Model Of Opinion Formation Research Articles

Role of conviction in nonequilibrium models of opinion formation

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value (± 1 or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability p (1-p), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point p(c) that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

BEYOND CUES AND POLITICAL ELITES: THE FORGOTTEN ZALLER

Zaller's Nature and Origins of Mass Opinion initially sets out an epistemic view of politics in which the ultimate determinants of political action are ideas about the society in which we act. These ideas are usually mediated to us by others, so Zaller begins the book by describing its topic as the influence of the media on public opinion, and he includes journalists among the “political elites” who exert this influence (along with politicians, public officials, and experts). But the book eventually reduces journalists to being messengers of politicians' cues to the public. This understanding of the media is built into the book's model of opinion formation, in which cued predispositions are pivotal to the acceptance or rejection of culturally mediated “messages”—but are themselves insulated from cultural influence. A cueing model of message reception, however, ignores messages that are differentially persuasive not because of the predispositions they cue but the content they convey. Gauging the heterogeneous persuasiveness of messages requires qualitative content analysis and cultural contextualization, and if this research is to contribute to a general understanding of public opinion, it will have to extend beyond news-media messages to ideational influences carried in high culture, formal education, and the entertainment media. All of these sources of ideas, in turn, may contribute to the shaping of predispositions, as suggested in part by public opinion regarding the Vietnam War. Research of this kind would signal a new type of political science that focused on the actual thoughts of real people trying to understand a complex environment: exactly the type of political science suggested at the beginning of Zaller's book.

WHAT NATURE AND ORIGINS LEAVES OUT

The Nature and Origins of Mass Opinion synthesizes leading studies of public opinion from the late 1980s in a top-down model of opinion formation and change. The core feature of this synthesis, the Receive-Accept-Sample (RAS) model, remains sound, but the book overstates the importance of the form of public opinion that it explains—elite-induced survey statements of issue positions—and understates the force of opinions that elites cannot easily shape and that citizens may not be able to articulate in response to survey prompts. Moreover, there are major problems in the book's Parable of Purple Land. What, then, becomes of the top-down view of elite-mass interaction outlined in Nature and Origins? To answer this question, I begin by characterizing the kinds of opinions Nature and Origins leaves out: Converse's “group interest” voters, “nature of the times” voters, and issue publics. I then add a model of political parties as policy-motivated organizers of Converse's voter types. The upshot is an account of elite/mass interactions that is still largely top-down and that has roles for both the elite-led attitudes that the RAS model explains and the less conventional and harder-to-shape attitudes that it overlooks.

Opinion formation model for markets with a social temperature and fear

In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the two-dimensional voter model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents toward market imbalances representing speculative risk. We use the knowledge about the discontinuous generalized voter model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized, and its relation to dynamics of opinion formation among investors in real markets is discussed.

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.

The Unraveling of Support for Authoritarianism

This work examines the dynamic relationship among elites, media, and the public during authoritarian rule. Using Brazil’s military regime (1964–85), it investigates whether changing press censorship influenced public support for military rule during the period of political liberalization. This paper uses the exposure-resistance model of opinion formation, in which a person’s probability of supporting a position depends first on her probability of exposure to and reception of an elite cue advocating that position, and secondarily on the probability that she resists that position once exposed. Her likelihood of exposure to and reception of elite cues increases with her attention to news media and the extent of her political awareness; her odds of accepting the positions advocated by elites depends on her political ideology and her critical capacity to evaluate the content and source of the cue. Using three public opinion surveys carried out between 1972 and 1982, and an analysis of newspaper content during the dictatorship, this research demonstrates that censored media convinced Brazilians to support military rule initially, only later during political liberalization, to expose them to increasingly critical coverage of the regime, convincing many to abandon their support for the regime.

