Building up of individual inflexibility in opinion dynamics

Spontaneous opinion swings in the voter model with latency

The cognitive process of opinion formation is often characterized by stubbornness or resistance of agents to changes of opinion. To capture this feature we introduce a constant latency time in the standard voter model of opinion dynamics: after switching opinion, an agent must keep it for a while. This seemingly simple modification drastically changes the stochastic diffusive behavior of the original model, leading to deterministic dynamical oscillations in the average opinion of the agents. We explain the origin of the oscillations and develop a mathematical formulation of the dynamics that is confirmed by extensive numerical simulations. We further characterize the rich phase space of the model and its asymptotic behavior. Our work offers insights into understanding and modeling the phenomenon of opinion swings, often observed in diverse social contexts.

Opinion inertia and coarsening in the persistent voter model

We consider the persistent voter model (PVM), a variant of the voter model (VM) that includes transient, dynamically induced zealots. Due to peer reinforcement, the internal confidence η_{i} of a normal voter increases in steps of size Δη. Once it surpasses a given threshold, it becomes a zealot. Its opinion remains frozen until enough interactions with the opposing opinion occur, resetting its confidence. No longer a zealot, the regular voter may change opinion once again. This mechanism of opinion inertia, though simplified, is responsible for an effective surface tension, and the PVM exhibits a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, akin to the Ising model at low temperature. The average time τ to attain consensus is nonmonotonic with respect to Δη and reaches a minimum at Δη_{min}. In this paper we elucidate the mechanisms that accelerate the system towards consensus close to Δη_{min}. Near the crossover at Δη_{min}, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large. The surface tension, albeit small, is sufficient to maintain the shape and reduce the domain fragmentation. The large size of the AR in the region of Δη_{min} has two important effects that accelerate the dynamics. First, it dislodges the zealots within the bulk of the domains. Secondly, it maximally suppresses the formation of slowly evolving stripes typical in Ising-like models. This suggests the importance of understanding the role of the AR, where opinion changes are facilitated, and the interplay between regular voters and zealots in disrupting polarized states.

Critical exponents of master-node network model

The dynamics of competing opinions in social network plays an important role in society, with many applications in diverse social contexts such as consensus, election, morality, and so on. Here, we study a model of interacting agents connected in networks in order to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with the shape of ring topology. Moreover, some agents are also connected to a hub, or master node, who has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous nonequilibrium phase transition to an absorbing state as a function of control parameters. By using the finite-size scaling method we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known.

Asynchrony rescues statistically optimal group decisions from information cascades through emergent leaders

It is usually assumed that information cascades are most likely to occur when an early but incorrect opinion spreads through the group. Here, we analyse models of confidence-sharing in groups and reveal the opposite result: simple but plausible models of naive-Bayesian decision-making exhibit information cascades when group decisions are synchronous; however, when group decisions are asynchronous, the early decisions reached by Bayesian decision-makers tend to be correct and dominate the group consensus dynamics. Thus early decisions actually rescue the group from making errors, rather than contribute to it. We explore the likely realism of our assumed decision-making rule with reference to the evolution of mechanisms for aggregating social information, and known psychological and neuroscientific mechanisms.

Curvature-driven growth and interfacial noise in the voter model with self-induced zealots

We introduce a variant of the voter model in which agents may have different degrees of confidence in their opinions. Those with low confidence are normal voters whose state can change upon a single contact with a different neighboring opinion. However, confidence increases with opinion reinforcement, and above a certain threshold, these agents become zealots, irreducible agents who do not change their opinion. We show that both strategies, normal voters and zealots, may coexist (in the thermodynamical limit), leading to competition between two different kinetic mechanisms: curvature-driven growth and interfacial noise. The kinetically constrained zealots are formed well inside the clusters, away from the different opinions at the surfaces that help limit their confidence. Normal voters concentrate in a region around the interfaces, and their number, which is related to the distance between the surface and the zealotry bulk, depends on the rate at which the confidence changes. Despite this interface being rough and fragmented, typical of the voter model, the presence of zealots in the bulk of these domains induces a curvature-driven dynamics, similar to the low temperature coarsening behavior of the nonconserved Ising model after a temperature quench.

