Satisfaction of the Condition of Order Preservation: A Simulation Study

TL;DR

This study investigates how different inconsistency levels in pairwise comparison matrices affect the satisfaction of order preservation, comparing eigenvalue and geometric mean methods across various matrix sizes.

Contribution

It provides a comparative analysis of EV and GM methods in maintaining order preservation under varying inconsistency levels in MPCMs.

Findings

GM and EV methods preserve order almost identically.

Frequency of violations increases linearly with inconsistency.

Results are illustrated with graphs for matrices of sizes 4, 7, and 9.

Abstract

We examine satisfaction of the condition of order preservation (COP) with respect to different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order n = {3,4,...,9}, where a priority vector is derived both by the eigenvalue method (EV) and the geometric mean (GM) method. Our results suggest the GM method and the EV method preserve the COP condition almost identically, both for the less inconsistent matrices (with Saaty's consistency index CI <0.10), and the more inconsistent matrices (with CI >= 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with increasing inconsistency of MPCMs measured by Koczkodaj's inconsistency index and Saaty's consistency index respectively, and we provide graphs to illustrate these relationships for MPCMs of the order n ={4, 7, 9}.