Higher order interactions destroy phase transitions in Deffuant opinion dynamics model

TL;DR

This paper generalizes the Deffuant opinion dynamics model to include higher order interactions via hypergraphs, revealing that such interactions can eliminate sharp phase transitions and induce smooth consensus transitions in certain topologies.

Contribution

The study introduces a higher order Deffuant model on hypergraphs and demonstrates how it alters phase transition behavior in opinion dynamics.

Findings

Higher order interactions eliminate phase transitions in random hypergraphs.

Regular hypergraphs retain the phase transition.

Consensus emerges smoothly in the generalized model on random hypergraphs.

Abstract

We define a higher order Deffuant model by generalizing the original pairwise interaction model for bounded-confidence opinion-dynamics to interactions involving a group of agents of size k. The generalized model is naturally encoded in a hypergraph. We study this dynamics in different hypergraph topologies, from random hypergraph ensembles, to spatially embedded hyper-lattices. We show that including higher order interactions induces a drastic change in the onset of consensus for random hypergraphs; instead of the sharp phase transition, characteristic of the dyadic Deffuant model, the system undergoes a smooth size independent crossover to consensus, as the confidence value increases. This phenomenon is absent from regular hypergraphs, which conserve a phase transition.