A Chi – Square based approach to consistency evaluation of multiplicative preference relations

In this paper we develop the idea introduced by Lipovetski and Conklin in 2002 of considering a pairwise comparison matrix (PCM) as a contingency table. Instead of focusing on outliers detection, we use the Chi-square value as an index to evaluate the deviation of a pairwise comparison matrix from consistency. We verify by means of numerical simulations that our new index satisfies a set of five properties recently introduced in order to characterize an inconsistency index. Therefore, we argue that our Chi-square based index can be considered as a suitable index for evaluating the inconsistency of a PCM.