Determining consensus thresholds for group decision making with preference relations

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.