Modified Hegselmann-Krause Model for Enhancing Opinion Diversity in Social Networks

Abstract

A goal of opinion dynamics modelers has long been to find a social science based model that generates strong diversity: smooth, stable, possibly multi-modal distributions of opinions. However, the classic Hegselmann-Krause (HK) model, which relies on similarity assumptions, is often criticized for producing only weak diversity. Here, weak diversity refers to the eventual convergence of group into several opinion clusters, where the gap between opinion clusters is limited by the confidence interval $\varepsilon $ , and all individuals within the same cluster share a single opinion. To address this limitation, this paper proposes a modified HK model (MHK) that incorporates social conformity and uniqueness theory from social psychology to enhance opinion diversity within the network. Social conformity theory accounts for the discrepancy between individuals’ expressed opinions and their implicit opinions, while uniqueness theory establishes a new lower bound for individuals’ confidence intervals. Our findings demonstrate that social conformity and uniqueness collectively promote strong diversity both within and between clusters. Consequently, our modified model effectively addresses the limitations of the classic HK model, thereby improving its capacity to capture strong diversity in opinion dynamics.

Keywords

• Opinion dynamics
• social conformity
• uniqueness theory
• bounded confidence
• strong diversity