Depolarization of echo chambers by random dynamical nudge

In social networks, users often engage with like-minded peers. This selective exposure to opinions might result in echo chambers, i.e., political fragmentation and social polarization of user interactions. When echo chambers form, opinions have a bimodal distribution with two peaks on opposite sides. In certain issues, where either extreme positions contain a degree of misinformation, neutral consensus is preferable for promoting discourse. In this paper, we use an opinion dynamics model that naturally forms echo chambers in order to find a feedback mechanism that bridges these communities and leads to a neutral consensus. We introduce the random dynamical nudge (RDN), which presents each agent with input from a random selection of other agents’ opinions and does not require surveillance of every person’s opinions. Our computational results in two different models suggest that the RDN leads to a unimodal distribution of opinions centered around the neutral consensus. Furthermore, the RDN is effective both for preventing the formation of echo chambers and also for depolarizing existing echo chambers. Due to the simple and robust nature of the RDN, social media networks might be able to implement a version of this self-feedback mechanism, when appropriate, to prevent the segregation of online communities on complex social issues.

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'.

Radicalism: The asymmetric stances of radicals versus conventionals

We study the conditions of propagation of an initial emergent practice qualified as extremist within a population adept at a practice perceived as moderate, whether political, societal, or religious. The extremist practice is carried by an initial ultraminority of radicals (R) dispersed among conventionals (C) who are the overwhelming majority in the community. Both R and C are followers, that is, agents who, while having arguments to legitimize their current practice, are likely to switch to the other practice if given more arguments during a debate. The issue being controversial, most C tend to avoid social confrontation with R about it. They maintain a neutral indifference, assuming it is none of their business. On the contrary, R aim to convince C through an expansion strategy to spread their practice as part of a collective agenda. However, aware of being followers, they implement an appropriate strategy to maximize their expansion and determine when to force a debate with C. The effect of this asymmetry between initiating or avoiding an update debate among followers is calculated using a weighted version of the Galam model of opinion dynamics. An underlying complex landscape is obtained as a function of the respective probabilities to engage in a local discussion by R and C. It discloses zones where R inexorably expand and zones where they get extinct. The results highlight the instrumental character of the above asymmetry in providing a decisive advantage to R against C. It also points to a barrier in R initial support to reach the extension zone. In parallel, the landscape reveals a path for C to counter R expansion, pushing them back into their extinction zone. It relies on the asymmetry of C being initially a large majority which puts the required involvement of C at a rather low level.

Opinion Evolution in Divided Community

Our agent-based model of opinion dynamics concerns the current vast divisions in modern societies. It examines the process of social polarization, understood here as the partition of a community into two opposing groups with contradictory opinions. Our goal is to measure how mutual animosities between parties may lead to their radicalization. We apply a double-clique topology with both positive and negative ties to the model of binary opinions. Individuals are subject to social pressure; they conform to the opinions of their own clique (positive links) and oppose those from the other one (negative links). There is also a chance of acting independently, which alters the system’s behavior in various ways, depending on its magnitude. The results, obtained with both Monte-Carlo simulations and the mean-field approach, lead to two main conclusions: in such a system, there exists a critical quantity of negative relations that are needed for polarization to occur, and (rather surprisingly) independent actions actually support the process, unless their frequency is too high, in which case the system falls into total disorder.

