  An axiomatic approach is applied to the problem of extracting a ranking of
the alternatives from a pairwise comparison ratio matrix. The ordering induced
by row geometric mean method is proved to be uniquely determined by three
independent axioms, anonymity (independence of the labelling of alternatives),
responsiveness (a kind of monotonicity property) and aggregation invariance,
which requires the preservation of group consensus, that is, the pairwise
ranking between two alternatives should remain unchanged if unanimous
individual preferences are combined by geometric mean.
