CMAA–AHP: combinatorial multicriteria acceptability analysis with the analytic hierarchy process

Abstract Combinatorial multi-criteria acceptability analysis (CMAA) is a framework for supporting multicriteria group decisions that provides both a detailed analysis of the effects of individual decision-maker inputs as well as interactive guidance for a consensus-building process. The analytical hierarchy process (AHP) is a widely-used model of decision-maker evaluations that is based on pairwise comparisons. The goal of this work is to show how CMAA can be integrated with AHP in order to make its benefits available to AHP users. We use a minimal input format for AHP which avoids a problem with inconsistency and also reduces the cognitive load on the decision-makers. We extend the CMAA method by introducing new judgement and preference sensitivity variables, which provide helpful insights for the facilitator of the group decision. An example illustrates the combined CMAA–AHP method and its ability to deliver consensus in a very small number of iterations. Monte Carlo simulation is used to study the convergence behavior of the method for a range of problem dimensions. It was found that the mean number of steps to reach consensus grows linearly with the number of alternatives and criteria. We consider two previously published group decisions that use the standard AHP approach of averaging decision-maker judgements and preferences. In both cases, CMAA–AHP delivers the same rankings based on the original input. However, the new method also provides insight into each decision and would have been able to guide each group to consensus within a small number of resolution steps.