Towards a Bibliometric Mapping of Network Public Opinion Studies

To grasp the current status of network public opinion (NPO) research and explore the knowledge base and hot trends from a quantitative perspective, we retrieved 1385 related papers and conducted a bibliometric mapping analysis on them. Co-occurrence analysis, cluster analysis, co-citation analysis and keyword burst analysis were performed using VOSviewer and CiteSpace software. The results show that the NPO is mainly distributed in the disciplinary fields associated with journalism and communication and public management. There are four main hotspots: analysis of public opinion, analysis of communication channels, technical means and challenges faced. The knowledge base in the field of NPO research includes social media, user influence, and user influence related to opinion dynamic modeling and sentiment analysis. With the advent of the era of big data, big data technology has been widely used in various fields and to some extent can be said to be the research frontier in the field. Transforming big data public opinion into early warning, realizing in-depth analysis and accurate prediction of public opinion as well as improving decision-making ability of public opinion are the future research directions of NPO.

Zealots in multistate noisy voter models

The noisy voter model is a stylized representation of opinion dynamics. Individuals copy opinions from other individuals, and are subject to spontaneous state changes. In the case of two opinion states this model is known to have a noise-driven transition between a unimodal phase, in which both opinions are present, and a bimodal phase, in which one of the opinions dominates. The presence of zealots can remove the unimodal and bimodal phases in the model with two opinion states. Here we study the effects of zealots in noisy voter models with M>2 opinion states on complete interaction graphs. We find that the phase behavior diversifies, with up to six possible qualitatively different types of stationary states. The presence of zealots removes some of these phases, but not all. We analyze situations in which zealots affect the entire population, or only a fraction of agents, and show that this situation corresponds to a single-community model with a fractional number of zealots, further enriching the phase diagram. Our study is conducted analytically based on effective birth-death dynamics for the number of individuals holding a given opinion. Results are confirmed in numerical simulations.

Bias in social interactions and emergence of extremism in complex social networks

Emergence of extremism in social networks is among the most appealing topics of opinion dynamics in computational sociophysics in recent decades. Most of the existing studies presume that the initial existence of certain groups of opinion extremities and the intrinsic stubbornness in individuals' characteristics are the key factors allowing the tenacity or even prevalence of such extreme opinions. We propose a modification to the consensus making in bounded-confidence models where two interacting individuals holding not so different opinions tend to reach a consensus by adopting an intermediate opinion of their previous ones. We show that if individuals make biased compromises, extremism may still arise without a need of an explicit classification of extremists and their associated characteristics. With such biased consensus making, several clusters of diversified opinions are gradually formed up in a general trend of shifting toward the extreme opinions close to the two ends of the opinion range, which may allow extremism communities to emerge and moderate views to be dwindled. Furthermore, we assume stronger compromise bias near opinion extremes. It is found that such a case allows moderate opinions a greater chance to survive compared to that of the case where the bias extent is universal across the opinion space. As to the extreme opinion holders' lower tolerances toward different opinions, which arguably may exist in many real-life social systems, they significantly decrease the size of extreme opinion communities rather than helping them to prevail. Brief discussions are presented on the significance and implications of these observations in real-life social systems.

Analysis of Flood Evacuation Process in Vulnerable Community with Mutual Aid Mechanism: An Agent-Based Simulation Framework

Timely and secure evacuation of residents during flood disasters or other emergency events is an important issue in urban community flood risk management, especially in vulnerable communities. An agent-based modeling framework was proposed in order to indicate how the community properties (e.g., community density and percentage of vulnerable residents), residents’ psychological attributes (e.g., flood risk tolerance threshold) and mutual aid mechanism affect the flood evacuation process. Results indicated that: (1) The community density negatively affected the flood evacuation efficiency. The greater the density of the community, the longer the evacuation time. (2) There was a negative correlation between the flood risk tolerance threshold of residents and evacuation efficiency. (3) The proportion of vulnerable resident agents had opposite effects on the evacuation efficiency of different types of communities, which was to negatively affect low-density communities and positively affect high-density communities. (4) Mutual aid mechanism can reduce evacuation time in low-density communities, and the effect was more pronounced with a higher proportion of vulnerable resident agents in the community. These findings can help managers to develop better emergency evacuation management for urban communities.

