We propose an opinion dynamics model based on Latané's social impact theory. Actors in this model are heterogeneous and, in addition to opinions, are characterised by their varying levels of persuasion and support. The model is tested for two and three initial opinions randomly distributed among actors. We examine how the noise (randomness of behaviour) and the flow of information among actors affect the formation and spread of opinions. Our main research involves the process of opinion formation and finding phases of the system in terms of parameters describing noise and flow of the information for two and three opinions available in the system. The results show that opinion formation and spread are influenced by both (i) flow of information among actors (effective range of interactions among actors) and (ii) noise (randomness in adopting opinions). The noise not only leads to opinions disorder but also it promotes consensus under certain conditions.
In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of the giant cluster. This order parameter reveals the non trivial effect of the network topology on the steady states of the dynamics, overlooked by previous works, which concentrated on the onset of unanimity, and allows to detect regions of polarization between the fragmented and the consensus phases. While the previous results on unanimity are confirmed, the …
In this paper, the results of computer simulations based on Nowak--Szamrej--Latané model with multiple (from two to five) opinions available in the system are presented. We introduce the noise discrimination level (which says how small the clusters of agents could be considered as negligible) as a quite useful quantity that allows qualitative characterization of the system. We show that depending on the introduced noise discrimination level, the range of actors' interactions (controlled indirectly by an exponent in distance scaling function, the larger the exponent the more influential the nea…
In this work we study a 3-state opinion formation model considering two distinct mechanisms, namely independence and conviction. Independence is introduced in the model as a noise, by means of a probability of occurrence $q$. On the other hand, conviction acts as a disorder in the system, and it is introduced by two discrete probability distributions. We analyze the effects of such two mechanisms on the phase transitions of the model, and we found that the critical exponents are universal over the order-disorder frontier, presenting the same universality class of the mean-field Ising model. In…
We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The random heterogeneities in the external perturbations are shown to affect the critical behavior of the network relative to networks without disorder. The size of the shift in the critical behavior essentially depends on th…
A general model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that consensus, polarisation and a spread of moderate opinions are all possible within this model. Using dynamic mean-field theory, we are able to identify the statistical features of the interactions between individuals that give rise to each of the aforementioned emergent phenomena. The nature of the transitions between each of the observed macroscopic states i…
We study a model of continuous opinion dynamics with both positive and negative mutual interaction. The model shows a continuous phase transition between a phase with consensus (order) and a phase having no consensus (disorder). The mean field version of the model was already studied. Using extensive numerical simulations, we study the same model in $2$ and $3$ dimensions. The critical points of the phase transitions for various cases and the associated critical exponents have been estimated. The universality class of the phase transitions in the model is found to be same as Ising model in the…
In this work we tackle a kinetic-like model of opinions dynamics in a networked population endued with a quenched plurality and polarization. Additionally, we consider pairwise interactions that are restrictive, which is modeled with a smooth bounded confidence. Our results show the interesting emergence of nonequilibrium hysteresis and heterogeneity-assisted ordering. Such counterintuitive phenomena are robust to different types of network architectures such as random, small-world and scale-free.
