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ABSTRACTTwo related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisfactorily resolved, although both date from the early 1980s. The first relates to ambiguity in the meaning of the relative importance of one criterion as compared to another. The second is concerned with reversals of rank alleged to be possible when new options are introduced in an AHP problem. Both proponents and critics of AHP agree that rank reversals occur, but disagree on the legitimacy of such reversals. This paper shows that there is a necessary correspondence between the manner in which criteria importances are interpreted and computed and the manner in which the weights of the options under each criterion are normalized. In general, if this relationship is ignored, incorrect weights are generated for options under consideration regardless of whether new options are added or deleted. A rank reversal on the addition of an option is merely symptomatic of this fact, and such reversals do not occur when the correspondence condition is met.

AbstractIn the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single‐criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships.

ABSTRACTIn an earlier paper [11], the problems of rank reversals and invalid composite priorities in AHP were addressed by modifications to the AHP procedure. That solution was subsequently criticized [5]. In this paper, we rebut these criticisms, and we show how rank reversals in AHP can arise merely from the process of normalizing local priorities.