  Is it possible to abstract a formal mechanism originating schisms and
governing the size evolution of social conversations? In this work a
constructive solution to such problem is proposed: an abstract model of a
generic N-party turn-taking conversation. The model develops from simple yet
realistic assumptions derived from experimental evidence, abstracts from
conversation content and semantics while including topological information, and
is driven by stochastic dynamics. We find that a single mechanism - namely the
dynamics of conversational party's individual fitness, as related to
conversation size - controls the development of the self-organized schisming
phenomenon. Potential generalizations of the model - including individual
traits and preferences, memory effects and more elaborated conversational
topologies - may find important applications also in other fields of research,
where dynamically-interacting and networked agents play a fundamental role.
