Satisfaction of the condition of order preservation: A simulation study

We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty’s consistency index below 0.10), and the more inconsistent matrices (Saaty’s consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj’s inconsistency index and Saaty’s consistency index, respectively, and we provide graphs to illustrate these relationships.