Think then act or act then think?

We introduce a new agent-based model of opinion dynamics in which binary opinions of each agent can be measured and described regarding both pre- and post-influence at both of two levels, public and private, vis-à-vis the influence source. The model combines ideas introduced within the q-voter model with noise, proposed by physicists, with the descriptive, four-dimensional model of social response, formulated by social psychologists. We investigate two versions of the same model that differ only by the updating order: an opinion on the public level is updated before an opinion on the private level or vice versa. We show how the results on the macroscopic scale depend on this order. The main finding of this paper is that both models produce the same outcome if one looks only at such a macroscopic variable as the total number of the individuals with positive opinions. However, if also the level of internal harmony (viz., dissonance) is measured, then significant, qualitative differences are seen between these two versions of the model. All results were obtained simultaneously within Monte Carlo simulations and analytical calculations. We discuss the importance of our studies and findings from three points of view: the theory of phase transitions, agent-based modeling of social systems, and social psychology.

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction ("telephoning"), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations.

Analysis and application of opinion model with multiple topic interactions

To reveal heterogeneous behaviors of opinion evolution in different scenarios, we propose an opinion model with topic interactions. Individual opinions and topic features are represented by a multidimensional vector. We measure an agent's action towards a specific topic by the product of opinion and topic feature. When pairs of agents interact for a topic, their actions are introduced to opinion updates with bounded confidence. Simulation results show that a transition from a disordered state to a consensus state occurs at a critical point of the tolerance threshold, which depends on the opinion dimension. The critical point increases as the dimension of opinions increases. Multiple topics promote opinion interactions and lead to the formation of macroscopic opinion clusters. In addition, more topics accelerate the evolutionary process and weaken the effect of network topology. We use two sets of large-scale real data to evaluate the model, and the results prove its effectiveness in characterizing a real evolutionary process. Our model achieves high performance in individual action prediction and even outperforms state-of-the-art methods. Meanwhile, our model has much smaller computational complexity. This paper provides a demonstration for possible practical applications of theoretical opinion dynamics.

Consensus in averager-copier-voter networks of moving dynamical agents

This paper deals with a hybrid opinion dynamics comprising averager, copier, and voter agents, which ramble as random walkers on a spatial network. Agents exchange information following some deterministic and stochastic protocols if they reside at the same site in the same time. Based on stochastic stability of Markov chains, sufficient conditions guaranteeing consensus in the sense of almost sure convergence have been obtained. The ultimate consensus state is identified in the form of an ergodicity result. Simulation studies are performed to validate the effectiveness and availability of our theoretical results. The existence/non-existence of voters and the proportion of them are unveiled to play key roles during the consensus-reaching process.

Competing opinions and stubborness: Connecting models to data

We introduce a general contagionlike model for competing opinions that includes dynamic resistance to alternative opinions. We show that this model can describe candidate vote distributions, spatial vote correlations, and a slow approach to opinion consensus with sensible parameter values. These empirical properties of large group dynamics, previously understood using distinct models, may be different aspects of human behavior that can be captured by a more unified model, such as the one introduced in this paper.

Inflexibility and independence: Phase transitions in the majority-rule model

In this work we study opinion formation in a population participating in a public debate with two distinct choices. We consider three distinct mechanisms of social interactions and individuals' behavior: conformity, nonconformity, and inflexibility. The conformity is ruled by the majority-rule dynamics, whereas the nonconformity is introduced in the population as an independent behavior, implying the failure of attempted group influence. Finally, the inflexible agents are introduced in the population with a given density. These individuals present a singular behavior, in a way that their stubbornness makes them reluctant to change their opinions. We consider these effects separately and all together, with the aim to analyze the critical behavior of the system. We perform numerical simulations in some lattice structures and for distinct population sizes. Our results suggest that the different formulations of the model undergo order-disorder phase transitions in the same universality class as the Ising model. Some of our results are complemented by analytical calculations.

