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Threshold q-voter opinion dynamics

##manager.scheduler.building##: Edificio Santa Maria

##manager.scheduler.room##: Auditorio San Agustin

Date: 2019-07-10 12:00 PM – 03:45 PM

Last modified: 2019-06-14

#### 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).

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).