in this paper allow analysts to accommodate the fully general consensus ranking problem with weights, ties, and partial inputs. Copyright © 2002 John Wiley & Sons, Ltd.