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The Analytic Hierarchy Process (AHP) and its variants have long been used in numerous scientific and engineering applications. The present paper demonstrates that the original AHP and one of its variants have the potential to reach the wrong conclusion under certain circumstances. This paper examines the effectiveness of these two methods under the assumption that in reality the pairwise comparisons, which are used in these methods, take on continuous values. This assumption is made in order to capture the majority of the real world cases. The computational results in this paper demonstrate that when the above assumption is made, the AHP and the revised AHP might yield a different ranking of the alternatives than the ranking that would result if the actual relative importances were known. The same results also reveal a dramatic increase in the probability that an incorrect ranking occurs as the number of …