Opinion formation in social networks with pairwise interactions and majority effects

Abstract

Human interactions are the building blocks of social networks, which in turn form the foundation of societies. Through these social engagements, people exchange information and evolve their opinions over time. The formation of consensus within these social networks is governed by two interrelated phenomena: pairwise interactions and majority effects. Pairwise interactions involve one-to-one exchanges of information between connected individuals, while majority effects pertain to social conformity that discourages people from making drastic changes to their opinions. In this study, we developed numerical models and simulations incorporating pairwise interactions and majority effects to examine opinion formation in social networks. We simulated opinion dynamics across two types of networks: a random network, represented by the Erdős-Rényi model, and a scale-free network, represented by the Barabási-Albert model, which captures the structure of real-world social networks. To simulate opinion dynamics and consensus formation in these networks, we utilized the classic Deffuant–Weisbuch bounded confidence model, later modifying it to study the majority effect. In our modified model, the opinions of two interacting nodes reach consensus only if the number of their neighbors with opinions within a specified threshold, also known as tolerance, increases or remains unchanged. In the classic Deffuant–Weisbuch bounded confidence model, where pairwise interactions are the key drivers of consensus formation, we observe that tolerance for opinion differences between interacting nodes plays a crucial role in consensus formation. When tolerance is low, nodes form multiple communities; when tolerance is higher, a global consensus is reached. When the majority effect is applied to the Deffuant–Weisbuch model, we observe a similar pattern: with low tolerance levels, most nodes form communities with extreme opinions at both ends of the opinion spectrum, while several smaller communities adopt intermediate opinions. However, when tolerance is high, the network can achieve global consensus. Thus, we demonstrate that varying tolerance levels among people in social networks results in vastly different consensus outcomes.