Most MCDM problems use subjective weights mainly obtained from AHP.
These weights are developed by preferences, qualified using a dubious table (as is the opinion of many researchers), and criticized since decades ago.
They are also obtained under the aggravating circumstance that the DM works only with criteria without considering the different projects, WHICH THEY MUST EVALUATE, according to AHP hierarchy.
That is, in comparing, say environment and disposable income, the DM decides, by intuition, that the first is more important than the second, and assigns a numerical value to that preference, using values of the above-mentioned table.
Then, this assumed weight, for it is not a weight, but a trade-off value, is used to select alternatives. On what grounds? None given.
Consequently, the DM decides that said preference is valid for everything in life, since he does not have any reference, other that a single objective, where this preference will be used.
Not too much thinking is needed to conclude that this process is invalid, because that preference may apply well to a certain project but not in others, or even in comparing alternatives within a scenario.
Now, the DM, using mathematical methods (The Eigen Value method, or the Geometrical Mean), determines priorities for each criterion - after his estimates are subject to the verdict of a formula - because the method demands that his estimates MUST fulfill, with a 10 % of tolerance, that they are consistent, or that meet transitivity.
That is that if criterion A = 3 times more important than criterion B, or 3B, and B =2C, then A=6C.
Now, one wonders why his estimates must be transitive?
Nobody knows, but what is worse, is that the AHP method assumes that said transitivity MUST also be satisfied by the real-world problem, not considering that in general, the world is intransitive.
And now the question:
On what ground, on what theory, on what relationship is it assumed that those preferences from a DM or from a group of DMs, are valid for the real world?
As a matter of fact, a very well-known theorem, the ‘Arrow’s Impossibility Theorem’, says the opposite.
I have posted several times this question. Is there anybody that can give a RATIONAL answer?
Your response and discussion will be greatly appreciated.
Thank you
Nolberto Munier
Nolberto, this is an interesting question.
Overall, it seems to me that there is a lot of confusion concerning preferences, weighting, and preference modeling. One reason might be that theory is currently detached from practice. Some people may develop theory with quite a little practical experience. On the other hand, some practitioners might be content with simply applying what seems to work without sufficiently thinking about what is going on. Maybe what we need is more bridge building and co-operation between theoreticians and practitioners.
I would love to see more realistic and practice oriented discussions concerning tools for supporting decision makers in various settings. There are beautiful theories and I fear we sometimes fall in love too much with the theory.
The following thoughts are speculation from top of mind, for the sake of discussion, nothing more:
A possible solution could be to forget modeling of preferences or preference elicitation as if preferences were something real.
A more pragmatic stance could to consider weighting as a decision: That is, the decision maker chooses the weights, which are connected to changes in outcome measures. The weights are then used to rank the alternatives.
In this approach we do not say "weights are valid representation of the preferences of the decision maker", we say "the decision maker chose these weights". Of course, then question becomes: Did the decision maker understand what he was deciding about? It would be important that sensitivity analyses etc are carried out so that the decision maker understands the implications of his or her choices.
Dear Tuomas
It is impossible not to agree with each paragraph of your answer.
You say: One reason might be ‘that theory is currently detached from practice’. That feeling has been in the back of my mind for years.
It appears that some developers maybe theoretical geniuses, but with scarce knowledge of real-life practice and experience. It seems that they applied their theories to blackboard trivial examples, then translating that experience to real-work scenarios, and thus assuming that if it worked in the class-room, there is no reason to believe that they can’t work in real-life. Unfortunately, the real-world is not that simple, direct and known.
Just as an example: Why most methods don’t consider that whatever a project, it needs resources and that these resources are limited?
Expressing in different words what you say in your first paragraph.
Why a lot of effort is devoted in explaining how to improve inconsistency in AHP, or applying fuzzy to data, and even intuitionism, when the decision matrix does not reflect reality? That research is of course welcome, but it appears that our researchers can’t see the forest because the trees.
They are improving details when the whole project significance is ignored, that is, when the number of criteria proposed does not represent some important characteristics of the scenario, as for instance, precedence among alternatives or inclusion or joint ventures.
This can be found in both developers and practitioners. The first because they are acting like pure mathematicians, and the second because they take for granted that if a certain MCDM method does not allow for representing a characteristic of a scenario, it does not matter……just don’t think about it, since possibly is not important.
As you say: ‘Maybe what we need is more bridge building and co-operation between theoreticians and practitioners’
Another hit on the nail comment of yours: ‘A possible solution could be to forget modeling of preferences or preference elicitation as if preferences were something real’. The key sentence here is which I underlined. Preferences are just a product of the mind, and normally not related whatever with the real thing.
Tuomas, your paragraph about weights is worth mentioning. It is well-known that subjective weights are not prepared to evaluate alternatives. Why researchers persist in using them? Shannon theorem as well as Arrow theorem, are not enough to prove their uselessness?
Your last paragraph, condenses everything. However, after do many years using MCDM methods, it is evident that ‘The eyes are useless when the mind is blind’
Hello Dear Professor @Nolberto Munier
I will meet you after a long time with a challenging discussion!
Contrary to previous discussions in late 2020, I feel that your critical theory is significant and close to reality!
I love AHP and especially ANP, especially the fuzzy version of them!
But the fact is that you are right, these methods have a logical flaw!
A kind of imposition and transmission of opinion!
Good luck
Dear Majid
Thank you for your message.
It is very important for me coming from a person that has used and love AHP and ANP, meaning that you don't have prejudice, and recognize a fact which you believe is right, even again your own beliefs.
By the way, and nothing to do with my comment on AHP. Did you know that Dr. Saaty himself said that using fuzzy in AHP is erroneous, since AHP, by nature, is already fuzzy?
Val Belton has done a lot of work in this domain, even suggesting problem structuring methods to help in the process of needs ellicitation.
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