  A broad range of dynamical systems involve multi-body interactions, or group
interactions, which may not be encoded in traditional graphical structures. In
this work, we focus on a canonical example from opinion dynamics, the Majority
Rule, and investigate the possibility to represent and analyse the system by
means of hypergraphs. We explore the formation of consensus and restrict our
attention to interaction groups of size $3$, in order to simplify our analysis
from a combinatorial perspective. We propose different types of hypergraph
models, incorporating modular structure or degree heterogeneity, and recast the
dynamics in terms of Fokker-Planck equations, which allows us to predict the
transient dynamics toward consensus. Numerical simulations show a very good
agreement between the stochastic dynamics and theoretical predictions for large
population sizes.
