ELECTRE TRI, because we don't compare the alternatives between themselves, but we compare them with fixed profiles.

I think the question you are putting is another. We know thar rank reversal happens a lot in the MCDM models, but it happens in the reality too?

Are there some real situation where a new alternative (worse or not) can change the order of the previews?

I think that if we are experts, we evaluate alternatives by using the all space of the problem (not only strictly a few alternative). I can not imagine a real situation

where a new alternative can change the order of the previews. Do you know any example?

I think that if we are experts, we evaluate alternatives by using the all space of the problem (not only strictly a few alternative). I can not imagine a real situation where a new alternative can change the order of the previews. Do you know any example?

it is many examples in real life where rank reversal happens, that is not the problem. The problem appears when we try to force the real life situation in order to adapt it to our limited configuration models.

By the way, in AHP/ANP one can modelling a problem with or without rank reversal. It depend if you are looking for an absolute or a relative kind of measurement (reversal only may happen in a relative measurement process). So, the study of Belton & Gear in 1983 is a large missunderstanding of what measuring process really means.

Mr. Garuti

Could you put examples where Rank  Reversal appears in real life?

You are the only person I have read that  question the Belton and Gear opinión, which was and is shared for most researchers. All of them are mistaken?

The fact that Saaty reluctanly chaned his mind and accepted using multiplication instead of summation proves that they were right.

You say that it does happen in relative process, however this relativity is the essence of AHP/ANP since the Eigen values add to unit.

I agree with Mr Salabun opinión. All posible combinations of alternatives are in a space whatever the model we use to select them. All are probable but not all of them are efficient

Mr. Munier,

You ask me about examples, Any axample that has feedback between alternatives and criteria may produce rank reversal (real life decisions). For instance, if we have to hire an especialist in computing, in a multicriteria model the value of that specialist comparatively decrease as we add more and more people (alternatives) with computer skill, until produce a rank reversal. There is another case (a famous paper) about rank reversal refered to the perimeter of some geometric figures. The paper tried to explain why the AHP was wrong, using a result know in advance, that is that all the perimeters were the same, but (due to rank reversal) on his AHP model he found different values for each perimeter, claiming that AHP was wrong since wasn't achieve the expected result. Again the error was in the modeling process. (In this case an error easy to fix if you know what you are doing).  There are a lot of other cases, but if you have one example of rank reversal on AHP that you would like to share with me I will be glad to analize it with you ([email protected])

Please, may you explain me what do you mean when you say:  "The fact that Saaty reluctanly chaned his mind and accepted using multiplication instead of summation proves that they were right". (what multiplication instead of summation?).

About relativity and eigen values:

Indeed, is just because the relativity of the measurement that rank reversal may happen. Relativity may produce dependency  and dependency may produce rank reversal, and that is also a physical effect. That's way adding (or deleting) alternatives may produce changes in the behavior of the complete set (even when adding copies).

By the way, is not the eigen values that add to one but the eigenvector.

Dear Mr Garuti

I don't really understand how the value of one person ( as a profesional for instance)diminishes if more persons are added. You evaluate each one independently and I don't understand how the 'value' of the first may vary because you evaluate another one.

Of course, if you compare both regarding for instance experience there will be a winner, as you do in AHP,  but it does not mean that the experince of one person changes because you compare with another. Let alone the fact that if you graduate one of them wiht say 7, the other gets 1/7, meaning that the second has only a mínimum of experience compared with the other.

Sorry, I cant comment on your second example because I have not seen it

There are literally dozens of examples of Rank Reversal in AHP as in other methods but most of them referred to AHP, and I w ould say in a 90 % negatives. I suggest you consult Triantaphyllou (2001)

Triantaphyllou, E. (2001). Two new cases on rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP – Journal of Multi-criteria Decision Analysis 10: 11-25 (2001)

There are also papers from Belton and Gear and many other researchers. I could find without any difficulty no less tha posible 15 analysts on this subject

In all honesty I was surpirsed with you not understanding how Saaty changed his mind due to Belton and Gear discovery on Rank Reveral. Many researchers studied the issue and are still doing that, unortunately with negative results (See Triantaphyllou).

I don't remember the name of the researcher that said that the problem with AHP is its additive structure and suggested Saaty to use a multiplicative one. Apparently in some circumstances this modification worked.

However, Saaty strongly  fought this modificatrion and there was a very heated debate (It is in Internet, it is not my invention, and became a part of the technical folklore, especially with Ryan, ) but finally Saaty  accepted it. However, the system continues to show Rank Reversal 

Sorry, I dont understand this paragraph where you seem recognizing Ran Reversal in AHP and in other methods.

Regarding eigen vectors I failed to understand how they can add unity. I was referretring to eigen values in the eigen vector.

As probably you have noticed I am precisely not a fan of AHP, and would really love to point out in private its advantages and disadvantages, which unfortunatelly outrank de advantages.

