Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom |
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| Authors: | László Csató |
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| Institution: | 1.Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems,Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI),Budapest,Hungary;2.Department of Operations Research and Actuarial Sciences,Corvinus University of Budapest (BCE),Budapest,Hungary |
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| 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. |
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