Dynamics Of Opinion Formation Research Articles

Polarization-induced stress in the noisy voter model

A new model for the dynamics of opinion formation is proposed and analysed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an intrinsic mechanism affected by the degree of polarization in the system. It also takes into account whether the agents enhance or reduce their intrinsic mechanism upon increasing polarization. Four phases or shapes of the steady-state probability of a fraction of agents in a given state are found (unimodal, bimodal, W and M). In the unimodal (resp. bimodal) phase, the copying (resp. intrinsic) mechanism is globally dominant, while in the W (resp. M) phase the copying (resp. intrinsic) mechanism is the relevant one close to the consensus states while it reduces its influence as approaching coexistence. In the thermodynamic limit, the bimodal and W phases disappear, while the unimodal and M phases prevail. The theoretical results, obtained analytically from the master equation, and the numerical simulations are in good agreement.

Discrete preference games with logic-based agents: Formal framework, complexity, and islands of tractability

Analyzing and predicting the dynamics of opinion formation in the context of social environments are problems that attracted much attention in literature. While grounded in social psychology, these problems are nowadays popular within the artificial intelligence community, where opinion dynamics are often studied via game-theoretic models in which individuals/agents hold opinions taken from a fixed set of discrete alternatives, and where the goal is to find those configurations where the opinions expressed by the agents emerge as a kind of compromise between their innate opinions and the social pressure they receive from the environments. As a matter of facts, however, these studies are based on very high-level and sometimes simplistic formalizations of the social environments, where the mental state of each individual is typically encoded as a variable taking values from a Boolean domain. To overcome these limitations, the paper proposes a framework generalizing such discrete preference games by modeling the reasoning capabilities of agents in terms of weighted propositional logics. It is shown that the framework easily encodes different kinds of earlier approaches and fits more expressive scenarios populated by conformist and dissenter agents. Problems related to the existence and computation of stable configurations are studied, under different theoretical assumptions on the structural shape of the social interactions and on the class of logic formulas that are allowed. Remarkably, during its trip to identify some relevant tractability islands, the paper devises a novel technical machinery whose significance goes beyond the specific application to analyzing opinion formation and diffusion, since it significantly enlarges the class of Integer Linear Programs that were known to be tractable so far.

Opinion Models, Election Data, and Political Theory.

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie-Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie-Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov-Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models.

Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

<abstract><p>In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.</p></abstract>

Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

<abstract><p>In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.</p></abstract>

Modelling opinion dynamics under the impact of influencer and media strategies

Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of “influencers” are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel framework for opinion dynamics that can accommodate various versions of opinion dynamics as well as account for different roles, namely that of individuals, media and influencers, who change their own opinion positions on different time scales. Numerical simulations of instances of this framework show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. The framework allows for mean-field approximations by partial differential equations, which reproduce those dynamics and allow for efficient large-scale simulations when the number of individuals is large. Based on the mean-field approximations, we can study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, our framework allows us to demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to a more flexible modelling approach in opinion dynamics and a better understanding of the different roles and strategies in the increasingly complex information ecosystem.

Conformity versus credibility: A coupled rumor-belief model

The opinion individuals hold about circulating information moderates their spreading behavior, as they may choose to spread rumors they believe in and remain silent about those they do not. Meanwhile, these opinions may be influenced by peers’ opinions and observed behaviors. We present coupled dynamics that integrate opinion formation and information spreading within two-layer multiplex social networks. In an influence layer, opinions are shaped by information credibility and social influence, the degree of which is determined by individual tendencies to conform. In a communication layer, information spreads conditioned on whether individuals believe in it. Using analytical and numerical tools, we demonstrate consistent behavior of the model by identifying the criteria for an evolutionary advantage in opinion formation and a critical spreading rate for rumor outbreaks. We then proceeded to examine two scenarios distinguished by considering credibility as either an intrinsic or a social property of information. Our results show that, for intrinsic credibility, higher degrees of conformity promote the spread of incredible information and inhibit the diffusion of credible information; for social credibility, higher degrees of conformity have an amplifying effect on the evolution of belief and rumor spreading. Additionally, the former scenario exhibits rich behaviors in the interplay between opinion evolution and information spreading, including paradigm shift, passive support, and fringe belief. We thus contribute to the understanding of the dynamics of opinion formation and information propagation in social groups. Empirical application may inform efforts to assess and combat the spread of misinformation.

Modeling opinion polarization on social media: Application to Covid-19 vaccination hesitancy in Italy.

The SARS-CoV-2 pandemic reminded us how vaccination can be a divisive topic on which the public conversation is permeated by misleading claims, and thoughts tend to polarize, especially on online social networks. In this work, motivated by recent natural language processing techniques to systematically extract and quantify opinions from text messages, we present a differential framework for bivariate opinion formation dynamics that is coupled with a compartmental model for fake news dissemination. Thanks to a mean-field analysis we demonstrate that the resulting Fokker-Planck system permits to reproduce bimodal distributions of opinions as observed in polarization dynamics. The model is then applied to sentiment analysis data from social media platforms in Italy, in order to analyze the evolution of opinions about Covid-19 vaccination. We show through numerical simulations that the model is capable to describe correctly the formation of the bimodal opinion structure observed in the vaccine-hesitant dataset, which is witness of the known polarization effects that happen within closed online communities.

