On the conjoint estimation of inconsistency and intransitivity of pairwise comparisons

Consistency and transitivity are two desirable properties of valued preferences which, however, are seldom satisfied in real-world applications. Different indices have been proposed to measure inconsistency and intransitivity separately, and recently scholars tried to merge these two concepts and use them in concert to estimate the irrationality of preferences. In this paper we formally investigate the existence (or non-existence) of functions capable of capturing both phenomena at the same time.