A Decentralized Approach to Solve Group AHP with Agreements by Consensus

The analytical hierarchical process (AHP) is a multi-criteria, decisionmaking process that has demonstrated to be of a high utility to achieve complex decisions. This work presents a method to apply it in grupal decisions, where the weights that each user assigns to the criteria are different and private. A combination of consensus process and gradient ascent is used to reach a common agreement that optimizes the utility of the decision using the information exchanged in the local neighborhood exclusively. The AHP problem is modeled through a multilayer network. Each one of the criteria are negotiated by consensus with the direct neighbors on each layer of the network. Furthermore, each node performs a transversal gradient ascent and corrects locally the deviations from the personal decision to keep the best option. The process locates the global optimal decision, taking into account that this global function is never calculated nor known by any of the participants. If there is not a global optimal decision where all the participants have a not null utility, but a set of suboptimal decisions, they are automatically divided into different groups that converges into these suboptimal decisions.