Vectorial-Opinion Dynamics With Familiarity Neighborhoods in Virtual Social Groups

Abstract

In this work, we mimic interactions among agents on social networks and examine their impact on the evolution of agents’ opinions. Each agent is entitled to an opinion represented by unit vectors of varying orientation. Agents are also characterized based on their inclination to alter their opinion and their susceptibility to the influence of peers with contrasting opinions. The agents constitute the nodes of a directed and time-varying influence network whose edges form their respective familiarity neighborhoods and govern their interactions. We also devise an interpersonal influence score to quantify the strength of the influence and the probability of acquisition, retention, or loss of a tie. This characterization of agents’ behavior and their interpersonal relationships differs from traditional bounded-confidence models based on the agreement in opinions alone. The agents with different traits form groups—liberal and conservative—distinguished by the distribution in opinions of their constituents. We analyze their interactions with different initial opinions, group compositions, network structures, and network evolution rates through simulations. The results reveal that flexible agents facilitate consensus among group members, while stubborn agents are instrumental in forming opinion clusters. This is substantiated by observing the average connectedness of the influence network and the average number of opinion clusters; groups with mostly flexible agents have better connectedness and fewer clusters than groups with stubborn agents in a majority. The simulations with stubborn agents reveal that new ties among agent pairs do not facilitate group consensus.