Rank from comparisons and from ratings in the analytic hierarchy/network processes

Rank preservation and reversal are important subjects in multi-criteria 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 naturally and without being tutored. 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.