## Open Conference Systems, StatPhys 27 Main Conference

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Threshold q-voter opinion dynamics
Allan Rodrigues Vieira, Celia Anteneodo

##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-10 12:00 PM – 03:45 PM

#### Abstract

In recent years, modeling social phenomena and social behaviors have
attracted interest in economics, technology and politics. Data Science
emerged with huge potential in this area. On the other hand, there are
still too much to understand about social dynamics.
One of the topics in this area is social dynamics, that aims to study
the emergence of collective states such as consensus, fragmentation,
polarization, from microscopic interactions among agents.  This can be
approached through agent-based models. For instances that can be reduced
to a binary case (e.g., for and against), one of the most famous binary
models in opinion dynamics is the Voter Model where a chosen agent
mimics the opinion of one of its neighbors. In 2009, C. Castellano et
al. proposed the $q$-voter model, where the unanimity among a group with
$q$ members (lobby group) formed from the neighborhood of certain agent
could change its own opinion. Besides that, they introduced a noise
$\varepsilon$ that represents changes of opinion independently of the
lobby group. Considering, that influence can occur even without
unanimity, we introduced a generalization of the $q$-voter model, where
an agent can change its mind when at least $q_0$ among $q$ neighbors
share the opposite opinion. This model allows the emergence of
collective behaviors not observed in the standard $q$-voter. The minimal
number $q_0$ among $q$, together with the stochasticity introduced by
$\varepsilon$, yields a phenomenology that mimics as particular cases
the $q$-voter with stochastic drivings such as nonconformity and
independence.
In particular, nonconsensus majority states are possible as well as
mixed phases. Continuous and discontinuous phase transitions can occur,
as well as transitions from fluctuating phases into absorbing states.
We analyze this model in fully connected networks, both numerically and
through a mean field approximation which agrees well with numerical results.

[1] P. Nyczka, K. Sznajd-Weron, J. Stat. Phys. 151, 174–202 (2013)
[2] A. R. Vieira, C. Anteneodo Phys. Rev. E 97, 052106 (2018)
[3] C. Castellano, M. A. Muñoz, and R. Pastor-Satorras, Phys. Rev.E 80, 041129 (2009).