A characterization of the Logarithmic Least Squares Method

•Derivation of preference vectors from pairwise comparison matrices is addressed.•We provide an axiomatic characterization of the Logarithmic Least Squares Method.•It is the only reasonable weight vector invariant to a transformation of triads.•The use of any other methods requires explaining the vi...

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Bibliographic Details
Published in:European journal of operational research Vol. 276; no. 1; pp. 212 - 216
Main Author: Csató, László
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2019
Subjects:
Axiomatic approach
Characterization
Decision analysis
Geometric mean
Pairwise comparisons
Axiomatic approach
Characterization
Pairwise comparisons
Decision analysis
Geometric mean
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•Derivation of preference vectors from pairwise comparison matrices is addressed.•We provide an axiomatic characterization of the Logarithmic Least Squares Method.•It is the only reasonable weight vector invariant to a transformation of triads.•The use of any other methods requires explaining the violation of this axiom. We provide an axiomatic characterization of the Logarithmic Least Squares Method (sometimes called row geometric mean), used for deriving a preference vector from a pairwise comparison matrix. This procedure is shown to be the only one satisfying two properties, correctness in the consistent case, which requires the reproduction of the inducing vector for any consistent matrix, and invariance to a specific transformation on a triad, that is, the weight vector is not influenced by an arbitrary multiplication of matrix elements along a 3-cycle by a positive scalar.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2018.12.046