This talk was given at the Network Science Society Conference 2020 - NetSci 2020. It is based on a joint paper with Andrew Mellor and Renaud Lambiotte (Multibody interactions and nonlinear consensus dynamics on networked systems, Physical Review E, 2020). In summary, the talk derives a general model for consensus dynamics on hypergraphs which reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, a specific nonlinear function is introduced which models three-body consensus, which incorporates reinforcing group effects such as peer pressure.