# 115

Dear Aqeel Asaad Al Salem

I read your paper

Investigating Rank Reversal in Preference Relation Based on Additive Consistency: Causes and Possible Solutions

My comments:

1- In the abstract you say: “inconsistency of information is the main cause of this phenomena in preference relations followed by ranking score aggregation”

I am afraid that I do not share your opinion. Why do you think that what is in the mind of a person, must be reflected in reality? We must adapt to reality, not the other way around.

Consistency or transitivity is a very convenient mathematical concept, but probably not to be used or seen in real life.

An example: Assume that John, Peter and Harris are close friends, however John finds that he has more affinity with Peter than with Harris. Peter, finds that he has more affinity with Harris than with John. Does it mean that John MUST have more affinity with Harris?

Obviously not. Well, the same happen in MCDM, especially considering that real-life is not consistent in most cases.

2- Regarding Rank Reversal (RR), suppose that three persons are discussing about a certain fact, for instance the advantage in living in the city, in the country side or in the mountains. Each one has his preferences, but at the end they believe that in general, all things considered, living in the mountains is better than in the country and better that living in a city.

Now, another friend arrives and joint them and asked for his opinion. The new guy analyses the comparative advantage of each location and proposes a different ranking. For him, the best is living in a city.

The arrival of the new friend may or may not influence what the others say, but he brings to the discussion new aspects that the original three did not consider.

Consequently, there is Rank Reversal. Is it wrong?

Not really, the guy brought new information, more knowledge that enriched the discussion, and even when the main subject is the same, the new information contributed to see the problem from other point of view, and reduced uncertainty

Similarly, when in MCDM we add a new alternative, the original matrix changed and was enriched with the new vector, and resulting ranking can be the same or not. Is this wrong?

3- In page 9 “Saaty(1987) linked rank reversal with the existence of near or similar copies within the set of alternatives”

I do not know if Saaty demonstrated his assertion, but in principle I agree with him, although for different reasons, certainly not for inconsistency.

4- In several paragraphs involving many pages, there is an insistent claim on that inconsistency causes RR, but none of them has proved it, consequently, they are only assumptions.

In my opinion, and I have proof of it, RR is an unavoidable phenomenon, provoked by the changes in geometrical dimensions spaces when adding or deleting alternatives. This hypothesis also explains why RR may or may not appear, it is again, a geometrical interpretation. However, normalization, especially min-max can generate RR because this procedure does not preserve the distances between values as other normalization methods.

Hope these few comments may help you

Nolberto Munier