  In this chapter, we derive and analyse models for consensus dynamics on
hypergraphs. As we discuss, unless there are nonlinear node interaction
functions, it is always possible to rewrite the system in terms of a new
network of effective pairwise node interactions, regardless of the initially
underlying multi-way interaction structure. We thus focus on dynamics based on
a certain class of non-linear interaction functions, which can model different
sociological phenomena such as peer pressure and stubbornness. Unlike for
linear consensus dynamics on networks, we show how our nonlinear model dynamics
can cause shifts away from the average system state. We examine how these
shifts are influenced by the distribution of the initial states, the underlying
hypergraph structure and different forms of non-linear scaling of the node
interaction function.
