Higher order interactions destroy phase transitions in Deffuant opinion dynamics model

Hendrik Schawe,Laura Hernández

doi:10.1038/s42005-022-00807-4

Abstract

Most opinion dynamics models are based on pairwise interactions. However in many real situations, discussions take place within groups of people. Here, 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.

Highlights

Most opinion dynamics models are based on pairwise interactions
The interest in multi-agent interactions[9] to model group dynamics at a large scale did rise sharply and several studies were published in the context of opinion dynamics[10–16], contagion[17–19] and other dynamical processes[20,21], which modelled the topology of interactions by hypergraphs
As for networks, the outcomes of the dynamics strongly depend on whether the hypergraph is regular or random and we explore the interplay of the dynamical rules and the interaction structure, paying particular attention to the finite-size effects that have been shown to be dominant in bounded confidence models in networks[22]

Summary

Introduction

Most opinion dynamics models are based on pairwise interactions. in many real situations, discussions take place within groups of people. Two outstanding models of this class are the Deffuant–Weisbuch (DW) model[3] and the Hegselmann–Krause (HK) model[4] Both model the opinion of the N agents in the population as a continuous variable xi ∈ [0, 1], ∀ i = 1, N and their main difference is that while the DW considers pairwise interactions and asynchronous updates, in the HK model, at each step, all the agents synchronously update their opinion by taking the average of each agent’s current opinion and those of their neighbours. Pairwise interactions do not describe all possible ways of discussion in real life, and the particularities of group discussion and decision making are still a matter of discussion in Social Psychology[5–7] This necessity of going beyond pairwise interactions has been first addressed by generalizing previous models to the case of group interactions mainly in the form of a majority rule, as in the voter model[8] or in the form of an aggregation rule that averages the opinion of the neighbours of the active agent, as in the Hegselmann–Krause model[4]. The interest in multi-agent interactions[9] to model group dynamics at a large scale did rise sharply and several studies were published in the context of opinion dynamics[10–16], (social) contagion[17–19] and other dynamical processes[20,21], which modelled the topology of interactions by hypergraphs

Methods

Results

Conclusion