How strongly do rank similarity coefficients differ used in decision making problems?

Abstract

It is common practice in the MCDA to use several multi-criteria decision methods and then compares obtained rankings with one or two different rank correlation coefficients. The problem is that different rank correlation coefficient gives different values for the same pair of rankings, and the number of studies which tries to investigate it is small. Studying the similarity of rankings is a very important challenge in multi-criteria decision support, and the coefficients themselves seem to be the most practical ways of evaluating rankings. This paper compares chosen rank correlation coefficients to show how much different they are. Spearman’s, Weighted Spearman’s, Kendall Tau and Rank similarity correlation coefficient are compared statistically. The paper confirms that the coefficients are closely related, and their dependence is graphically represented, which initiates research towards allows for their better selection in the future. In conclusions, directions of further development are indicated.

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