Inconsistency and Rank Reversal in Pairwise Comparison

We study the relationship between Rank Reversal phenomenon and various consistency / transitivity properties for a pairwise comparison matrix. It is known that consistency condition can be weakened by considering different less demanding transitivity-related properties as R-transitivity, weak consistency, (restricted) max-min or max-max transitivity. We study the influence of the different types of transitivity-related properties on the Rank Reversal phenomenon and we determine which type of consistency properties can prevent Rank Reversal. We prove some general results and we report and comment outcomes from numerical simulations. We take into account different known prioritization methods, as the principal eigenvector and the Logarithmic Least Squares. We discuss and compare our results with numerous other studies in the literature.