Spatial opinion dynamics incorporating both positive and negative influence in small-world networks

When we consider tipping points of political and social opinions in groups, we often rely on a physics-based opinion dynamics approach. Despite the many studies on simple models, studies on more realistic situations have yet to be done. In this paper, we extend the basic model of opinion dynamics in two ways. The first extension incorporates negative influence between individuals. The second arranges individuals in a small-world network and fixes them in neighborhoods to consider their relationships. Our results show that a consensus tends to result with a higher positive trust ratio in the network, a denser network, and a milder degree of trust between individuals. In a real society, the development of consensus opinions depends on frequent communication, reliable people, and mild opinions. Moreover, we explore the conditions for merging the majority with a minority of individuals who are strongly connected. Our dense city model shows that the opinions of two parties connecting in dense interactions will gradually attract each other, and when a certain threshold is exceeded, those opinions will be integrated at once like a phase transition.