  Agent-based models are a natural choice for modeling complex social systems.
In such models simple stochastic interaction rules for a large population of
individuals can lead to emergent dynamics on the macroscopic scale, for
instance a sudden shift of majority opinion or behavior. Here, we are concerned
with studying noise-induced tipping between relevant subsets of the agent state
space representing characteristic configurations. Due to the large number of
interacting individuals, agent-based models are high-dimensional, though
usually a lower-dimensional structure of the emerging collective behaviour
exists. We therefore apply Diffusion Maps, a non-linear dimension reduction
technique, to reveal the intrinsic low-dimensional structure. We characterize
the tipping behaviour by means of Transition Path Theory, which helps gaining a
statistical understanding of the tipping paths such as their distribution, flux
and rate. By systematically studying two agent-based models that exhibit a
multitude of tipping pathways and cascading effects, we illustrate the
practicability of our approach.