Opinion Dynamics Explain Price Formation in Prediction Markets.

Prediction markets are heralded as powerful forecasting tools, but models that describe them often fail to capture the full complexity of the underlying mechanisms that drive price dynamics. To address this issue, we propose a model in which agents belong to a social network, have an opinion about the probability of a particular event to occur, and bet on the prediction market accordingly. Agents update their opinions about the event by interacting with their neighbours in the network, following the Deffuant model of opinion dynamics. Our results suggest that a simple market model that takes into account opinion formation dynamics is capable of replicating the empirical properties of historical prediction market time series, including volatility clustering and fat-tailed distribution of returns. Interestingly, the best results are obtained when there is the right level of variance in the opinions of agents. Moreover, this paper provides a new way to indirectly validate opinion dynamics models against real data by using historical data obtained from PredictIt, which is an exchange platform whose data have never been used before to validate models of opinion diffusion.

Will you infect me with your opinion?

Opinion formation is one of the most fascinating phenomena observed in human communities, and the ability to predict and to control the dynamics of this process is interesting from the theoretical as well as practical point of view. Although there are many sophisticated models of opinion formation, they often lack the connection with real life data, and there are still sociological processes that need to be explained. To address this, we propose a model describing the dynamics of opinion formation which mimics the process of the virus or disease spreading in the population. The introduced model is motivated by the model of disease spread with three possible channels — direct contact, indirect contact, and contact with “contaminated” elements. We demonstrate that the presence of “contaminated” elements, which in the case of on-line communities can be represented as the content published on the Internet, has considerable impact on the process of opinion formation. We argue that by using a simple mechanism of opinion spreading via passive elements, the introduced model captures the meaningful elements of opinion formation in complex communities. The presented work provides a step towards formulating universal laws governing social as well as physical or technical systems.

Coevolutionary Dynamics with Global Fields.

We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and adaptive rewiring on the space of parameters of the system. The model represents an adaptive society subject to global mass media such as a directed opinion influence or feedback of endogenous cultural trends. We show that, in both situations, global mass media contribute to consensus and to prevent the fragmentation of the social network induced by the coevolutionary dynamics. We present a discussion of these results in the context of dynamical systems and opinion formation dynamics.

A relative approach to opinion formation

ABSTRACT Formal models of opinion formation commonly represent an individual’s opinion by a value on a fixed opinion interval. We propose an alternative modeling method wherein interpretation is only provided to the relative positions of opinions vis-à-vis each other. This method is then considered in a similar setting as the discrete-time Altafini model (an extension of the well-known DeGroot model), but with more general influence weights. Even in a linear framework, the model can describe, in the long run, polarization, dynamics with a periodic pattern, and (modulus) consensus formation. In addition, in our alternative approach key characteristics of the opinion dynamic can be derived from real-valued square matrices of influence weights, which immediately allows one to transfer matrix theory insights to the field of opinion formation dynamics under more relaxed conditions than in the DeGroot or discrete-time Altafini models. A few specific themes are covered: (i) We demonstrate how stable patterns in relative opinion dynamics are identified which are hidden when opinions are considered in an absolute opinion framework. (ii) For the two-agent case, we provide an exhaustive closed-form description of the relative opinion model’s dynamic in the long run. (iii) We explore group dynamics analytically, in particular providing a non-trivial condition under which a subgroup’s asymptotic behavior carries over to the entire population.

Opinion dynamics: public and private.

We study here the dynamics of opinion formation in a society where we take into account the internally held beliefs and externally expressed opinions of the individuals, which are not necessarily the same at all times. While these two components can influence one another, their difference, both in dynamics and in the steady state, poses interesting scenarios in terms of the transition to consensus in the society and characterizations of such consensus. Here we study this public and private opinion dynamics and the critical behaviour of the consensus forming transitions, using a kinetic exchange model. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

On a kinetic opinion formation model for pre-election polling.

Motivated by recent successes in model-based pre-election polling, we propose a kinetic model for opinion formation which includes voter demographics and socio-economic factors like age, sex, ethnicity, education level, income and other measurable factors like behaviour in previous elections or referenda as a key driver in the opinion formation dynamics. The model is based on Toscani's kinetic opinion formation model (Toscani G. 2006 Kinetic models of opinion formation. Commun. Math. Sci. 4, 481-496.) and the leader-follower model of Düring et al. (Düring B. et al. 2009 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. A 465, 3687-3708.), and leads to a system of coupled Boltzmann-type equations and associated, approximate Fokker-Planck-type systems. Numerical examples using data from general elections in the UK show the effect different demographics have on the opinion formation process and the outcome of elections. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Modelling how social network algorithms can influence opinion polarization

The study of the dynamics of opinion formation and transmission in social networks has attracted lots of attention. Here, we propose a model that simulates communication in an online social network, in which randomly created posts represent external information. We consider users and friendship relations to be encoded as nodes and edges of a network. The dynamic of information diffusion is divided into two processes, referred to as post transmission and post distribution, representing the users’ behavior and the social network algorithm, respectively. Individuals also interact with the post content by slightly adjusting their own opinion and sometimes redefining friendships. Our results show that the dynamic converge to various scenarios, which go from consensus formation to polarization. Importantly, friendship rewiring helps promote echo chamber formation, which can also arise for particular networks with well-defined community structures. Altogether, our results indicate that the social network algorithm is crucial to mitigate or promote polarization.

