A Systemic Rebuttal to the Criticism of Using the Eigenvector for Priority Assessment in the Analytic Hierarchy Process for Decision Making

Arguments have been provided against the use of the eigenvector as the operator that derives priorities. A highlight of the arguments is that the eigenvector solution does not always respect the condition of ordinal preference (COP) based on the decision maker’s judgments. While this condition may be reasonable when dealing with measurable concepts (such as distance or time) that lead to consistent matrices, it is questionable whether it is to be expected in all situations, particularly when the information provided by the decision maker is not fully consistent. The judgments that lead to inconsistency may also contain valuable information that must be considered in the priority assessment process as well. By the other hand, the analytic hierarchy process (AHP) use the eigenvector operator to derive the priorities that represent the cardinal decision maker preferences from a pairwise comparison matrix, which do not always respect the COP condition. The AHP and still deeper the ANP (the mathematical generalization of AHP) start from concepts of ordinal metric of dominance and system theory, which is well supported by graph theory and ordinal topology with the Cesaro sum as its fundamental pillar to build metric of dominance. These mathematic concepts has no relation with COP preservation moreover, this two way of thinking are in a course of collision since the second (COP) inhibit the first (Cesaro sum). Systems theory claims that the whole is more than its standalone components, and that internal relationships provide additional information as well. Given that the pairwise comparison matrix is an interrelated system and not just a collection of standalone judgments, we plan to show that the eigenvector, because it is a systemic operator, is the most suitable to represent and capture the behavior of the whole system and its emerging properties.