Contribution of individual judgments toward inconsistency in pairwise comparisons

• A new measure is proposed for inconsistency in pair-wise comparison judgments.
• The measure finds the contribution of individual judgments toward overall inconsistency.
• To address ordinal inconsistency, another measure is proposed as a supplement.
• The two measures are shown to be useful to detect and correct inconsistent judgments.

Pairwise comparison (PC) is a well-established method to assist decision makers in estimating their preferences. In PCs, the acquired judgments are used to construct a PC matrix (PCM) that is used to check whether the inconsistency in judgments is acceptable or requires revision. The use of Consistency Ratio (CR)—a widely used measure for inconsistency—has been widely debated and the literature survey has identified a need for a more appropriate measure. Considering this need, a new measure, termed congruence, is proposed in this paper. The measure is shown to be useful in finding the contribution of individual judgments toward overall inconsistency of a PCM and, therefore, can be used to detect and correct cardinally inconsistent judgments. The proposed measure is applicable to incomplete sets of PC judgments without modification, unlike CR which requires a complete set of PC judgments. To address ordinal inconsistency, another measure termed dissonance, is proposed as a supplement to the congruence measure. The two measures appear useful in detecting both outliers and the phenomenon of consistency deadlock where all judgments equally contribute toward the overall inconsistency.