Model Of Opinion Formation Research Articles

Opinion Formation with Imperfect Agents as an Evolutionary Process

We develop and simulate an interaction-based model of continuous opinion formation under bounded confidence to identify conditions and understand circumstances that lead a society into either a consensus, multiple opinion classes or perpetual opinion dynamics. The society is modeled as a social network and random meetings are presumed. When only regular agents are present, we have shown that the small world networks may bring the society very close to consensus for even small threshold levels, but require higher tolerance than the complete network to reach consensus. We have identified the conditions under which the process with stubborn agents generates long-run consensus, permanent disagreement or permanent fluctuation in opinions. There cannot be a persistent fluctuation in opinions in the environment of regular agents nor in the presence of a single group of stubborn agents. In the runs with a single group of stubborn extremists, we have identified the Popper paradox despite the existence of a tolerance span in which the proportion of extremism decreases as the tolerance level increases. Further, in a highly tolerant society with two competing extremist groups, they have no supporters among the regular agents whose opinions are oscillating around the center of the opinion space. The influence of inconsistent agents is persistent and induces a perpetual opinion dynamics. The model is non-equilibrium and emerging, while consensus, if attainable, can be reached in a finite time.

Differential inequalities in multi-agent coordination and opinion dynamics modeling

Many distributed algorithms for multi-agent coordination employ the simple averaging dynamics, referred to as the Laplacian flow. Besides the standard consensus protocols, examples include, but are not limited to, algorithms for aggregation and containment control, target surrounding, distributed optimization and models of opinion formation in social groups. In spite of their similarities, each of these algorithms has been studied using separate mathematical techniques. In this paper, we show that stability and convergence of many coordination algorithms involving the Laplacian flow dynamics follow from the general consensus dichotomy property of a special differential inequality. The consensus dichotomy implies that any solution to the differential inequality is either unbounded or converges to a consensus equilibrium. In this paper, we establish the dichotomy criteria for differential inequalities and illustrate their applications to multi-agent coordination and opinion dynamics modeling.

Sparse Jurdjevic–Quinn stabilization of dissipative systems

For control-affine systems with a proper Lyapunov function, the classical Jurdjevic–Quinn procedure (see Jurdjevic and Quinn, 1978) gives a well-known and widely used method for the design of feedback controls that asymptotically stabilize the system to some invariant set. In this procedure, all controls are in general required to be activated, i.e. nonzero, at the same time.In this paper we give sufficient conditions under which this stabilization can be achieved by means of sparse feedback controls, i.e., feedback controls having the smallest possible number of nonzero components. We thus obtain a sparse version of the classical Jurdjevic–Quinn theorem.We propose three different explicit stabilizing control strategies, depending on the method used to handle possible discontinuities arising from the definition of the feedback: a time-varying periodic feedback, a sampled feedback, and a hybrid hysteresis. We illustrate our results by applying them to opinion formation models, thus recovering and generalizing former results for such models.

Measuring and moderating opinion polarization in social networks

The polarization of society over controversial social issues has been the subject of study in social sciences for decades (Isenberg in J Personal Soc Psychol 50(6):1141–1151, 1986, Sunstein in J Polit Philos 10(2):175–195, 2002). The widespread usage of online social networks and social media, and the tendency of people to connect and interact with like-minded individuals has only intensified the phenomenon of polarization (Bakshy et al. in Science 348(6239):1130–1132, 2015). In this paper, we consider the problem of measuring and reducing polarization of opinions in a social network. Using a standard opinion formation model (Friedkin and Johnsen in J Math Soc 15(3–4):193–206, 1990), we define the polarization index, which, given a network and the opinions of the individuals in the network, it quantifies the polarization observed in the network. Our measure captures the tendency of opinions to concentrate in network communities, creating echo-chambers. Given this numeric measure of polarization, we then consider the problem of reducing polarization in the network by convincing individuals (e.g., through education, exposure to diverse viewpoints, or incentives) to adopt a more neutral stand towards controversial issues. We formally define the ModerateInternal and ModerateExpressed problems, and we prove that both our problems are NP-hard. By exploiting the linear-algebraic characteristics of the opinion formation model we design polynomial-time algorithms for both problems. Our experiments with real-world datasets demonstrate the validity of our metric, and the efficiency and the effectiveness of our algorithms in practice.