Multi-Level Opinion Dynamics under Bounded Confidence

Opinion dynamics focuses on the opinion evolution in a social community. Recently, some models of continuous opinion dynamics under bounded confidence were proposed by Deffuant and Krause, et al. In the literature, agents were generally assumed to have a homogeneous confidence level. This paper proposes an extended model for a group of agents with heterogeneous confidence levels. First, a social differentiation theory is introduced and a social group is divided into opinion subgroups with distinct confidence levels. Second, a multi-level heterogeneous opinion formation model is formulated under the framework of bounded confidence. Finally, computer simulations are conducted to study the collective opinion evolution, focusing on three key factors: the fractions of heterogeneous agents, the initial opinions, and the group size. The simulation results demonstrate that the number of final opinions depends on the fraction of close-minded agents when the group size and the initial opinions are fixed; the final opinions converge more easily when the initial opinions are closer; and the number of final opinions can be approximately modeled by a linear increasing function of the group size and the increasing rate is the fraction of close-minded agents.

Opinion formation in time-varying social networks: The case of the naming game

We study the dynamics of the naming game as an opinion formation model on time-varying social networks. This agent-based model captures the essential features of the agreement dynamics by means of a memory-based negotiation process. Our study focuses on the impact of time-varying properties of the social network of the agents on the naming game dynamics. In particular, we perform a computational exploration of this model using simulations on top of real networks. We investigate the outcomes of the dynamics on two different types of time-varying data: (1) the networks vary on a day-to-day basis and (2) the networks vary within very short intervals of time (20 sec). In the first case, we find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the naming game in these networks maintains clusters of coexisting opinions indefinitely leading to metastability. In the second case, we investigate the evolution of the naming game in perfect synchronization with the time evolution of the underlying social network shedding new light on the traditional emergent properties of the game that differ largely from what has been reported in the existing literature.

A hybrid model for opinion formation

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulations.

Adaptive-network models of collective dynamics

Complex systems can often be modelled as networks, in which their basic units are represented by abstract nodes and the interactions among them by abstract links. This network of interactions is the key to understanding emergent collective phenomena in such systems. In most cases, it is an adaptive network, which is defined by a feedback loop between the local dynamics of the individual units and the dynamical changes of the network structure itself. This feedback loop gives rise to many novel phenomena. Adaptive networks are a promising concept for the investigation of collective phenomena in different systems. However, they also present a challenge to existing modelling approaches and analytical descriptions due to the tight coupling between local and topological degrees of freedom. In this work, which is essentially my PhD thesis, I present a simple rule-based framework for the investigation of adaptive networks, using which a wide range of collective phenomena can be modelled and analysed from a common perspective. In this framework, a microscopic model is defined by the local interaction rules of small network motifs, which can be implemented in stochastic simulations straightforwardly. Moreover, an approximate emergent-level description in terms of macroscopic variables can be derived from the microscopic rules, which we use to analyse the system’s collective and long-term behaviour by applying tools from dynamical systems theory. We discuss three adaptive-network models for different collective phenomena within our common framework. First, we propose a novel approach to collective motion in insect swarms, in which we consider the insects’ adaptive interaction network instead of explicitly tracking their positions and velocities. We capture the experimentally observed onset of collective motion qualitatively in terms of a bifurcation in this non-spatial model. We find that three-body interactions are an essential ingredient for collective motion to emerge. Moreover, we show what minimal microscopic interaction rules determine whether the transition to collective motion is continuous or discontinuous. Second, we consider a model of opinion formation in groups of individuals, where we focus on the effect of directed links in adaptive networks. Extending the adaptive voter model to directed networks, we find a novel fragmentation mechanism, by which the network breaks into distinct components of opposing agents. This fragmentation is mediated by the formation of self-stabilizing structures in the network, which do not occur in the undirected case. We find that they are related to degree correlations stemming from the interplay of link directionality and adaptive topological change. Third, we discuss a model for the evolution of cooperation among self-interested agents, in which the adaptive nature of their interaction network gives rise to a novel dynamical mechanism promoting cooperation. We show that even full cooperation can be achieved asymptotically if the networks’ adaptive response to the agents’ dynamics is sufficiently fast.

