Soft consensus cost models for group decision making and economic interpretations

In a group decision-making (GDM) process, experts reach a consensus after discussion and persuasion, which requires a moderator to spend time and resource to persuade experts to change their original opinions. Since a unanimous agreement is hard to achieve and costly, a consensus degree or soft consensus was used and various approaches have been proposed to measure the level of consensus in GDM. Though cost is an important factor in GDM, few works have calculated consensus cost occurred during the process. Moreover, the degree of consensus was not considered in the minimum cost consensus study. The objective of this paper is to propose consensus models under a certain degree of consensus, which considers both consensus degree and cost in GDM. To do this, we develop a generalized soft cost consensus model under a certain degree of consensus, which is built by defining a consensus level function and a generalized aggregation operator. A soft minimum cost consensus model is constructed based on arithmetic weighted average operator (AWAO), and the maximum return model is constructed through its dual model. The cost (compensation) is studied from both the perspectives of a moderator and individual experts. The relationships between the two soft consensus cost models are analyzed, and the economic significance of the models are also discussed. Numerical examples are used to explain the proposed models. In addition, to show the usability of the proposed models in real-world context, we apply the proposed models to a loan consensus scenario using data from an online peer-to-peer lending platform.