  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.
