# 112

Dear Majid Mohammadi, Damian A. Tamburri, Jafar Rezae

I read you paper

Unveiling and Unraveling Aggregation and Dispersion Fallacies in Group MCDM

My comments

1- In page 3 you say” While the methods for aggregating multiple DMs’ preferences are often statistically sound, applying the same statistical operations to the priorities is incorrect because the priorities are ratios lying on a simplex and not on the real space”

This is absolutely true and it is the first time I read an article expressing so correctly in where these ratios are. I assume that you refer to alternative’s priorities. These alternatives define the number of dimensional spaces of a problem, and where linear relationships apply. However, you should explain what a simplex is. For instance, you could define it as a generalization of a notion of a triangle to arbitrary dimensions, which is, by the way, what happens when we have more that two alternatives.

2- In addressing criteria weights why don’t you use a rational system like entropy instead of invented subjective weights?

3- In page 4 “We show that the proper way to aggregate the priorities is to use the geometric mean method (GMM)”

In addition, using the EV method is no adequate when the number of alternatives is greater than 3

4- “Pairwise comparison matrices (PCMs) were first introduced”

This is incorrect. Pair-wise comparison method was pioneered by Benjamin Franklin and developed by Thurstone in 1927, and of course Saaty used the concept

5- Page 7 “While reaching a consensus among the group members by following sharing or comparing approaches is desirable, a unanimous agreement is not always guarantee”

Of course not. Another group may produce a different set of weights, and another also a different one. In addition, in a complex problem where criteria involve may be 6 or 7 different areas, it is unreasonable to expect that one DM expert say, in economics, may discuss with another DM expert in environment, since none of them knows the area of the other. How can they reach an agreement?

You mention a moderate, and that this means that this personal needs to have a knowledge on all the fields, something not very usual.

6- Page 7 “Examples could be arriving at a decision in a municipality by collecting the preferences of citizens of a town or formulating a policy by collecting the preferences of electric vehicle users in a region”

This is the only rational way, since the DMs. Do not represent interested people. They cannot vote representing thousands, and according to Arrow’s Theorem, that is dictatorship

I hope these few comments may be useful to you

Nolberto Munier