Evaluating Relationship of Consistency Ratio and Number of Alternatives on Rank Reversal in the AHP

ABSTRACT This article shows the simulation result of the rank reversal phenomenon with respect to the changing values of consistency ratio and the number of alternatives. The simulation result reveals that the number of alternatives and the consistency ratio have significant effect on the occurrence of rank reversal. The more the number of alternatives is, the higher the probability of rank reversal occurrence becomes. The more inconsistent the judgment is, the more likely the rank reversal will occur. This result is based on two-way analysis of variance in which the number of alternatives and the consistency ratio are considered as factors, and the probability of rank reversal occurrence is regarded as the response variable. The number of alternatives of 4 to 7 and the consistency ratios ranging between 0.02 and 0.20 are investigated. The observation is based on the rank reversal that occurs after adding a copy of the best existing alternative.

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