#173

Dear Evangelos Triantaphyllou, and Juri Yanase

I have read your paper

The Use of Pairwise Comparisons for Decision Making May Lead to Grossly Inaccurate Results

My comments:

1-“This study demonstrates that under a highly optimistic assumption, called the ultra-accurate decision maker (UADM) assumption, the results obtained from such matrices may be grossly inaccurate”.

100% in agreement, in reality, to pretend that quality results can be obtained from arbitrary weights derived from these matrices, borders the illogical. In my opinion, it is a matter of common sense, not of mathematics

2- In page 3 you say “This success of the AHP method in real-world managerial problems, is based on the intuitive appeal the method has to researchers and practitioners and also to its interesting mathematical properties.”

Of course, a method that only ask to use intuitive values, and making people believe that real-life problems can be solved with opinions and wishes, effortless, and not using reasoning, is very appealing.

I wonder which are the interesting mathematical properties. The only mathematic in the method is the use of Eigen Values, not attributable to the method

3- My qualification as illogical does not refer to using pair-wise comparisons, we do it constantly, what is irrational and inexplicable, is that the DM assigning a value on how much is more important one criterion over another. Try to put a value of relative importance to criteria like love and tenderness, or in a column for a building, asserting that a timber is say 2.5 more important than concrete. I still do not understand how many universities are teaching this non-sense. I have seen students laughing when the professor was explaining AHP

4- The so-called fundamental table of Saaty is only a fabricated assumption. It is based (Saaty dixit), on the psychologic Weber – Fechter law that relates how incentives, that is a premium, or an increase, that could be a better wage for work well done, delivers a logarithmic value as a measure of individual performance, or more efficiency.

One does not need mathematics to explain these relationships. This is a logical and proved law, that map incentives in performances using a log function. Saaty assumes that his fundamental table is equivalent, and then, it is assumed that invented preferences values of one criterion over another produce a log absolute response. Too bad that incentives are not the same as preferences. The first produces a true change on something, the second is only an invented ratio

5- Page 4 “That is, even when it is used in a setting that assumes highly consistent pairwise matrices, the pairwise comparisons approach may still yield strongly questionable results”

Please do not forget, that consistency in AHP is mandatory,and the DM is FORCED by the software to modify his/her estimates, like it or not. Is this mathematics? Now, why consistency is a sine qua non condition? Why a DM must be consistent?

6- Page 5. To be fair, Rank Reversal (RR) is not an AHP exclusivity, since it happens in all MCDM methods. As per my research, and I can prove it, RR is unavoidable and at random, and obeys to dimensional changes when adding or deleting alternatives in the system. One cannot pretend that the ranking in a problem with two dimensions or two alternatives or 2D, MUST be preserved when adding a new alternative, when the problem is now in 3D. It may or may be not, because it depends of the values of the new vector added or deleted, therefore, its occurrence is at random. If you are interested, I can send you the proof of what I say.

In my opinion, RR is a geometric natural consequence, and pair-wise comparisons or consistency or lack of it, have no relation with it, which is not a phenomenon, but a logical geometric consequence when dimensional spaces are changed. I have an extensive paper on this, that is being published.

7- Page 7 “In those publications Saaty considered a total of 6 real-world case studies where the real preferences exist and can be computed objectively”

I hope you are not referring to the geometric forms experiment, a blackboard example used by Saaty, where the DM is guided by the visual observation of these geometric forms. This is a biased example, because it is not abstract.

8- “In the empirical studies described in this paper it is assumed that the decision maker who elicits pairwise comparisons is an ultra-accurate one. We will call this the ultra-accurate decision maker(or UADM) assumption”

On wheat grounds are you based to sustain this assumption?

9- Page 33 “As result of these findings from psychology, Saaty had asserted that his scale of discrete choices is the best balance between the need for high granularity and the capability of people to distinguish between adjacent domination relationships”

I fail to understand how Saaty was able to make that assertion. Based on psychology? And why some people proclaim that MCDM is related to psychology? The Weber-Fechter Law is not related to closeness of values. In my understanding psychology has no intervention in MCDM, except perhaps in AHP and ANP that follow a descriptive process instead of a normative one. Projects, except personal ones,are built in mathematics not on wishes.

10- “Using pairwise comparisons is a widely accepted approach for eliciting the people’s preferences needed to solve important real-life decision-making problems”

Pair-wise comparison is not a widely accepted approachand you also said that at the beginning of your paper. In addition, AHP is unable to solve even medium complex problems. I am not blaming the method because it has been designed to work with hierarchical structures, which was OK in the 1970s but non longer applicable, due to the high complexity of present-day problems with multiple interrelationships vertical and transversal, and from bottom to top and vice-versa. I do not think that it was just coincidence that Saaty, as an authentic and honest researcher, recognized that change and the limitations oh AHP, and created ANP

Then, researchers continue talking and wrighting on pair-wise comparisons and consistency related to RR, but nobody could prove that. As a fact. It is rather impossible than in an original matrix of say 2D they can ask for ranking invariance when they expand to 4D, 6D, or whatever other dimensions, because nornmally it is very difficult that consistency is maintained along 6 different dimensional spaces.

These are my comments

Nolberto Munier