Consistency measures for pairwise comparison matrices

We propose new measures of consistency of additive and multiplicative pairwise comparison matrices. These measures, the relative consistency and relative error, are easy to compute and have clear and simple algebraic and geometric meaning, interpretation and properties. The correspondence between these measures in the additive and multiplicative cases reflects the same correspondence which underpins the algebraic structure of the problem and relates naturally to the corresponding optimization models and axiom systems. The relative consistency and relative error are related to one another by the theorem of Pythagoras through the decomposition of comparison matrices into their consistent and error components. One of the conclusions of our analysis is that inconsistency is not a sufficient reason for revision of judgements.