Distance-based measures of incoherence for pairwise comparisons

Coherence of preferences, and the measurement of its violation, has been a long standing issue in decision analysis. This paper focuses on preferences expressed by means of Pairwise Comparison Matrices. Whereas the consistency, that represents the full coherence, has been quantitatively measured by means of many indices proposed in literature, the same cannot be said for the other coherence conditions; as an example, thus far, the deviation of a set of preferences from transitivity condition has been represented by simple counts of how many times the transitivity condition is violated. As simple counts use only ordinal information discarding the information related with intensities of preferences, this manuscript introduces a cardinal approach where the deviation from the transitivity, and from further coherence levels, is seen as a matter of degree. This approach seems more suitable to cardinal preference relations where the decision makers’ preferences themselves are a matter of degree.