A new parsimonious AHP methodology: assigning priorities to many objects by comparing pairwise few reference objects

We propose a development of the Analytic Hierarchy Process (AHP) permitting to use the methodology also for decision problems with a very large number of alternatives and several criteria. While the application of the original AHP method involves many pairwise comparisons between considered objects, that can be alternatives with respect to considered criteria or criteria between them, our parsimonious proposal is composed of five steps: (i) direct evaluation of the objects at hand; (ii) selection of some reference evaluations; (iii) application of the original AHP method to reference evaluations; (iv) check of the consistency of the pairwise comparisons of AHP and the compatibility between the rating and the prioritization with a subsequent discussion with the decision maker who can modify the rating or pairwise comparisons of reference points; (v) revision of the direct evaluation on the basis of the prioritization supplied by AHP on reference evaluations. Our approach permits to avoid the distortion of comparing more relevant objects (reference points) with less relevant objects. Moreover, our AHP approach avoids rank reversal problems, that is, changes of the order in the prioritizations due to adding or removing one or more objects from the set of considered objects. The new proposal has been tested and experimentally validated.