Managing Public Opinions Based on the Self-Confidence-Driven Hegselmann–Krause Model

Abstract

Public opinion management plays a vital role in both government governance and corporate competition. Opinion dynamics provides a key framework for its study, with the classic Hegselmann–Krause (HK) model using confidence thresholds to define individuals’ opinion exploration and interaction ranges. However, many existing studies treat these thresholds as exogenous, overlooking the influence of internal psychological traits—particularly self-confidence—on external exploratory behavior. To bridge this gap, we propose a self-confidence-driven HK (SCD-HK) model by establishing a driving relationship between individuals’ internal self-confidence levels and their external confidence thresholds. Based on this, we develop an optimal intervention model under time constraints to guide public opinion evolution. Numerical analyses, including sensitivity tests, comparative experiments, and a case study, reveal that: 1) moderate self-confidence levels better promote consensus than extreme values; 2) a concave relationship between self-confidence and confidence thresholds better facilitates consensus; and 3) our SCD-HK model outperforms traditional models in consensus ratio, convergence speed, and intervention cost. This article highlights the importance of incorporating the relationship between individuals’ inherent self-confidence levels and external confidence thresholds in opinion evolution, and our findings offer practical insights for more effective opinion management.