Characterization of the row geometric mean ranking with a group consensus axiom

Abstract

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.

17 pages, 2 figures

References in corpus (4)

• Characterization of an inconsistency ranking for pairwise comparison matrices
• Some impossibilities of ranking in generalized tournaments
• An impossibility theorem for paired comparisons
• Eigenvector Method and rank reversal in group decision making revisited

Cited by in corpus (7)

• A characterization of the Logarithmic Least Squares Method
• University rankings from the revealed preferences of the applicants
• On the monotonicity of the eigenvector method
• Axiomatizations of inconsistency indices for triads
• Right-left asymmetry of the eigenvector method: A simulation study
• The logarithmic least squares priorities and ordinal violations in the best-worst method
• Almost optimal manipulation of a pair of alternatives