Best regards

Nolberto

[email protected]

Dear Mr. Munier,

The problem beging when one think that rank reversal is an issue itself, leaving no place in head to think this as a fact of life. Even Einsten had to deal with this effect in his general theory of relativity (last number of the IJAHP journal).

Geting to the point, the issue about how one alternative can affect the behavior of another is quite simple and is called feedback.   Feedback (and this is the important part) may happen between alternatives, between criteria and betwen alternatives and criteria, changing the weights of the elements in the model and of course the behavior (hence the rank) of the alternatives. This effect may appear only in relative measurement, when comparing the alternatives among them respect the criteria. In this case the weight (importance) of one alternative can change depending the behavior of the rest of them (also the weight of the criteria respect to the alternatives may change), and it is nothing wrong with that (all countrary in many cases it is a necessary freedom to well modelling the reality).

Of course, if you are rating the alternatives one at the time (as you seem to suggest) this feedback effect disappear, in this case you are (intentionally or not) disconnecting the existing relationship between the alternatives or the alternatives with the criteria and then, modelling/resolving another problem (nothing worse than resolve perfectly the wrong problem).

This method of measure alternatives (one at the time) is called rating (AHP has this option too called rating mode within absolute measurment), which is usefull if you want to avoid rank reversal effect. But, (as you may guess at this point), the real question here is to know when to avoid rank reversal and when do not, since rank reversal is a fact of life. (By the way, did you know that in marketing field this effect is used intensively to change the perceptions of the potential customers?).  

At less for me, what is not acceptable is when the method force you to take one option, limiting your capacity of representing the reality.

Two more clarifications about your last statement:

First: Each eigenvalue is connected to a specific eigenvector, they are not "in" (inside) the eigenvector. The elements inside the eigenvector (which are not the eigenvalues) represent priorities in this context, those elements should sum to one (making stochastic the operator, as it is).

Second clarification (less relevant):  the multiplicative AHP is a very limited version of the AHP (in my opinion just an academic discussion not for real life problems).

Finally, I have no problem to share in private with you about measurement, order topology, AHP or ANP.  Let me know, my email is: [email protected]

Regards,

Claudio Garuti

Rank reversal occurs because the collection of rankings, called a profile, contains what Don Saari calls Condorcet n-tuples.  For example, a Condorcet triple is A ≻ B ≻ C, B ≻ C ≻ A, and C ≻ A ≻ B where ≻ means “is preferred to.”  Any positional voting scheme aggregating this set of rankings will yield a tie.  If one of the candidates is removed or another is added, however, the tie is broken.  If a profile contains Condorcet n-tuples, it can result in inconsistencies of this type.   An excellent reference is Donald G. Saari, Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis, 2008, Cambridge University Press: New York.

Note that any attempt to avoid rank reversal generally involves discarding critical information provided by the rankings, for example, looking only at the relative position of two alternatives and ignoring any that are in between.  In other words, when comparing A and B, failing to differentiate between A ≻ B ≻ C ≻ D and A ≻ C ≻ D ≻ B.  This can result in an overall or aggregate ranking that is nontransitive or irrational!  Saari has examples. 

This issue is related to a property called Independence of Irrelevant Alternatives (IIA).  Saari showed that this property negates another property, transitivity of outcome, and substitutes one called Intensity form of Independence of Irrelevant Alternatives (IIIA) that considers not only the relative position of two candidates but also some measure of the strength of preference.  In the case of the Borda Count, the number of alternatives between the two being considered is the measure of strength of preference.

I refer you to a paper I coauthored entitled “Deflecting Arrow by Aggregating Rankings of Multiple Correlated Criteria According to Borda.”  It appears in the Journal of Multi-Criteria Decision Analysis http://onlinelibrary.wiley.com/doi/10.1002/mcda.1568/full.

Article Deflecting Arrow by Aggregating Rankings of Multiple Correla...

I totaly agree that rank reversal is one of the most important issue in MCDM. I found some interesting papers about this topic. I want to share with you.

Thak you very much

I present a new simple experiment about rank reversla and AHP method. I would like to share with you:

[1] Sałabun, W., Ziemba, P., & Wątróbski, J. (2016). The Rank Reversals Paradox in Management Decisions: The Comparison of the AHP and COMET Methods. In Intelligent Decision Technologies 2016 (pp. 181-191). Springer International Publishing.

Best Regards WS

Dear Wojcieh

In my opinion the only MCDM model that does not produce rank reversal is Linear Programming.

The reason is that the Simplex algorithm that solves this problem does not allow it, since it will never select and added project that is worse than the others.

However, if the added new project is somehow better that any of the existing projects in the ranking, this new project will be added with the corresponding preference, but, and this is important, without altering the original precedence order. Then this is not rank reversal

Regarding your offer I am interested in receiving a copy of your work

Mr. Salabun

I don't understand how is RR related with AHP in your work. Are you saying that AHP does not produce it or have you found another weakness or strength of the method to this respect?

Could I have a copy of your work?