Systemic decision making in AHP: a Bayesian approach

Abstract

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).

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

“…The tolerance distribution on the group's priorities vector, proposed by Moreno-Jiménez et al (2014), was used. Based on this distribution, two systematic search strategies are proposed to find the largest compatible set of actors in order to facilitate subsequent negotiation and debate.…”

“…. , r , Moreno-Jiménez et al (2014) introduce the tolerance distribution, defined below, which forms the basis for the consensus searching procedures proposed in the paper.…”

“…It can be proved (Moreno-Jiménez et al 2014) that the tolerance distribution (2.1) is a synthesis of the individual priorities vectors, which minimises the weighted KullbackLeibler distance of π to the set {π k (w); k = 1,…,r}, which is defined as follows:…”

“…This distribution does not have standard form and a Monte Carlo method based on the SIR algorithm of Rubin (1987) could be used to make inferences from it (see Moreno-Jiménez et al 2014 for details). We take n 0 = 0.0001 and s 0 = 0.1.…”

“…This new framework was presented in Moreno-Jiménez et al (2014), who applied a Bayesian approach to define a tolerance probability distribution for the priorities of the multi-actor setting and study its properties.…”