*Article* **Homogeneous Groups of Actors in an AHP-Local Decision Making Context: A Bayesian Analysis**

### **Alfredo Altuzarra, Pilar Gargallo, José María Moreno-Jiménez \* and Manuel Salvador**

Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain; altuzarr@unizar.es (A.A.); pigarga@unizar.es (P.G.); salvador@unizar.es (M.S.)

**\*** Correspondence: moreno@unizar.es

Received: 15 February 2019; Accepted: 16 March 2019; Published: 21 March 2019

**Abstract:** The two procedures traditionally followed for group decision making with the Analytical Hierarchical Process (AHP) are the Aggregation of Individual Judgments (AIJ) and the Aggregation of Individual Priorities (AIP). In both cases, the geometric mean is used to synthesise judgments and individual priorities into a collective position. Unfortunately, positional measures (means) are only representative if dispersion is reduced. It is therefore necessary to develop decision tools that allow: (i) the identification of groups of actors that present homogeneous and differentiated behaviours; and, (ii) the aggregation of the priorities of the near groups to reach collective positions with the greatest possible consensus. Following a Bayesian approach to AHP in a local context (a single criterion), this work proposes a methodology to solve these problems when the number of actors is not high. The method is based on Bayesian comparison and selection of model tools which identify the number and composition of the groups as well as their priorities. This information can be very useful to identify agreemen<sup>t</sup> paths among the decision makers that can culminate in a more representative decision-making process. The proposal is illustrated by a real-life case study.

**Keywords:** Analytic Hierarchy Process (AHP); group decision making; homogeneous groups; Bayesian analysis
