The impact of environment-based heterogeneous bounded confidence on opinion dynamics

Abstract

In the bounded confidence model of opinion dynamics, agents only consider opinion interaction when the difference between their opinions is smaller than the bounded confidence. It is commonly assumed in previous studies that individuals possess homogeneous bounded confidence. However, in real life, agents in different environments may have different bounded confidences. This paper proposes a ring-based model that links the bounded confidences of agents to their local order parameters by introducing parameters $\alpha$ and $ϵ$ to modulate their functional relationship, where $\alpha$ controls the social attitudes of individuals in the population and $ϵ$ represents the maximum allowed bounded confidence. The results indicate that smaller values of $\alpha$ promote a higher probability of consensus in the system. By examining the evolution of agents’ local order parameters and bounded confidences from a microscopic perspective, we explain how $\alpha$ influences opinion dynamics. Subsequently, we investigate opinion evolution under different degrees for each agent and find that, although parameter selection affects the final outcome to some extent, an optimal degree generally exists that maximizes the system’s consensus probability. Finally, we discuss the impact of the parameter $ϵ$ on opinion dynamics, revealing that for larger values of $\alpha$, there exists an optimal $ϵ$ that maximizes the probability of consensus.