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 lowerlevel 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 duallayer 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.