  Bounded-confidence models in social dynamics describe multi-agent systems,
where each individual interacts only locally with others. Several models are
written as systems of ordinary differential equations with discontinuous
right-hand side: this is a direct consequence of restricting interactions to a
bounded region with non-vanishing strength at the boundary. Various works in
the literature analyzed properties of solutions, such as barycenter invariance
and clustering. On the other side, the problem of giving a precise definition
of solution, from an analytical point of view, was often overlooked. However, a
rich literature proposing different concepts of solution to discontinuous
differential equations is available. Using several concepts of solution, we
show how existence is granted under general assumptions, while uniqueness may
fail even in dimension one, but holds for almost every initial conditions.
Consequently, various properties of solutions depend on the used definition and
initial conditions.
