On the similarity between ranking vectors in the pairwise comparison method

TL;DR

This paper compares two popular ranking methods derived from pairwise comparison matrices, providing an estimation of their differences based on matrix inconsistency and supported by theoretical analysis and Monte Carlo experiments.

Contribution

It introduces an estimation of the difference between eigenvalue and geometric mean methods based on matrix inconsistency, enhancing understanding of their relationship.

Findings

The methods yield similar results for consistent matrices.

Inconsistency increases the discrepancy between the methods.

Monte Carlo experiments confirm the theoretical estimates.

Abstract

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.