Determining consensus thresholds for group decision making with preference relations

Abstract

Consensus thresholds play a significant role in consensus checking and reaching in group decision-making problems. The existing studies contribute very few guidelines and leave the task of determining consensus thresholds to decision makers. This paper presents an effective process to determine the thresholds in the setting of group decision-making with preference relations (PRs). The process employs a concept called random consensus indices which refer to the expected values of consensus indices of randomly generated PRs. Instead of determining the thresholds directly, decision makers are only required to express that, to what extent, the information provided by the authorized experts should be better than the random case. From the view of decision makers, the process is independent to specific consensus measures and thus could be applied easily. The process is implemented with different types of PRs and discussed in distinct situations. Besides, for the applications of frequently considered scenarios, the values of random consensus indices are provided and the consensus thresholds are recommended.

Keywords:

• Group decision-making
• decision analysis
• preference relations
• consensus measures
• consensus thresholds

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (Nos. 71971119, 71601092), the social science foundation of Jiangsu Province (No. 19GLC009), the Key University Science Research Project of Jiangsu Province (No. 18KJB413006), the 2018 Youth Teacher Research Project of Nanjing Audit University, and Collaborative Innovation Center of Audit Information Engineering and Technology (No. 18CICA01).