Analysis of the Final Ranking Decisions Made by Experts After a Consensus has Been Reached in Group Decision Making

Traditional approaches to group decision making (GDM) problems for ranking a finite set of alternatives terminate when the experts involved in the GDM process reach a consensus. This paper proposes ways for analyzing the final results after a consensus has been reached in GDM. Results derived from this last step can be used to further enhance the understanding of possible hidden dynamics of the problem under consideration. The proposed approach for post-consensus analysis is in part based on a novel idea, known as preference maps (PMs) introduced recently in the literature on how rankings should be described when ties in the rankings are allowed. An original contribution of this paper is how to define the difference between two PMs. This is achieved by using a metric known as the Marczewski–Steinhaus distance. Approaches for analyzing the final results of a GDM process after consensus has been reached may reveal hidden but crucial insights in the way the experts reached the consensus and also new insights related to the alternatives. These approaches rely on the concept of differences in the rankings, defined by traditional means or as the difference between two PMs as defined in this paper. This is the second group of original contributions made in this paper. The various issues are illustrated with numerical examples and an application inspired from a real-world problem described in the literature. The new contributions described in this study offer an exciting potential to enrich the group decision making process considerably.