Consensus Formation in the Social Network DeGroot Model: The Role of Leaders’ Self-Confidence

This study investigates how leaders’ self-confidence levels (LSLs) influence consensus formation in the social network DeGroot (SNDG) model and develops an optimization framework that regulates LSLs to minimize overall opinion loss across individuals. This study first presents an exact closed-form expression for the consensus opinion, which reveals how leaders’ initial opinions, LSLs, and the social network among leaders jointly determine the final consensus outcome. Building on these findings, a self-confidence level optimization model with bounded confidence (SLOMBC) is proposed. The model minimizes total opinion loss by optimizing LSLs while incorporating bounded confidence to enhance leaders’ willingness to adjust. Numerical examples based on a topology-free network, a small-world network, and a scale-free network illustrate the application of the SLOMBC. Results show that the proposed model reduces total opinion loss by an average of at least 6% and up to 13%. Comparative analyses further demonstrate its superiority across different network structures. This study advances the SNDG model by incorporating the critical role of LSLs into consensus formation analysis, offering a novel methodological perspective for managing consensus opinion formation and reducing overall opinion loss.