We introduce and analyse a three-body consensus model (3CM) for non-linear
consensus dynamics on hypergraphs. Our model incorporates reinforcing group
effects, which can cause shifts in the average state of the system even in if
the underlying graph is complete (corresponding to a mean-field interaction), a
phenomena that may be interpreted as a type of peer pressure. We further
demonstrate that for systems with two clustered groups, already a small
asymmetry in our dynamics can lead to the opinion of one group becoming clearly
dominant. We show that the nonlinearity in the model is the essential
ingredient to make such group dynamics appear, and demonstrate how our system
can otherwise be written as a linear, pairwise interaction system on a rescaled
network.