On rank reversal in decision analysis

Authors:
Ying-Ming Wang;Ying Luo
Affiliations:
School of Economics and Management, Tongji University, Shanghai 200092, PR China and School of Public Administration, Fuzhou University, Fuzhou 350002, PR China;School of Management, Xiamen University, Xiamen 361005, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

Analytic hierarchy process (AHP) has been criticized for its possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper shows the fact that the rank reversal phenomenon occurs not only in the AHP but also in many other decision making approaches such as the Borda-Kendall (BK) method for aggregating ordinal preferences, the simple additive weighting (SAW) method, the technique for order preference by similarity to ideal solution (TOPSIS) method, and the cross-efficiency evaluation method in data envelopment analysis (DEA). Numerical examples are provided to illustrate the rank reversal phenomenon in these popular decision making approaches.