Consensus from group interactions: An adaptive voter model on hypergraphs

TL;DR

This paper investigates how group interactions on hypergraphs influence consensus formation in opinion dynamics, revealing that heterogeneity in group sizes accelerates consensus and amplifies initial biases, diverging from classical voter model behavior.

Contribution

It introduces an adaptive voter model on hypergraphs with variable group sizes and provides both simulation results and an analytical approach to understand consensus dynamics.

Findings

Group interactions amplify initial opinion biases.

Heterogeneity in group sizes accelerates consensus formation.

Average magnetization drifts, losing conservation property.

Abstract

We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions $\{0,1\}$ form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can also split and merge (adaptation). In a hypergraph, these groups are represented by hyperedges of different sizes. The heterogeneity of group sizes is controlled by a parameter $\beta$. To study the impact of $\beta$ on reaching consensus, we provide extensive computer simulations and compare them with an analytic approach for the dynamics of the average magnetization. We find that group interactions amplify small initial opinion biases, accelerate the formation of consensus and lead to a drift of the average magnetization. The conservation of the initial magnetization, known for basic voter models, is no longer obtained.