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This paper examines consensus building in AHP-group decision making from a Bayesian perspective. In accordance with the multicriteria procedural rationality paradigm, the methodology employed in this study permits the automatic identification, in a local context, of “agreement” and “disagreement” zones among the actors involved. This approach is based on the analysis of the pairwise comparison matrices provided by the actors themselves. In addition, the study integrates the attitudes of the actors implicated in the decision-making process and puts forward a number of semiautomatic initiatives for establishing consensus. This information is given to the actors as the first step in the negotiation processes. The knowledge obtained will be incorporated into the system via the learning process developed during the resolution of the problem. The proposed methodology, valid for the analysis of incomplete or imprecise pairwise comparison matrices, is illustrated by an example.

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 agreement 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.

Systemic decision making is a new approach for dealing with complex multiactor decision making problems in which the actors' individual preferences on a fixed set of alternatives are incorporated in a holistic view in accordance with the "principle of tolerance". The new approach integrates all the preferences, even if they are encapsulated in different individual theoretical models or approaches; the only requirement is that they must be expressed as some kind of probability distribution. In this paper, assuming the analytic hierarchy process (AHP) is the multicriteria technique employed to rank alternatives, the authors present a new methodology based on a Bayesian analysis for dealing with AHP systemic decision making in a local context (a single criterion). The approach integrates the individual visions of reality into a collective one by means of a tolerance distribution, which is defined as the weighted geometric mean of the individual preferences expressed as probability distributions. A mathematical justification of this distribution, a study of its statistical properties and a Monte Carlo method for drawing samples are also provided. The paper further presents a number of decisional tools for the evaluation of the acceptance of the tolerance distribution, the construction of tolerance paths that increase representativeness and the extraction of the relevant knowledge of the subjacent multiactor decisional process from a cognitive perspective. Finally, the proposed methodology is applied to the AHP-multiplicative model with lognormal errors and a case study related to a real-life experience in local participatory budgets for the Zaragoza City Council (Spain).

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This work extends the AHP-Bayesian Prioritization procedure proposed by the authors for a local context (a single criterion) to a global context (a hierarchy) and presents a taxonomy of criteria that contribute to the ranking of the alternatives. In this global context, the paper defines and characterizes: (i) the influence of a criterion in the final prioritization of the alternatives by means of cross-validation techniques; (ii) its degree of discordance with the rest of the criteria of the hierarchy utilizing new discrepancy measures; (iii) its relevance in the final decision. Along with the taxonomy and its corresponding methodology, the paper introduces new decisional tools for the establishment of the classification and demonstrates their use from a cognitive perspective (knowledge extraction) whilst paying special attention to the resolution of the P.α and P.γ problems. The proposed methodology is illustrated by a case study on an e-participation process developed for the Zaragoza City Council (Spain) and implemented by the Zaragoza Multicriteria Decision Making Group.

The challenges of the knowledge society and the development of the information and communication technologies favour the participation of multiple, spatially distributed actors in decision making processes. In this context, Systemic Decision Making (Moreno-Jiménez et al. in Systemic decision making in AHP: a Bayesian approach, 2014) provides a new approach to dealing with complex multi-actor decision making problems in which individual preferences in a fixed set of alternatives are viewed from a holistic standpoint under the "principle of tolerance". Moreno-Jiménez et al. (Systemic decision making in AHP: a Bayesian approach, 2014) base the integration of preferences on the tolerance distribution, which can be used to reach a holistic, joint decision solution in a Bayesian AHP-Systemic Decision Making context. As with any aggregation procedure or synthesis measure, however, some of the actors involved in the resolution process may not be in agreement with the joint solution. In this paper, we propose a measure (which we call the compatibility index) to evaluate the level of tolerance of the actors involved in the decision making process with regard to the resulting tolerance distribution (inner compatibility). We also develop two algorithms to improve the level of tolerance. The methodology is illustrated with a case study based on a simplified version of a real e-cognocracy application (MorenoJiménez and Polasek in J Multi-Criteria Decis Anal 12: [163][164][165][166][167][168][169][170][171][172][173][174][175][176] 2003) carried out in cooperation with the City Council of Zaragoza.

The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a new Bayesian stochastic search methodology for large-scale problems (number of decision-makers greater than 20). The new methodology, based on Bayesian tools for model comparison and selection, takes advantage of the individual preference structures distributions obtained from stochastic AHP to allow the identification of homogeneous groups of actors with a maximum common incompatibility threshold. The methodology offers a heuristic approach with several near-optimal partitions, calculated by the Occam’s window, that capture the uncertainty that is inherent when considering intangible aspects (AHP). This uncertainty is also reflected in the graphs that show the similarities of the decision-maker’s opinions and that can be used to achieve representative collective positions by constructing agreement paths in negotiation processes. If a small number of actors is considered, the proposed algorithm (AHP Bayesian clustering) significantly reduces the computational time of group identification with respect to an exhaustive search method. The methodology is illustrated by a real case of citizen participation based on e-Cognocracy.