A Monte Carlo Study of Pairwise Comparisons

Abstract: Consistent approximations obtained by geometric means ($GM$) and the principal eigenvector ($EV$), turned out to be close enough for 1,000,000 not-so-inconsistent pairwise comparisons matrices. In this respect both methods are accurate enough for most practical applications. As the enclosed Table 1 demonstrates, the biggest difference between average deviations of $GM$ and $EV$ solutions is 0.00019 for the Euclidean metric and 0.00355 for the Tchebychev metric. For practical applications, this precision is far better than expected. After all we are talking, in most cases, about relative subjective comparisons and one tenth of a percent is usually below our threshold of perception.