  The diffusion of opinions in Social Networks is a relevant process for
adopting positions and attracting potential voters in political campaigns.
Opinion polarization, bias, targeted diffusion, and the radicalization of
postures are key elements for understanding voting dynamics. In particular,
social bots are a new element that can have a pronounced effect on the
formation of opinions during elections by, for instance, creating fake accounts
in social networks to manipulate elections. Here we propose a voter model
incorporating bots and radical or intolerant individuals in the decision-making
process. The dynamics of the system occur in a multiplex network of interacting
agents composed of two layers, one for the dynamics of opinions where agents
choose between two possible alternatives, and the other for the tolerance
dynamics, in which agents adopt one of two tolerance levels. The tolerance
accounts for the likelihood to change opinion in an interaction, with tolerant
(intolerant) agents switching opinion with probability $1.0$ ($\gamma \le 1$).
We find that intolerance leads to a consensus of tolerant agents during an
initial stage that scales as $\tau^+ \sim \gamma^{-1} \ln N$, who then reach an
opinion consensus during the second stage in a time that scales as $\tau \sim
N$, where $N$ is the number of agents. Therefore, very intolerant agents
($\gamma \ll 1$) could considerably slow down dynamics towards the final
consensus state. We also find that the inclusion of a fraction
$\sigma_{\mathbb{B}}^-$ of bots breaks the symmetry between both opinions,
driving the system to a consensus of intolerant agents with the bots' opinion.
Thus, bots eventually impose their opinion to the entire population, in a time
that scales as $\tau_B^- \sim \gamma^{-1}$ for $\gamma \ll
\sigma_{\mathbb{B}}^-$ and $\tau_B^- \sim 1/\sigma_{\mathbb{B}}^-$ for
$\sigma_{\mathbb{B}}^- \ll \gamma$.

Physics and Society