Dynamical properties of the herding voter model with and without noise.

Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion formation model, we show that, in the herding phase, a group of agents become effectively the leaders of the dynamics while the rest of the population follow blindly their opinion. Interestingly, in some cases such herding dynamics accelerates the time to consensus, which then becomes size independent or, on the contrary, makes the consensus nearly impossible. These behaviors have important consequences when an external noise is added to the system that makes consensus (absorbing) states to disappear. We analyze this model, which shows an interesting phase diagram, with a purely diffusive phase, a herding (or two-states) phase, and mixed phases where both behaviors are possible.

Opinion evolution in time-varying social influence networks with prejudiced agents

Investigation of social influence dynamics requires mathematical models that are “simple” enough to admit rigorous analysis, and yet sufficiently “rich” to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals’ ongoing attachments to their initial opinions, or prejudices. The “anchorage” of individuals to their prejudices may disable reaching consensus and cause disagreement in a social influence network. Further elaboration of this model may be achieved by relaxing its restrictive assumption of a time-invariant influence network. During opinion dynamics on an issue, arcs of interpersonal influence may be added or subtracted from the network, and the influence weights assigned by an individual to his/her neighbors may alter. In this paper, we establish new important properties of the (Friedkin and Johnsen, 1999) opinion formation model, and also examine its extension to time-varying social influence networks.

Simulation study on opinion formation models of heterogeneous agents based on game theory and complex networks

This study investigates a new opinion formation model of heterogeneous agents, a network stubborn individuals and orators (NSO) model based on game theory and complex social networks. Game theory solves economists’ rational choice-making problems, and complex social networks reflect the social impact on opinion evolution. The NSO model involves both social and individual heterogeneous characteristics. In a society, the more unequal the members, and the closer the social distances, the faster opinions spread. In the real world, the power-law degree distribution and the short paths in social networks can generate the rapid spread of an opinion. This study also investigates opinion control under the NSO model. The results show that opinion guidance is most likely to separate the public into different groups rather than converge to the guide’s opinion.

Interacting opinion and disease dynamics in multiplex networks: Discontinuous phase transition and nonmonotonic consensus times.

Opinion formation and disease spreading are among the most studied dynamical processes on complex networks. In real societies, it is expected that these two processes depend on and affect each other. However, little is known about the effects of opinion dynamics over disease dynamics and vice versa, since most studies treat them separately. In this work we study the dynamics of the voter model for opinion formation intertwined with that of the contact process for disease spreading, in a population of agents that interact via two types of connections, social and contact. These two interacting dynamics take place on two layers of networks, coupled through a fraction of links present in both networks. The probability that an agent updates its state depends on both the opinion and disease states of the interacting partner. We find that the opinion dynamics has striking consequences on the statistical properties of disease spreading. The most important is that the smooth (continuous) transition from a healthy to an endemic phase observed in the contact process, as the infection probability increases beyond a threshold, becomes abrupt (discontinuous) in the two-layer system. Therefore, disregarding the effects of social dynamics on epidemics propagation may lead to a misestimation of the real magnitude of the spreading. Also, an endemic-healthy discontinuous transition is found when the coupling overcomes a threshold value. Furthermore, we show that the disease dynamics delays the opinion consensus, leading to a consensus time that varies nonmonotonically with in a large range of the model's parameters. A mean-field approach reveals that the coupled dynamics of opinions and disease can be approximately described by the dynamics of the voter model decoupled from that of the contact process, with effective probabilities of opinion and disease transmission.

