Search

There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary. The presented work formulates an estimation of the difference between priority vectors in the two most popular ranking methods: the eigenvalue method and the geometric mean method. The estimation provided refers to the inconsistency of the pairwise comparison matrix. Theoretical considerations are accompanied by Montecarlo experiments showing the discrepancy between the values of both methods., 18 pages, 4 figures

This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient $\tau$ and Spearman's rank coefficient $\rho$. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided., Comment: 13 pages, 4 figures