**5. Conclusions**

This paper has proposed a methodology for the identification of homogenous opinion groups with AHP in a local context. The methodology is based on the use of Bayesian processes for the selection of hierarchical models that describe the judgments issued by each decision maker in their matrices of pairwise comparisons based on a set of priorities common to each of the members of the group.

Using an exhaustive search method of the most compatible partitions with the judgments issued, the Occam's window of the compared models is defined. From these models it has been shown how it is possible to describe the existing opinions in the groups, information that can be very useful to identify consensus paths among the decision makers that can culminate in a more representative decision-making process.

The search method works in a local AHP context, but has some limitations. First, it functions if the number of decision makers is not very high (≤11). The total number of partitions of the set of decision makers is equal to the Bell number BK= K−1 ∑ K − 1 k!Bkwith B0= 1, B1= 1. The larger

k=0 the number of decision makers, the more computationally infeasible is the problem. In our case (K = 11), the number of possible partitions is 687,570, which is computationally feasible. For instance, if K = 22 the number is 4507 × 1015, then it is necessary to use algorithms that approximately determine Occam'swindow.

We are currently experimenting with stochastic search algorithms and the results obtained will be published in a future work. A second limitation is that it is necessary that the groups constitute a partition of the set of decision makers and this implies that a decision maker cannot belong to more than one group. Even though this requirement decreases the computational time of the algorithm, it also reduces the flexibility of the method. The development of search strategies that eliminate this unrealistic assumption is worthy of consideration. Finally, it would be interesting to extend the methodology to a global context in which a hierarchy of criteria and sub-criteria is used.

**Author Contributions:** The paper has been elaborated jointly by the four authors.

**Funding:** This research was funded by the Spanish Ministry of Economy and Competitiveness and FEDER funding, projects ECO2015-66673-R (first and third authors) and ECO2016-79392-P (second and fourth authors).

**Acknowledgments:** The authors would like to acknowledge the work of English translation professional David Jones in preparing the final text.

**Conflicts of Interest:** The authors declare no conflict of interest.
