Research on the Mechanism of Social Emotion Formation in Public Emergencies Based on the DeGroot Model

In recent years, the frequent occurrence of public emergencies has often triggered the rapid spread and amplification of social emotions. The accumulation and intensification of negative emotions can lead to collective behaviors and even pose a threat to social stability. To better understand the formation and evolution of social emotions in such contexts, this study constructs a theoretical framework and simulation approach that combines opinion dynamics with emotional and trust interactions. First, we propose a clustering method that incorporates emotional similarity and trust relationships among users to delineate group structures involved in social emotion formation. Second, a dynamic trust adjustment mechanism is also proposed to capture how trust evolves as individuals interact emotionally. Third, a large-scale group emotional consensus decision-making approach, based on the DeGroot model, is developed to simulate how emotional exchanges and resonance drive groups toward consensus in public emergencies. Additionally, we present a strategy for guiding emotional interactions to reach a desired consensus that ensures minimal modifications to collective preference values while achieving an acceptable consensus level, helping to manage emotional escalation. To validate the proposed model, we conduct simulations using the “Fat Cat” incident as a case study. The results reveal key mechanisms underlying social emotion formation during public emergencies and highlight critical influencing factors, including user participation, opinion leader influence, and trust relationships. This study provides a clear understanding of how social emotions are generated and offers practical insights for managing emotional dynamics and improving group decision-making during crises.