A new adaptive two-layer model for opinion spread in hypergraphs: parameter sensitivity and estimation

Abstract

When opinion spread is studied, peer pressure is often modeled by interactions of more than two individuals (higher-order interactions). In our work, we introduce a two-layer random hypergraph model, in which hyperedges represent households and workplaces. Within this overlapping, adaptive structure, individuals react if their opinion is in majority in their groups. The process evolves through random steps: individuals can either change their opinion, or quit their workplace and join another one in which their opinion belongs to the majority. Based on computer simulations, our first goal is to describe the effect of the parameters responsible for the probability of changing opinion and quitting workplace on the homophily and speed of polarization. We also analyze the model as a Markov chain, and study the frequency of the absorbing states. Then, we quantitatively compare how different statistical and machine learning methods, in particular, linear regression, xgboost and a convolutional neural network perform for estimating these probabilities, based on partial information from the process, for example, the distribution of opinion configurations within households and workplaces. Among other observations, we conclude that all methods can achieve the best results under appropriate circumstances, and that the amount of information that is necessary to provide good results depends on the strength of the peer pressure effect.

Summary

This research introduces a novel two-layer hypergraph model to simulate opinion dynamics in social networks, considering the influence of households and workplaces. The key innovation lies in allowing individuals to adapt their opinions and even switch workplaces based on group dynamics, offering a more realistic view of how social structures and opinions co-evolve.

Key Insights

• •The two-layer hypergraph model effectively captures the intertwined influence of households (fixed hyperedges) and workplaces (adaptive hyperedges) on individual opinions.
• •The model incorporates parameters for opinion change (β) and workplace switching (q), along with thresholds (r1, r2) and workplace influence weight (λ), allowing for nuanced control over the simulation's dynamics.
• •The distinction between a linear model (r1=r2=1) and a non-linear model (r1=r2=0.5) reveals that stronger peer pressure in the non-linear model can lead to mixed opinions within groups, preventing complete polarization.
• •Simulations demonstrate that the linear model exhibits higher standard deviations in final opinion distributions compared to the non-linear model, indicating more volatile opinion dynamics.
• •The homophily index, measuring the prevalence of homogeneous groups, reveals a competitive interplay between opinion change and workplace change in driving polarization.

Practical Implications

• •The model can be used to study the formation of opinion bubbles and polarization in online social networks, providing insights into the spread of misinformation and the impact of echo chambers.
• •The parameter estimation using machine learning techniques suggests the possibility of predicting opinion dynamics in real-world social systems based on observed group behavior.
• •Future research can extend the model to incorporate more complex social structures, such as varying household sizes and more intricate network topologies, to enhance its realism.
• •The model's findings could inform strategies for promoting consensus and reducing polarization in online communities by manipulating parameters that affect opinion change and group affiliation.

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