  We describe a framework for random pairwise comparisons matrices, inspired by
selected constructions releted to the so called inconsistency reduction of
pairwise comparisons (PC) matrices. In to build up structures on random
pairwise comparisons matrices, the set up for (deterministic) PC matrices for
non-reciprocal PC matrices is completed. The extension of basic concepts such
as inconsistency indexes 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.