In this work we study a 3-state ($+1$, $-1$, $0$) opinion model in the presence of noise and disorder. We consider pairwise competitive interactions, with a fraction $p$ of those interactions being negative (disorder). Moreover, there is a noise $q$ that represents the probability of an individual spontaneously change his opinion to the neutral state. Our aim is to study how the increase/decrease of the fraction of neutral agents affects the critical behavior of the system and the evolution of opinions. We derive analytical expressions for the order parameter of the model, as well as for the s…
We investigate opinion formation in a kinetic exchange opinion model, where opinions are represented by numbers in the real interval $[-1,1]$ and agents are typified by the individual degree of conviction about the opinion that they support. Opinions evolve through pairwise interactions governed by competitive positive and negative couplings, that promote imitation and dissent, respectively. The model contemplates also another type of nonconformity such that agents can occasionally choose their opinions independently of the interactions with other agents. The steady states of the model as a fu…
In this work, we investigate interactions that simultaneously order a system locally, while keeping it globally disordered. The study is done in the context of the emergence of diversity in opinion propagation models with interactions rooted in conformity, but some suggestions on how this could be extended to other topics (like ecology and neuroscience) are also made. We do this by introducing a generic modification that can be added to different opinion propagation models (and other agent based models) and that seems to introduce a global tendency towards diversity without leading the system …
In this work we consider the presence of contrarian agents in discrete 3-state kinetic exchange opinion models. The contrarians are individuals that adopt the choice opposite to the prevailing choice of their contacts, whatever this choice is. We consider binary as well as three-agent interactions, with stochastic parameters, in a fully-connected population. Our numerical results suggest that the presence of contrarians destroys the absorbing state of the original model, changing the transition to the para-ferromagnetic type. In this case, the consequence for the society is that the three opin…
We show using scaling arguments and Monte Carlo simulations that a class of binary interacting models of opinion evolution belong to the Ising universality class in presence of an annealed noise term of finite amplitude. While the zero noise limit is known to show an active-absorbing transition, addition of annealed noise induces a continuous order-disorder transition with Ising universality class in the infinite-range (mean field) limit of the models.
In this paper Nowak--Szamrej-Latané model is reconsidered. This computerised model of opinion formation bases on Latané theory of social impact. We modify this model to allow for multi (more than two) opinions. With computer simulations we show that in the modified model the signatures of order/disorder phase transition are still observed. The transition may be observed in the average fraction of actors sharing the $i$-th opinion, its variation and also average number of clusters of actors with the same opinion and the average size of the largest cluster of actors sharing the same opinion. Als…
We investigate the non-equilibrium dynamics of a three state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter $q$. The mean field dynamical equations are derived and analysed for any $q$. The fate of the system under the evolutionary rules used in \cite{BCS} shows that it is dependent on the value of $q$ and the initial state in general. For $q=1$, which allows the extreme switches maximally, a quasi-conservation in the dynamics is obtained which renders it equivalent to the voter model. For general $q$ value…
In this work we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular D-dimensional lattice has a probability $q$ to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability $1-q$ the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes nonequilibrium phase transitions at critic…
The q-voter model, a variant of the classic voter model, has been analyzed by several authors: while allowing to study opinion dynamics, this model is also believed to be one of the most representative among the many defined in the wide field of sociophysics. Here, we investigate the consequences of conformity on the consensus reaching process, by numerically simulating a q-voter model with agents behaving either as conformists or non-conformists, embedded on heterogeneous network topologies (as small-world and scale-free). In fact, although it is already known that conformity enhances the rea…
Polarization of societies is getting more and more attention from researchers working at the intersection of many fields, because it seems to be a defining feature of many public domains. In this paper, we are going to investigate how the unwillingness to yield to the group pressure, also known as independence, influences this phenomenon. In particular, we would like to answer the question whether independent choices of people could alter the dynamics of a system that otherwise would become polarized. A modified version of the $q$-voter model will be used for that purpose. From our findings it…
Biswas-Chatterjee-Sen (BChS) kinetic exchange opinion model on modular networks
School of Computational & Integrative Sciences, Jawaharlal Nehru University（计算与整合科学学院，贾瓦哈拉尔·尼赫鲁大学）；Department of Physics, SRM University - AP（物理系，SRM大学-安得拉邦分校）
In this work we study the majority-vote model with the presence of two distinc noises. The first one is the usual noise $q$, that represents the probability that a given agent follows the minority opinion of his/her social contacts. On the other hand, we consider the independent behavior, such that an agent can choose his/her own opinion $+1$ or $-1$ with equal probability, independent of the group's norm. We study the impact of the presence of such two kinds of stochastic driving in the phase transitions of the model, considering the mean field and the square lattice cases. Our results sugges…
