Bounded confidence dynamics generates opinion cascades on growing scale-free networks (2506.02669v3)

Abstract: We study the pairwise bounded confidence model on scale-free networks where new agents regularly arrive over time. The probability that arriving agents form links to preexisting ones depends on both agent degree and opinion proximity. In parameter value ranges where both factors impact the link choice, a new phenomenon is observed. Minor clusters continuously form on the periphery of the opinion space and remain stable for a time, before suddenly merging with a major cluster in the network. We label these processes as "opinion cascades", and analyse their origin and behavior. They are triggered by the arrival of agents acting as "bridges" between the previously disconnected minor and major clusters. Lastly, we propose theoretical approximations to describe the varying shapes and merging behavior of opinion cascades under different conditions.

• The paper demonstrates that bounded confidence dynamics trigger opinion cascades by merging minor clusters with dominant ones via bridge agents.
• It employs simulations and probabilistic models to validate how network growth and agent connectivity influence opinion merging.
• The research highlights that while bridge agents rapidly assimilate opinions, distinct community structures persist within the evolving network.

Bounded Confidence Dynamics and Opinion Cascades on Scale-Free Networks

Abstract

The paper explores the role of the pairwise bounded confidence model in forming opinion cascades within scale-free networks. The research highlights phenomena where minor opinion clusters form and merge with major clusters, constituting 'opinion cascades.' These phenomena are fueled by bridge agents who establish connectivity between disparate clusters. Theoretical models describe the probabilistic behaviors driving these dynamics, which are confirmed through simulations.

Introduction

Opinion dynamics, particularly information cascades, play a crucial role in diverse socio-political contexts. Bounded confidence models facilitate understanding these dynamics by modeling how individuals' opinions evolve through interactions among agents. This model demonstrates that under certain parameters, minor clusters emerge and undergo opinion cascades by merging with major clusters, catalyzed by bridge agents.

Opinion Cascades in Scale-Free Networks: The research identifies a unique phenomenon within growing scale-free networks, differing from behavior in fully connected networks. Unlike stable clusters observed in static networks, scale-free networks continually form minor clusters that merge with larger clusters, highlighting the dynamic and cascading nature of opinion formations.

Figure 1: Representative simulation results in which opinion cascades happen. The confidence bound is $\epsilon = 0.3$, with new links $m =3$, influence $\mu = 0.5$, $N_0 = 10$, and $\delta = 3$.

Model Description

The model incorporates two key processes: opinion dynamics with bounded confidence and network growth through new agent integration. Each new agent's probability of connecting with existing nodes depends on node degree and opinion proximity, introducing homophily within network link formation.

Network Growth Dynamics

• Initial Setup: Beginning with $N_0$ fully connected nodes, agents arrive and form new links based on probability functions concerning existing node degrees and opinion proximities.
• Link Formation Probability: This combines traditional preferential attachment with homophily through a parameter $\beta$, where $\beta$ modulates the impact of opinion proximity versus node degree on connectivity.

Algorithm Implementation: The algorithm iterates through time, allowing agent interactions that influence opinions and introducing new agents who connect with the network based on calculated probabilities.

Simulation Results

Opinion Cascade Patterns: Simulations demonstrate that minor clusters appear at the boundary of major cluster influence (at distance $\epsilon$). These clusters merge into major clusters under the influence of bridge agents, displaying notable cascades under certain $\beta$ ranges.

Figure 2: Simulation result after detecting communities via the Louvain method. Each community is distinguished by different colors.

Community Detection: Utilizing the Louvain method reveals distinct communities forming around minor clusters. These communities persist post-merge, indicating that while opinions assimilate, underlying community structures remain distinct.

Theoretical Analysis of Opinion Cascades

Bridge Agents: The paper isolates the role of bridge agents in triggering opinion cascades. These agents, connecting major and minor clusters, facilitate the rapid merging of opinions.

• Probability Models: Probabilities are derived to predict the likelihood of agent roles upon network entry, strongly correlating with simulation outcomes.

Figure 3: Theoretical probability distributions and experimental frequencies of an arriving agent by type at various times and $\beta$ values.

Conclusion

The interplay between network structure and opinion dynamics fosters complex behaviors such as opinion cascades. These cascades, catalyzed by bridge agents, underline the challenges minor opinion clusters face against dominant clusters. The paper offers insights into ensuring diversity in opinion dynamics and mitigating rapid assimilation within networks. Future research directions include exploring varying confidence bounds and their effect on network stability and diversity maintenance.

Implications: Understanding these dynamics assists in designing networks resilient to misinformation and promotes the retention of diverse opinions essential for balanced socio-political dialogue.