  The noisy voter model is a stylised representation of opinion dynamics.
Individuals copy opinions from other individuals, and are subject to
spontaneous state changes. In the case of two opinion states this model is
known to have a noise-driven transition between a unimodal phase, in which both
opinions are present, and a bimodal phase in which one of the opinions
dominates. The presence of zealots can remove the unimodal and bimodal phases
in the model with two opinion states. Here, we study the effects of zealots in
noisy voter models with M>2 opinion states on complete interaction graphs. We
find that the phase behaviour diversifies, with up to six possible
qualitatively different types of stationary states. The presence of zealots
removes some of these phases, but not all. We analyse situations in which
zealots affect the entire population, or only a fraction of agents, and show
that this situation corresponds to a single-community model with a fractional
number of zealots, further enriching the phase diagram. Our study is conducted
analytically based on effective birth-death dynamics for the number of
individuals holding a given opinion. Results are confirmed in numerical
simulations.
