A Bayesian Approach to Maximising Inner Compatibility in AHP-Systemic Decision Making

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 (Moreno-Jiménez and Polasek in J Multi-Criteria Decis Anal 12:163–176, 2003) carried out in cooperation with the City Council of Zaragoza.