A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

The aim of this paper is to compare selected iterative algorithms for inconsistency reduction in pairwise comparisons by Monte Carlo simulations. We perform simulations for pairwise comparison matrices of the order
$n = 4 $
and
$n = 8 $
with the initial inconsistency
$0.10 < CR < 0.80 $
and entries drawn from Saaty’s fundamental scale. Subsequently, we evaluate the algorithms’ performance with respect to four measures that express the degree of original preference preservation. Our results indicate that no algorithm outperforms all other algorithms with respect to every measure of preference preservation. The Xu and Wei’s algorithm is the best with regard to the preservation of an original priority vector and the ranking of objects, the Step-by-Step algorithm best preserves the original preferences expressed in the form of a pairwise comparison matrix, and the algorithm of Szybowski keeps the most matrix entries unchanged during inconsistency reduction.