Consensus modeling with nonlinear utility and cost constraints: A case study

In complex group decision making (GDM), reaching a consensus needs both the adequate communication and exchange between the individual decision makers (DMs) and the input of a moderator, who may take various effective actions, such as providing financial compensation (collectively referred to as “consensus cost”), to convince the DMs to gradually modify their opinions and to reach a final consensus. This study constructs new consensus models that aim to maximize the GDM utility under the premise of limited consensus cost and nonlinear utility/preference constraints for both the individual DMs and the moderator. The objective function (the utility level of the entire GDM) derived from the proposed models can be seen as a measurement of the group consensus degree. Moreover, using the pollutant reduction negotiations between the government and manufacturing enterprises as a case background, we construct a group reduction consensus model based on nonlinear preference constraints and limited consensus cost and economically interpret the model parameters. Results show that different preference combinations of the DM and moderator will affect the optimal consensus values. Additionally, the moderator’s preference structure influences the final GDM results to some extent. The modeling mechanism used in this paper will be reference for solving real-life consensus GDM problems.