Exploring the foundation of social diversity and coherence with a novel attraction–repulsion model framework

Opinion evolution is generally subject to global neutral consensus, fragmentation state or polarization. Additionally, there is one widely-existed state –“harmony with diversity” in which individuals freely express various viewpoints to sustain integration of social diversity, but at the same time shared values ensure social coherence. Such state can thus be considered as the foundation of social diversity and coherence, however, which has never attracted research attention. Its formation mechanism still remains unclear. To address this issue, this study proposes an attraction–repulsion model based on the general simple assumption that individuals tend to either reach an agreement with shared opinions or to amplify difference from others with distant opinions. It allows us to take account into the three core parameters: interaction strength, individuals’ susceptibility and tolerance to others’ opinions. We are concerned with the effect of not only time-varying topology but also fixed interactions imposed by static social network, where the tasks of heterogeneous individuals’ attributes are also performed. Remarkably, the simple model rules successfully generate the three above phases except for fragmentation, along with three different transitions and the triple points. We find that sufficient susceptibility, intermediate interaction strength and high tolerance can benefit a balance between repulsive and attractive forces, and thus the emergence of “harmony with diversity”. However, fixed interactions can introduce cluster-level self-reinforced mechanism which can unexpectedly promote polarization. Heterogeneous susceptibility or tolerance turns out to be an inhibiting factor, which should be avoided. A method to identify the phase boundaries through computing the maximum susceptibility of entropy and stand deviation of opinions, confirmed by numerical simulations, allows us to build phase diagrams and to locate where the triple points are. For the first time, this study focuses on the formation of “harmony with diversity”, and the findings provide profound insights into the foundation of societal diversity and coherence.