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A re-examination of the algebraic properties of the AHP as a ratio-scaling technique

Michele Bernasconi (), Christine Choirat and Raffaello Seri

No 2009_23, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: The 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.

Keywords: Separable representations; reciprocally symmetric matrices; consistency indexes. (search for similar items in EconPapers)
JEL-codes: C44 (search for similar items in EconPapers)
Pages: 33
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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