On random pairwise comparisons matrices and their geometry

Abstract

Abstract We describe a framework for random pairwise comparisons matrices, inspired by selected constructions related to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In order to build up structures on random pairwise comparisons matrices, the set up for (deterministic) PC matrices for non-reciprocal PC matrices is completed. Basic concepts such as inconsistency indices and geometric mean method are extended to random pairwise comparisons matrices and completed by new notions which seem useful to us. Two procedures for (random) inconsistency reduction are sketched, based on well-known existing objects, and a fiber bundle-like decomposition of random pairwise comparisons is proposed.