Personal Experience and Public Opinion: A Theory and Test of Conditional Policy Feedback

Using a regression discontinuity design, we show that personal experience with public health insurance programs exerts a causal influence on attitudes toward both Medicare and the Affordable Care Act. However, we argue that the conditional dynamics of these policy feedback effects differ from standard models of opinion formation and change. Specifically, we find that personal experience can shape preferences among those whose partisanship might otherwise make them resistant to elite messaging; in the case of support for health policy, we find effects of public programs are most pronounced among Republicans. In addition, we find that the effects of personal experience, unlike attempts to shape attitudes through elite political messaging, are concentrated among low-information voters who might otherwise not be attuned to the political environment.

Modeling opinion dynamics: Theoretical analysis and continuous approximation

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion and the agreement is reached because the new arguments are incorporated. Given the wide range of opinion formation mathematical approaches, there are however no models of opinion dynamics with nonlocal pair interactions analytically solvable. In this paper we present a novel analytical framework developed to solve the master equations with non-local kernels. For this we used a simple model of opinion formation where individuals tend to get more similar after each interactions, no matter their opinion differences, giving rise to nonlinear differential master equation with non-local terms. Simulation results show an excellent agreement with results obtained by the theoretical estimation.

Consensus formation simulation in a social network modeling controversial opinion dynamics with pairwise interactions

In this work, we consider a system of coupled finite-difference equations which incorporates a variety of opinion formation models, and use it to describe the dynamics of opinions on controversial subjects. The social network consists of a finite number of agents with pairwise interactions at discrete times. Meanwhile, the opinion of each agent is updated following a general nonlinear law which considers parameters identified as the personal constants of each of the members. We establish conditions that guarantee the existence of global attracting points (strong consensus) and intervals (weak consensus). Moreover, we note that these conditions are independent of the weight matrix and the number of agents of the network. Two particular scenarios are investigated numerically in order to confirm the validity of the analytical results.

Political awareness and support for redistribution

Traditional research on preferences for redistributive social policy suggest increasingly complex models of public opinion formation that envision individuals balancing normative concerns against sophisticated calculations of economic self-interest. This research largely ignores the large body of evidence demonstrating significant differences in levels of political awareness across the population that strongly influence the quality, structure, and determinants of political preferences. Analyzing public opinion data for 14 European countries reveals that large sections of the population do not appear to hold or express social policy preferences that are internally consistent or well-grounded in either their self-interests or ideological predispositions. At low levels of political awareness, little discernible connection exists between seemingly related preferences for redistribution, levels of social spending, left–right positioning, tolerance for inequality, or overall support for the welfare state. Moreover, income, a theoretically central causal variable, has no effect on attitudes toward redistribution when political awareness is low. These results pose a significant challenge to existing models of social policy preferences.

How, when and where can Spatial Segregation Induce Opinion Polarization? Two Competing Models

Increasing ethnic diversity fosters scholarly interest in how the spatial segregation of groups affects opinion polarization in a society. Despite much empirical and theoretical research, there is little consensus in the literature on the causal link between the spatial segregation of two groups and the emergence of opinion polarization. We contribute to the debate by investigating theoretically the conditions under which the former fosters or hinders the latter. We focus on two processes of opinion polarization (negative influence and persuasive argument communication) that, according to previous modeling work, can be expected to make conflicting predictions about the relationship between segregation and opinion polarization. With a Schelling-type agent-based model of residential segregation, we generate initial environments with different levels of group segregation. Then we simulate the two processes of opinion dynamics. We show that the negative influence model predicts segregation to hinder the emergence of opinion polarization. On the other hand, the persuasive argument model predicts that segregation does not substantially foster polarization. Moreover, we explore how the spatial patterns of opinion distribution differ between the models: in particular, we investigate the likelihood that group membership and opinion align. We show that the alignment of group membership and opinions differs between the two opinion formation models, and that the scale at which we measure alignment plays a crucial role.

