A re-examination of the algebraic properties of the AHP as a ratio-scaling technique
AbstractThe Analytic Hierarchy Process (AHP) ratio-scaling approach is re-examined in view of the recent developments in mathematical psychology based on the so-called separable representations. The study highlights the distortions in the estimates based on the maximum eigenvalue method used in the AHP distinguishing the contributions due to random noises from the effects due to the nonlinearity of the subjective weighting function of separable representations. The analysis is based on the second order expansion of the Perron eigenvector and Perron eigenvalue in reciprocally symmetric matrices with perturbations. The asymptotic distributions of the Perron eigenvector and Perron eigenvalue are derived and related to the eigenvalue-based index of cardinal consistency used in the AHP. The results show the limits of using the latter index as a rule to assess the quality of the estimates of a ratio scale. The AHP method to estimate the ratio scales is compared with the classical ratio magnitude approach used in psychophysics.
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Bibliographic InfoPaper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2009_23.
Date of creation: 2009
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Separable representations; reciprocally symmetric matrices; consistency indexes.;
Find related papers by JEL classification:
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-11-27 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Michele Bernasconi & Christine Choirat & Raffaello Seri, 2009.
"The Analytic Hierarchy Process and the Theory of Measurement,"
2009_24, Department of Economics, University of Venice "Ca' Foscari".
- Michele Bernasconi & Christine Choirat & Raffaello Seri, 2010. "The Analytic Hierarchy Process and the Theory of Measurement," Management Science, INFORMS, vol. 56(4), pages 699-711, April.
- Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
- Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
- Michele Bernasconi & Christine Choirat & Raffaello Seri, 2013. "Empirical properties of group preference aggregation methods employed in AHP. Theory and evidence," Working Papers 2013:10, Department of Economics, University of Venice "Ca' Foscari".
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