In this paper, we describe a process of validation for an already published model, which relies on the M2M paradigm of work. The initial model showed that over-confident agents, which refuse to communicate with agents whose beliefs differ, disturb collective learning within a population. We produce an analytical model based on probabilistic analysis, that enables us to explain better the process at stake in our first model, and demonstrates that this process is indeed converging. To make sure that the convergence time is meaningful for our question (not just for an infinite number of agents living for an infinite time), we use the analytical model to produce very simple simulations and assess that the result holds in finite contexts.