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Another potential strong shortcoming of AHP

Listed author(s):
  • Joaquín Pérez, José L. Jimeno, Ethel Mokotoff

    (Departamento de Fundamentos de Economía. Universidad de Alcalá (Spain))

In the last twenty years many features of Saaty's Analytical Hierarchy Process (AHP) have been criticised, especially the additive hierarchical composition of conventional AHP, which leads to the possibility of occurrence of the Rank Reversal phenomenon (adding an irrelevant alternative may cause a reversal in the ranking at the top). In the context of a variable number of alternatives this rank reversal possibility is likely to be a shortcoming of the aggregation method, since the global priorities obtained and the corresponding rankings can be seen, to some extent, as arbitrary. In this paper we show another feature of AHP which may be, and in many application contexts will indeed be, an even stronger shortcoming of the method. It consists in the fact that the addition of indifferent criteria (for which all alternatives perform equally) causes a significant alteration of the aggregated priorities of alternatives, with important consequences. Although not in three-level hierarchies, in more complex hierarchies rank reversal may happen. Since in almost all applications of AHP the set of criteria is not fixed ex-ante but is variable and is constructed in accordance with reasons of relevance and simplicity, almost all applications of AHP are potentially flawed.

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Paper provided by Programa de doctorado en Economía. Universidad de Alcalá. in its series Doctorado en Economía- documentos de trabajo with number 8/02.

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Length: pages 14
Date of creation: 01 May 2001
Date of revision: 01 Jun 2002
Handle: RePEc:alc:alcddt:8/02
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  1. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
  2. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
  3. Thomas L. Saaty, 1990. "An Exposition of the AHP in Reply to the Paper "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 259-268, March.
  4. Saaty, Thomas L & Vargas, Luis G, 1984. "The legitimacy of rank reversal," Omega, Elsevier, vol. 12(5), pages 513-516.
  5. Joaquin Pérez, 1995. "Some Comments on Saaty's AHP," Management Science, INFORMS, vol. 41(6), pages 1091-1095, June.
  6. Belton, Valerie & Gear, Tony, 1983. "On a short-coming of Saaty's method of analytic hierarchies," Omega, Elsevier, vol. 11(3), pages 228-230.
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