lkio related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisk t o r i l y 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 normali7ed. In general, if this relationship is ignored, incorrect weights are generated f o r 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 riot occur when the correspondence condition is met.
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