Lending Sociodynamics and Drivers of the Financial Business Cycle

We extend sociodynamic modeling of the financial business cycle to the Euro Area andJapan. Using an opinion-formation model and machine learning techniques we find stable modelestimation of the financial business cycle using central bank lending surveys and a few selectedmacroeconomic variables. We find that banks have asymmetric response to good and bad economicinformation, and that banks adapt to their peers’ opinions when changing lending policies.

Modelling heterogeneity and an open-mindedness social norm in opinion dynamics

We study heterogeneous interactions in a time-continuous bounded confidence model for opinion formation. The key new modelling aspects are to distinguish between open-minded and closed-minded behaviour and to include an open-mindedness social norm. The investigations focus on the equilibria supported by the proposed new model; particular attention is given to a novel class of equilibria consisting of multiple connected opinion clusters, which does not occur in the absence of heterogeneity. Various rigorous stability results concerning these equilibria are established. We also incorporate the effect of media in the model and study its implications for opinion formation.

Continuum dynamics of the intention field under weakly cohesive social interaction

We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.

Opinion formation in social networks: a time-variant and non-linear model

This paper develops a discrete-time, non-linear, and time-variant model of opinion formation in a social network with global interactions to investigate the relationship between the final consensus belief and the set of agents’ initial opinions. The model uses a novel and considerably intuitive updating rule, according to which the weight placed by an agent on another one’s opinion in each period decreases continuously with the distance between their beliefs in the previous period. In this context, the first part of our analysis proves that agents’ beliefs converge and reach a consensus over time (under a fairly general set of conditions). For the two-agent case, it is then shown that the consensus belief is the simple arithmetic mean of the initial opinions. When there are three agents in the network, the combined use of computational and analytical methods reveals a relatively more complex polynomial relationship between long-run and initial beliefs. In particular, our results for the three-agent case imply that the deviation of the limiting belief from the corresponding average of the initial beliefs can be expressed as a third degree polynomial function incorporating the pairwise differences of agents’ starting beliefs.

Introducing a more realistic model for opinion formation considering instability in social structure

Opinion formation is a process through which interactions of individuals and dynamism of their opinions in effect of neighbors are modeled. In this paper, in an effort to model the opinion formation more realistically, we have introduced a model that considers the role of network structure in opinion dynamics. In this model, each individual changes his opinion in a way so as to decrease its difference with the opinion of trusted neighbors while he intensifies his dissention with the untrusted ones. Considering trust/distrust relations as a signed network, we have defined a structural indicator which shows the degree of instability in social structure and is calculated based on the structural balance theory. It is also applied as feedback to the opinion formation process affecting its dynamics. Our simulation results show formation of a set of clusters containing individuals holding opinions having similar values. Also, the opinion value of each individual is far from the ones of distrusted neighbors. Since this model considers distrust and instability of relations in society, it can offer a more realistic model of opinion formation.

Noise-induced absorbing phase transition in a model of opinion formation

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 stationary fraction of each opinion, and we show that there are distinct phase transitions. One is the usual ferro–paramagnetic transition, that is in the Ising universality class. In addition, there are para-absorbing and ferro-absorbing transitions, presenting the directed percolation universality class. Our results are complemented by numerical simulations.

Bistability and multistability in opinion dynamics models

In this paper, we analyze a few opinion formation or election game dynamics models. For a simple model with two subpopulations with opposing opinions A and B, if the fraction of committed believers of opinion A (“A zealots”) is less than a critical value, then the system has two bistable equilibrium points. When the fraction is equal to the critical value, the system undergoes a saddle-node bifurcation. When the fraction is larger than the critical value, a boundary equilibrium point is globally asymptotically stable, suggesting that the entire population reaches a consensus on A. We find a similar bistability property in the model in which both opinions have their own zealots. We also extend the model to include multiple competitors and show the dynamical behavior of multistability. The more competitors subpopulation A has, the fewer zealots opinion A needs to obtain consensus.