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

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  • Michele Bernasconi

    ()
    (Department of Economics, University Of Venice CĂ  Foscari)

  • Christine Choirat

    (Department of Quantitative Methods, School of Economics and Business Management, Universidad de Navarra.)

  • Raffaello Seri

    (Dipartimento di Economia, UniversitĂ  dell'Insubria.)

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.

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Bibliographic Info

Paper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2009_23.

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Length: 33
Date of creation: 2009
Date of revision:
Handle: RePEc:ven:wpaper:2009_23

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Keywords: Separable representations; reciprocally symmetric matrices; consistency indexes.;

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  1. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 497-528, May.
  2. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, INFORMS, vol. 32(7), pages 841-855, July.
  3. Michele Bernasconi & Christine Choirat & Raffaello Seri, 2010. "The Analytic Hierarchy Process and the Theory of Measurement," Management Science, INFORMS, INFORMS, vol. 56(4), pages 699-711, April.
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Cited by:
  1. Michele Bernasconi & Christine Choirat & Raffaello Seri, 2013. "Empirical properties of group preference aggregation methods employed in AHP. Theory and evidence," Working Papers, Department of Economics, University of Venice "Ca' Foscari" 2013:10, Department of Economics, University of Venice "Ca' Foscari".

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