  We introduce a DeGroot-based model for opinion dynamics in social networks. A
community of agents is represented as a weighted directed graph whose edges
indicate how much agents influence one another. The model is formalized using
labeled transition systems, henceforth called opinion transition systems (OTS),
whose states represent the agents' opinions and whose actions are the edges of
the influence graph. If a transition labeled $(i,j)$ is performed, agent $j$
updates their opinion taking into account the opinion of agent $i$ and the
influence $i$ has over $j$. We study (convergence to) opinion consensus among
the agents of strongly-connected graphs with influence values in the interval
$(0,1)$. We show that consensus cannot be guaranteed under the standard strong
fairness assumption on transition systems. We derive that consensus is
guaranteed under a stronger notion from the literature of concurrent systems;
bounded fairness. We argue that bounded-fairness is too strong of a notion for
consensus as it almost surely rules out random runs and it is not a
constructive liveness property. We introduce a weaker fairness notion, called
$m$-bounded fairness, and show that it guarantees consensus. The new notion
includes almost surely all random runs and it is a constructive liveness
property. Finally, we consider OTS with dynamic influence and show convergence
to consensus holds under $m$-bounded fairness if the influence changes within a
fixed interval $[L,U]$ with $0<L<U<1$. We illustrate OTS with examples and
simulations, offering insights into opinion formation under fairness and
dynamic influence.
