On Intensity of Preference Rank Reversal in the AHP

TL;DR

This paper investigates a new form of rank reversal in AHP caused by uniformly increasing preference intensities, revealing that the eigenvector method is affected while the geometric mean method remains robust.

Contribution

It introduces a novel type of rank reversal in AHP related to preference intensity and compares the robustness of eigenvector and geometric mean methods.

Findings

Eigenvector method can produce different rankings when preference intensities are uniformly increased.

Geometric mean method remains unaffected by intensity-of-preference rank reversal.

Real-world NASA case study demonstrates the practical relevance of the findings.

Abstract

The analytic hierarchy process (AHP) is one of the most widely used multicriteria decision-making methods, with applications from agriculture to space engineering. Despite its popularity, AHP has been repeatedly criticised for rank reversal, a phenomenon in which the ranking of alternatives changes after the addition or removal of an irrelevant or duplicate alternative. This paper introduces a new type of rank reversal in AHP, arising when the intensity of preferences is uniformly increased. We show that even when all pairwise preferences preserve their direction and are intensified identically, the eigenvector method may produce a different ordering of alternatives. In contrast, the geometric mean (GM) method is robust to this intensity-of-preference (IOP) rank reversal. The applicability of this result is shown through a real decision-making problem taken from a NASA manual concerning capability prioritisation for the planned lunar Gateway orbital station.