Another potential strong shortcoming of AHP
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.
|Date of creation:||01 May 2001|
|Date of revision:||01 Jun 2002|
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- 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.
- Joaquin Pérez, 1995. "Some Comments on Saaty's AHP," Management Science, INFORMS, vol. 41(6), pages 1091-1095, June.
- James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
- Saaty, Thomas L & Vargas, Luis G, 1984. "The legitimacy of rank reversal," Omega, Elsevier, vol. 12(5), pages 513-516.
- James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
- 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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