Facilitating large-scale group decision-making in social networks: A bi-level consensus model with social influence

Nowadays, more and more decision-makers (DMs) are engaging in group decision-making (GDM) within certain social relationship networks. Therefore, understanding how to leverage differences in DMs’ opinions and social relationships to promote consensus in large-scale group decision-making (LSGDM) is an important issue. This study proposes a bi-level consensus model for LSGDM in social networks, well considering social influence to achieve the objective of minimum cost of the upper-level mediator and maximum satisfaction of lower-level subgroups. Firstly, the Louvain algorithm is employed to reduce the dimensions of LSGDM, segmenting DMs in social networks into distinct subgroups in a directed graph. Then, a dynamic opinion experiment based on the Friedkin–Johnsen model is utilized to assess the confidence levels of subgroup members and enhance opinion coherence within subgroups. Operating at the subgroup perspective and adopting a dual-layer framework, this study establishes the minimum cost maximum satisfaction consensus model (MCMSCM) to better balance the objectives between the upper and lower levels. Furthermore, a bi-level nested algorithm, based on genetic algorithm, is employed to determine corresponding unit costs and adjusted opinions, thereby achieving consensus rapidly and effectively. The proposed methodology provides a robust tool for LSGDM in social networks. Finally, through an illustrative example accompanied by corresponding analysis, the rationality and effectiveness of this pattern are demonstrated.