Probabilistic neighbors' selection competes with confirmation bias in a bounded confidence model

Abstract

In this work, we investigate three modified versions of the classic Hegselmann-Krause opinion dynamics model, incorporating features that are typical of many real-world systems, such as uncertainty in the selection of interacting agents and a weighted evaluation of the relevance of their opinions in the influence function to enhance confirmation bias. Through extensive simulations across different network topologies, ranging from stylized network models (Barabási-Albert, Erdős-Rényi, and Watts-Strogatz networks) to empirical networks with community structure, we identify the influence of each modification on opinion evolution and convergence. Our findings reveal that they exert opposite effects on the bounded confidence threshold required for consensus. We further explore an extension based on a data-driven opinion initialization on the empirical networks, where initial opinions are drawn from Gaussian distributions specific to each detected community. While the qualitative effects of the three modified models remain consistent, this new initialization strategy reveals distinct dynamics within the network communities. These insights provide a new and comprehensive perspective on how realistic variations of the Hegselmann-Krause model, in terms of both interaction rules and initial opinion distributions, affect opinion dynamics and shed light on the mechanisms of consensus formation within structured communities.