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Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom

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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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Acknowledgements

We are grateful to Sándor Bozóki and Matteo Brunelli for useful advice. We thank two anonymous referees for beneficial remarks and suggestions. The research was supported by OTKA Grant K111797 and by the MTA Premium Post Doctorate Research Program.

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Authors and Affiliations

  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

    László Csató

  2. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE), Budapest, Hungary

    László Csató

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  1. László Csató
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Csató, L. Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom. Group Decis Negot 27, 1011–1027 (2018). https://doi.org/10.1007/s10726-018-9589-3

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