A characterization of the Logarithmic Least Squares Method
arXiv:1704.05321 · doi:10.1016/j.ejor.2018.12.046
Abstract
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.
11 pages
References in corpus (6)
- An application of incomplete pairwise comparison matrices for ranking top tennis players
- Efficient weight vectors from pairwise comparison matrices
- Characterization of an inconsistency ranking for pairwise comparison matrices
- Axiomatizations of inconsistency indices for triads
- Characterization of the row geometric mean ranking with a group consensus axiom
- Eigenvector Method and rank reversal in group decision making revisited
Cited by in corpus (9)
- The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices
- University rankings from the revealed preferences of the applicants
- On the monotonicity of the eigenvector method
- Axiomatizations of inconsistency indices for triads
- An alternative quality of life ranking on the basis of remittances
- Right-left asymmetry of the eigenvector method: A simulation study
- A clustering approach for pairwise comparison matrices
- The logarithmic least squares priorities and ordinal violations in the best-worst method
- The Fundamental Theorem of Barzilai does not hold