  This study investigates a powerful model, targeted to subjective assessments,
based on pairwise comparisons. It provides a proof that a distance-based
inconsistency reduction transforms an inconsistent pairwise comparisons (PC)
matrix into a consistent PC matrix which is generated by the geometric means of
rows of a given inconsistent PC matrix. The distance-based inconsistency
indicator was defined in 1993 for pairwise comparisons. Its convergence was
analyzed in 1996 (regretfully, with an incomplete proof; finally completed in
2010). However, there was no clear interpretation of the convergence limit
which is of considerable importance for applications and this study does so.
