On the Combinatorial Acceptability Entropy Consensus Metric for Multi-Criteria Group Decisions

In group decisions, achieving consensus is important, because it increases commitment to the result. For cooperative groups, Combinatorial Multicriteria Acceptability Analysis (CMAA) is a group decision framework that can achieve consensus efficiently. It is based on a novel Combinatorial Acceptability Entropy (CAE) consensus metric. As an output measure, the CAE metric is unique in its ability to identify the evaluations that have the greatest impact on consensus and to prevent premature consensus. This paper is intended to complement the original CMAA publication by providing additional insights into the CAE consensus metric. The design requirements for the CAE algorithm are presented, and it is shown how these requirements follow from the properties of cooperative decisions. The CAE-based consensus-building algorithm is contrasted both qualitatively and quantitatively with a representative example of the conventional input distance and input averaging approach to multi-criteria consensus-building. A simulation experiment illustrates the ability of the CAE-based algorithm to converge quickly to the correct decision as defined for cooperative decisions. The metric is able to meet a new, more stringent definition of hard consensus. The CAE approach highlights the need to distinguish between competitive and cooperative group decisions. Attention in the literature has been paid almost exclusively to the former type; the CAE approach demonstrates the greater efficiency and effectiveness that can be achieved with an approach that is designed specifically for the latter.