Kinetic models of opinion formation in the presence of personal conviction

We consider a nonlinear kinetic equation of Boltzmann type, which takes into account the influence of conviction during the formation of opinion in a system of agents, which interact through the binary exchanges, introduced by Toscani [G. Toscani, Commun. Math. Sci. 4, 481 (2006)]. The original exchange mechanism, which is based on the human tendency to compromise and change of opinion through self-thinking, is here modified in the parameters of the compromise and diffusion terms, which now are assumed to depend on the personal degree of conviction. The numerical simulations show that the presence of conviction has the potential to break symmetry, and to produce clusters of opinions. The model is partially inspired by the recent work [L. Pareschi and G. Toscani, Phil. Trans. R. Soc. A 372, 20130396 (2014)], in which the role of knowledge in the formation of wealth distribution has been investigated.

Opinion formation on social media: an empirical approach

Opinion exchange models aim to describe the process of public opinion formation, seeking to uncover the intrinsic mechanism in social systems; however, the model results are seldom empirically justified using large-scale actual data. Online social media provide an abundance of data on opinion interaction, but the question of whether opinion models are suitable for characterizing opinion formation on social media still requires exploration. We collect a large amount of user interaction information from an actual social network, i.e., Twitter, and analyze the dynamic sentiments of users about different topics to investigate realistic opinion evolution. We find two nontrivial results from these data. First, public opinion often evolves to an ordered state in which one opinion predominates, but not to complete consensus. Second, agents are reluctant to change their opinions, and the distribution of the number of individual opinion changes follows a power law. Then, we suggest a model in which agents take external actions to express their internal opinions according to their activity. Conversely, individual actions can influence the activity and opinions of neighbors. The probability that an agent changes its opinion depends nonlinearly on the fraction of opponents who have taken an action. Simulation results show user action patterns and the evolution of public opinion in the model coincide with the empirical data. For different nonlinear parameters, the system may approach different regimes. A large decay in individual activity slows down the dynamics, but causes more ordering in the system.

Impact of contrarians and intransigents in a kinetic model of opinion dynamics

In this work we study opinion formation on a fully connected population participating of a public debate with two distinct choices, where the agents may adopt three different attitudes (favorable to either one choice or to the other, or undecided). The interactions between agents occur by pairs and are competitive, with couplings that are either negative with probability p or positive with probability 1-p. This bimodal probability distribution of couplings produces a behavior similar to the one resulting from the introduction of Galam's contrarians in the population. In addition, we consider that a fraction d of the individuals are intransigent, that is, reluctant to change their opinions. The consequences of the presence of contrarians and intransigents are studied by means of computer simulations. Our results suggest that the presence of inflexible agents affects the critical behavior of the system, causing either the shift of the critical point or the suppression of the ordering phase transition, depending on the groups of opinions to which the intransigents belong. We also discuss the relevance of the model for real social systems.

Social influence and the collective dynamics of opinion formation

Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing how participants answering factual questions revise their initial judgments after being exposed to the opinion and confidence level of others. Based on the observation of 59 experimental subjects exposed to peer-opinion for 15 different items, we draw an influence map that describes the strength of peer influence during interactions. A simple process model derived from our observations demonstrates how opinions in a group of interacting people can converge or split over repeated interactions. In particular, we identify two major attractors of opinion: (i) the expert effect, induced by the presence of a highly confident individual in the group, and (ii) the majority effect, caused by the presence of a critical mass of laypeople sharing similar opinions. Additional simulations reveal the existence of a tipping point at which one attractor will dominate over the other, driving collective opinion in a given direction. These findings have implications for understanding the mechanisms of public opinion formation and managing conflicting situations in which self-confident and better informed minorities challenge the views of a large uninformed majority.