encoded by a nonlocal transport term taking into account the presence, among the overall population, of a restricted number of “leaders” promoting their opinion with a strong influence on the “followers”. It is natural to postulate, as the authors do (see [@BMPW2009 Section 3.b] for a detailed discussion), that opinion leadership is not constant over time: someone who is an opinion leader today may lose this role tomorrow, or a follower may become a leader in the future.

Summarizing, the multi-population dynamics we are interested in attaches to an agent sitting at a position $x$ a probability measure $\lambda\in{\mathcal P}(U)$, where $U$ is a compact space of labels accounting for the population to which the agent belongs. In fact, we find it natural not to assume any deterministic knowledge of the label of a single agent, since transitions are usually modeled as the outcome of a stochastic process. Hence, $\lambda$ expresses the probability that the agent has, at a certain moment in time, of belonging to a subset of $U$, and may itself evolve as a consequence of the interaction among the agents. The minimal model for evolution that we propose[^1] consists of the coupling of a non-local transport dynamics 