How to determine the consensus threshold in group decision making: a method based on efficiency benchmark using benefit and cost insight

In the past 10 years, a large number of consensus-reaching approaches for group decision making (GDM) have been proposed. While these methods either focus on the cost of the consensus reaching or the convergency of the consensus process, the consensus efficiency has long been ignored. Meanwhile, the measurements of consensus threshold are often determined by some subjective and intuitive judgements, such as management experience and estimations for the degree of satisfaction, which lack a theoretical foundation. In management applications, how to measure consensus and how to evaluate a consensus reaching method are also ambiguous. To tackle these questions, we introduce efficiency measures into the consensus reaching process of GDM and achieve a comprehensive evaluation of current consensus methods through an efficiency analysis of consensus costs and consensus improvement. From the perspective of efficiency, we propose a benchmark in consensus reaching by data envelopment analysis without explicit input benchmark models, and then present an objective method for consensus threshold determination in GDM. Finally, we use numerical examples to illustrate the usability of our method.