Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

Abstract

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 con- cerning 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 τ and Spearman’s rank coef-ficient ρ . Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided.