Abstract
Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper we present a version of the $q$-voter model of opinion dynamics with two types of response to social influence: conformity (like in original $q$-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the systems undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point consensus in the entire system is possible. Thus two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point the system ends up in a polarized state.
Highlights
What do affirmative action and gun control [1], same-sex marriage and sexual minority rights [2], abortion [3] stem cell research [4], global warming [5], attitudes toward political candidates [6] or the recent refugee crisis in Europe [7] have in common? All of these keywords are examples of topics known to ignite polarized debates in society
It is sometimes referred to as bi-polarization [9] to distinguish it from the so-called group polarization, i.e., the tendency for a group to make decisions that are more extreme than the initial inclination of its members [10,11]
Asch found that conformity is reduced dramatically by the presence of a social supporter: targets of influence having a partner sharing the same opinion were far more independent when opposed to a seven-person majority than targets without a partner opposed to a three-person majority [59]
Summary
What do affirmative action and gun control [1], same-sex marriage and sexual minority rights [2], abortion [3] stem cell research [4], global warming [5], attitudes toward political candidates [6] or the recent refugee crisis in Europe [7] have in common? All of these keywords are examples of topics known to ignite polarized debates in society. Studying them could shed more light on the phenomenon of polarization, which is one of the central issues in the recent opinion dynamics research. It could for instance help to avoid segregation and conflicts in the society [8] or to control polarized debates and predict their outcomes [12]. As far as the theoretical part is concerned, mathematical and computational approaches are dominant in modeling of opinion dynamics [27]. Mathematical models allow for some theoretical and/or numerical analysis [28,29,30,31,32,33].
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