Opinion formation dynamics — Swift collective disillusionment triggered by unmet expectations

We propose a microscopic model to describe how individual opinions shared between interacting agents initiate excessive collective expectations about a new idea or an innovation, followed by a swift collapse towards a dramatic collective disillusionment. The basic assumption which underlies the dynamics is that the information gathering process is not instantaneous but requires maturation. Agents steadily refine and update their personal opinion via a recurrent consultation of a public pool which stores information tokens (ITs). The expectation for the innovative idea is monitored in real-time by counting the number of stored ITs. The flow dynamics of ITs is assimilated to a single node queuing system (QS) with feedback loop. It incorporates the information pool (the waiting room), an IT inflow, and a service outflow that stylizes the information gathering process. Contrary to basic queuing theory, here the ITs roaming the QS are endowed with time-dependent internal variables. This additional dynamic information is used to construct the information maturation process. Such a maturation of the information introduces response delays into the dynamics, which ultimately generates the collective disillusionment trough. We illustrate the introduced generic modeling framework by considering in details the hype cycle dynamics, a key managerial topic when dealing with diffusion of innovation. In a second part of the paper, we introduce a stylized framework to detect, as soon as possible, the onset of the collective disillusionment phase, while minimizing the frequency of false alarms.

Majority-vote model with limited visibility: An investigation into filter bubbles

The dynamics of opinion formation in a society is a complex phenomenon where many variables play essential roles. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model, an individual adopts an opinion contrary to the majority of its neighbors with probability q, defined as the noise parameter. Here, we introduce a visibility parameter V in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For V=0.5 each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility qc(V) and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of V favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.

Supporting Policy Design for the Diffusion of Cleaner Technologies: A Spatial Empirical Agent-Based Model

Renewable energy resources and energy-efficient technologies, as well as building retrofitting, are only some of the possible strategies that can achieve more sustainable cities and reduce greenhouse gas emissions. Subsidies and incentives are often provided by governments to increase the number of people adopting these sustainable energy efficiency actions. However, actual sales of green products are currently not as high as would be desired. The present paper applies a hybrid agent-based model (ABM) integrated with a Geographic Information System (GIS) to simulate a complex socio-economic-architectural adaptive system to study the temporal diffusion and the willingness of inhabitants to adopt photovoltaic (PV) systems. The San Salvario neighborhood in Turin (Italy) is used as an exemplary case study for testing consumer behavior associated with this technology, integrating social network theories, opinion formation dynamics and an adaptation of the theory of planned behavior (TPB). Data/characteristics for both buildings and people are explicitly spatialized with the level of detail at the block scale. Particular attention is given to the comparison of the policy mix for supporting decision-makers and policymakers in the definition of the most efficient strategies for achieving a long-term vision of sustainable development. Both variables and outcomes accuracy of the model are validated with historical real-world data.

Collective effects of the cost of opinion change

We study the dynamics of opinion formation in the situation where changing opinion involves a cost for the agents. To do so we couple the dynamics of a heterogeneous bounded confidence Hegselmann–Krause model with that of the resources that the agents invest on each opinion change. The outcomes of the dynamics are non-trivial and strongly depend on the different regions of the confidence parameter space. In particular, a second order phase transition, for which we determine the corresponding critical exponents, is found in the region where a re-entrant consensus phase is observed in the heterogeneous Hegselmann–Krause model. For regions where consensus always exist in the heterogeneous Hegselmann–Krause model, the introduction of cost does not lead to a phase transition but just to a continuous decrease of the size of the largest opinion cluster. Finally in the region where fragmentation is expected in the heterogeneous HK model, the introduction of a very small cost surprisingly increases the size of the largest opinion cluster.

Polarizing crowds: Consensus and bipolarization in a persuasive arguments model.

Understanding the opinion formation dynamics in social systems is of vast relevance in diverse aspects of society. In particular, it is relevant for political deliberation and other group decision-making processes. Although previous research has reported different approaches to model social dynamics, most of them focused on interaction mechanisms where individuals modify their opinions in line with the opinions of others, without invoking a latent mechanism of argumentation. In this paper, we present a model where changes of opinion are due to explicit exchanges of arguments, and we analyze the emerging collective states in terms of simple dynamic rules. We find that, when interactions are equiprobable and symmetrical, the model only shows consensus solutions. However, when either homophily, confirmation bias, or both are included, we observe the emergence and dominance of bipolarization, which appears due to the fact that individuals are not able to accept the contrary information from their opponents during exchanges of arguments. In all cases, the predominance of each stable state depends on the relation between the number of agents and the number of available arguments in the discussion. Overall, this paper describes the dynamics and shows the conditions wherein deliberative agents are expected to construct polarized societies.