Robustness of priority deriving methods for pairwise comparison matrices against rank reversal: a probabilistic approach

This work aims to answer the natural question of how probable it is that a given method produces rank reversal in a priority vector (PV) if a decision maker (DM) introduces perturbations to the pairwise comparison matrix (PCM) under concern. We focus primarily on the concept of robustness against rank reversal, independent of specific methods, and provide an in-depth statistical insight into the application of the Monte Carlo (MC) approach in this context. This concept is applied to three selected methods, with a special emphasis on scenarios where a method may not provide outputs for all possible PCMs. All results presented in this work are replicable using our open-source implementation.