In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

Pairwise comparisons constitute a popular and important tool for multiple-criteria decision making. Consistency is one particular aspect of pairwise comparisons that has been studied thoroughly in recent decades since human judgements are seldom fully consistent. The aim of this paper is to propose a new simple and intuitive iterative Step-by-Step (SBS) algorithm for inconsistency reduction of a (multiplicative) pairwise comparison matrix based on step-by-step changes of the most inconsistent matrix element, where the inconsistency is measured by a modified Koczkodaj’s inconsistency index. A comparison of the proposed SBS algorithm with other algorithms for inconsistency reduction is provided as well.

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.