The analytic hierarchy process: a note on an approach to sensitivity which preserves rank order

Within the framework of the AHP as it applies to multicriteria decisions, it is frequently the case that decision makers are certain about the rank order of the objects for a particular pairwise comparison matrix but uncertain about the precise numerical weights that the AHP produces for that matrix. This uncertainty translates directly into uncertainty about whether the best alternative obtained from the AHP is actually the best alternative. However, if the weights of an AHP pairwise comparison matrix can be varied in a way that preserves the rank order of the objects, and at the same time, this perturbation does not result in the best alternative changing, then the decision maker is typically much more confident about what the AHP recommends. In this paper, I detail a simple approach to sensitivity within the AHP which preserves the rank order of the objects.