Abstract
We study properties of weight extraction methods for pairwise comparison matrices that minimize suitable measures of inconsistency, ‘average error gravity’ measures, including one that leads to the geometric row means. The measures share essential global properties with the AHP inconsistency measure. By embedding the geometric mean in a larger class of methods we shed light on the choice between it and its traditional AHP competitor, the principal right eigenvector. We also suggest how to assess the extent of inconsistency by developing an alternative to the Random Consistency Index, which is not based on random comparison matrices, but based on judgemental error distributions. We define and discuss natural invariance requirements and show that the minimizers of average error gravity generally satisfy them, except a requirement regarding the order in which matrices and weights are synthesized. Only the geometric row mean satisfies this requirement also. For weight extraction we recommend the geometric mean.
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Acknowledgments
The constructive comments and questions by the reviewers are greatly appreciated. References to Aczél and Saaty (1983), Tuma (1987) and Blanquero et al. (2006) are gratefully acknowledged.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Dijkstra, T.K. On the extraction of weights from pairwise comparison matrices. Cent Eur J Oper Res 21, 103–123 (2013). https://doi.org/10.1007/s10100-011-0212-9
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DOI: https://doi.org/10.1007/s10100-011-0212-9