Opinion dynamics under double thresholds

Abstract

In this letter, we introduce a double threshold model to investigate opinion formation in social networks, considering bi-directional binary opinion changes. We derive the law of motion for opinion evolution analytically and explore the conditions for achieving oscillation, convergence, and even consensus comprehensively. Our findings demonstrate that under asymmetric thresholds with synchronous updating, the initial fraction of both opinions tends to approach the respective switching thresholds, facilitating rapid opinion convergence. Additionally, we observe that both lower and higher levels of connectivity promote consensus formation, while moderate connectivity can lead to opinion oscillations. Furthermore, network structures with longer connections or hubs expedite consensus emergence. However, under synchronous updating, both asymmetric and symmetric double thresholds may induce opinion oscillations, impeding stable state attainment. Conversely, with asynchronous updating, opinions consistently converge. Overall, our study enhances understanding of opinion dynamics, providing insights into consensus formation and offering a theoretical foundation to address socio-political issues in diverse communities.