Key words: Analytic Hierarchy/Network Processes (AHP/ANP), rank, pairwise comparisons, ratings

Abstract

Rank preservation and reversal are important subjects in multicriteria decision-making particularly if a theory uses only one of two ways of creating priorities: rating alternatives one at a time with respect to an ideal or standard, or comparing them in pairs. It is known that our minds can do both. When rating alternatives, they must be assumed to be independent and rank should be preserved. When comparing alternatives, they must be assumed to be dependent and rank may not always be preserved. However, even in making comparisons rank can be preserved if one uses idealization instead of normalization with the original set of alternatives and preserves that ideal from then on unless that ideal itself is deleted for some reason. So often it is a matter of judgment as to whether it is desirable to force rank preservation or allow rank to adjust as necessary. Examples are given to illustrate the foregoing ideas.

INTRODUCTION

The Harvard psychologist Arthur Blumenthal (1977) tells us in his book The Process of Cognition that there are two types of judgment:

In the AHP we call the first relative measurement and the second absolute measurement. In relative measurement we compare each alternative with many other alternatives and in absolute measurement we compare each alternative with one ideal alternative we know of or can imagine, a process we call rating the alternative. The first is descriptive and the second is normative. Comparisons must precede ratings because ideals can only be created through experience. Since memory needs experience to develop standards, making comparisons is fundamental and intrinsic in us. They are not an intellectual invention nor are they something we can ignore.