Optimal resources allocation to support the consensus reaching in group decision making

In group decision making (GDM), the minimum cost consensus model (MCCM) to assist a group to reach a consensus with the minimum cost has gained widespread attention. However, determining the unit costs for adjusting decision makers' opinions in the MCCM is a challenging problem that limits its practical applications. Meanwhile, the MCCM is not modeled as a resources allocation problem in an explicit manner, and the opinions in the MCCM do not represent utilities/satisfactions, leading to the unclear implications of opinions' adjustments. To overcome these limitations of the MCCM, this paper proposes the optimal resources allocation consensus model (ORACM) to assist the moderator to allocate resources without determining unit costs to support consensus reaching, through the introduction of the resources allocation problem and utility functions in its modeling. Furthermore, we present a theoretical analysis framework to reveal the properties of the ORACM and the connection between the ORACM and the MCCM, justifying the theoretical advantages of the ORACM. Moreover, the ORACM is applied to the transboundary river pollution control negotiations of Sichuan's Tuojiang River, and the effectiveness and feasibility of the ORACM are further validated with detailed simulation and comparison analyses.