Higher order interactions destroy phase transitions in Deffuant opinion dynamics model
Hendrik Schawe, Laura Hernández
Abstract
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.