https://doi.org/10.1140/epjs/s11734-021-00151-8
Regular Article
Bi-layer voter model: modeling intolerant/tolerant positions and bots in opinion dynamics
1
Institute of Computing, University of Campinas (Unicamp), Campinas, SP, Brazil
2
Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA
3
National Institute for Space Research (INPE), Sao Jose dos Campos, SP, Brazil
4
URPP Social Networks, Universität Zürich, Andreasstrasse 15, 8050, Zurich, Switzerland
5
Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina
Received:
5
December
2020
Accepted:
23
April
2021
Published online:
6
June
2021
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 the voting dynamics’ challenges. In particular, social bots are currently a new element that can have a pronounced effect on the formation of opinions during electoral processes 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 the 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 (
). We find that intolerance leads to a consensus of tolerant agents during an initial stage that scales as 
, who then reach an opinion consensus during the second stage in a time that scales as 
, where N is the number of agents. Therefore, very intolerant agents (
) could considerably slow down dynamics towards the final consensus state. We also find that the inclusion of a fraction 
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 
for 
and 
for 
.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
