On the relativity of relative measures  accommodating both rank preservation and rank reversals in the AHP
The analytic hierarchy process (AHP) has been criticized for allowing the introduction of new alternatives to cause rank reversals among existing alternatives. While in many cases this is a perfectly valid phenomenon there are also many cases where rank should be preserved. To address both contingencies the AHP now supports two types of synthesis procedures  one that preserves rank and one that does not. This paper proposes guidelines for the selection of one synthesis mode over the other. It also proposes several modifications to software implementations of the AHP to better support both synthesis modes and to reduce user stress over the choice.
analytic hierarchy process multi criteria analysis decision theory