An iterative approach for achieving consensus when ranking a finite set of alternatives by a group of experts

This paper proposes a novel iterative approach for achieving consensus when a group of experts is given the task to rank a finite set of alternatives. Unlike traditional approaches which use various metrics to express expert disagreements, the proposed approach is based on a premetric concept to express such disagreements. This premetric approach can capture more effectively the nature of agreements or disagreements that naturally occur when experts rank alternatives. The proposed approach is very flexible in that it considers a wide spectrum of ways to approach the problem of reaching consensus. These ways are based on an assignment formulation where one may consider various alternative consensus improving strategies. Which strategy to consider depends on the nature of the group decision making (GDM) problem under consideration and it can change as the GDM process evolves. In particular, this paper examines and provides novel solutions for the following fundamental problems: (1) How to evaluate the level of consensus? (2) How to identify the most appropriate disagreements to consider next when the consensus is not at a desired level? and (3) How to derive a reasonably ’close’ solution when experts are not in perfect consensus while they are not able or not willing to further improve the consensus? Furthermore, this paper provides a theoretical foundation of the proposed premetric-based approach and then it uses this theoretical foundation to compare the new approach with some traditional ones.