Robust Minimum-Cost Consensus Model with Non-Cooperative Behavior: A Data-Driven Approach
Jiangyue Fu, Xingrui Guan, Xun Han, Gang Chen · Mathematics · 2025
Achieving consensus in group decision-making is both essential and challenging, especially in which non-cooperative behaviors can significantly hinder the process under uncertainty. These behaviors may distort consensus outcomes, leading to increased costs and reduced efficiency. To address this issue, this study proposes a data-driven robust minimum-cost consensus model (MCCM) that accounts for non-cooperative behaviors by leveraging individual adjustment willingness. The model introduces an adjustment willingness function to identify non-cooperative participants during the consensus-reached process (CRP). To handle uncertainty in unit consensus costs, Principal Component Analysis (PCA) and Kernel Density Estimation (KDE) are employed to construct data-driven uncertainty sets. A robust optimization framework is then used to minimize the worst-case consensus cost within these sets, improving the model’s adaptability and reducing the risk of suboptimal decisions. To enhance computational tractability, the model is reformulated into a linear equivalent using the duality theory. Experimental results from a case study on house demolition compensation negotiations in Guiyang demonstrate the model’s effectiveness in identifying and mitigating non-cooperative behaviors. The proposed approach significantly improves consensus efficiency and consistency, while the data-driven robust strategy offers greater flexibility than traditional robust optimization methods. These findings suggest that the model is well-suited for complex real-world group decision-making scenarios under uncertainty.