Interplay between social debate and propaganda in an opinion formation model

We introduce a simple model of opinion dynamics in which a two-state agent modified Sznajd model evolves due to the simultaneous action of stochastic driving and a periodic signal. The stochastic effect mimics a social temperature, so the agents may adopt decisions in support for or against some opinion or position, according to a modified Sznajd rule with a varying probability. The external force represents a simplified picture by which society feels the influence of the external effects of propaganda. By means of Monte Carlo simulations we have shown the dynamical interplay between the social condition or mood and the external influence, finding a stochastic resonance-like phenomenon when we depict the noise-to-signal ratio as a function of the social temperature. In addition, we have also studied the effects of the system size and the external signal strength on the opinion formation dynamics.

Are Opinions Based on Science: Modelling Social Response to Scientific Facts

As scientists we like to think that modern societies and their members base their views, opinions and behaviour on scientific facts. This is not necessarily the case, even though we are all (over-) exposed to information flow through various channels of media, i.e. newspapers, television, radio, internet, and web. It is thought that this is mainly due to the conflicting information on the mass media and to the individual attitude (formed by cultural, educational and environmental factors), that is, one external factor and another personal factor. In this paper we will investigate the dynamical development of opinion in a small population of agents by means of a computational model of opinion formation in a co-evolving network of socially linked agents. The personal and external factors are taken into account by assigning an individual attitude parameter to each agent, and by subjecting all to an external but homogeneous field to simulate the effect of the media. We then adjust the field strength in the model by using actual data on scientific perception surveys carried out in two different populations, which allow us to compare two different societies. We interpret the model findings with the aid of simple mean field calculations. Our results suggest that scientifically sound concepts are more difficult to acquire than concepts not validated by science, since opposing individuals organize themselves in close communities that prevent opinion consensus.

How information influences an individual opinion evolution

We propose an opinion formation model which takes an individual’s opinion transition probability into consideration. In the model, each individual updates his/her opinion based on the probability of reception and acceptance. We describe the process of opinion evolution by using individual’s awareness Wi, message intensity a0 and message credibility b0. Results show that if a message’s view stays below 1 and its credibility takes a value around 2, it can win the trust of individuals with a high value of awareness (Wi≥1), leading the public opinion to support the message’s own view within 100 steps and then decide the opinion formation. The final average opinion is closely related to the first message’s credibility and individual’s awareness.

Opinion Dynamics Under Conformity

We present a model of opinion formation where individuals repeatedly engage in discussion and update their opinion in a social network similarly to the DeGroot model. Abstracting from the standard assumption that individuals always report their opinion truthfully, agents in our model interact strategically in the discussion such that their stated opinion can differ from their true opinion. The incentive to do so is induced by agents' preferences for conformity. Highly conforming agents will state an opinion which is close to their neighbors' while agents with low level of conformity may be honest or even overstate their opinion. We model opinion formation as a dynamic process and identify conditions for convergence to consensus. Studying the consensus in detail, we show that an agent's social influence on the consensus opinion is increasing in network centrality and decreasing in the level of conformity. Thus, lower conformity fosters opinion leadership. Moreover, assuming that the initial opinion is a noisy signal about some true state of the world, we consider the mean squared error of the consensus as an estimator for the true state of the world. We show that a society is wise, i.e. the mean squared error is smaller, if players who are well informed are less conform, while uninformed players conform more with their neighbors.

PageRank model of opinion formation on social networks

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of the Universities of Cambridge and Oxford, LiveJournal, and Twitter. In this model, the opinion formation of linked electors is weighted with their PageRank probability. Such a probability is used by the Google search engine for ranking of web pages. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion on a significant fraction of the society. However, for a homogeneous distribution of two opinions, there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that the LiveJournal and Twitter networks have a stronger tendency to a totalitarian opinion formation than the university networks. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.

Fragmentation transitions in multistate voter models

Adaptive models of opinion formation among humans can display a fragmentation transition, where a social network breaks into disconnected components. Here we investigate this transition in a class of models with arbitrary number of opinions. In contrast to previous work we do not assume that opinions are equidistant or arranged on a one-dimensional conceptual axis. Our investigation reveals detailed analytical results on fragmentations in a three-opinion model, which are confirmed by agent-based simulations. Furthermore, we show that in certain models the number of opinions can be reduced without affecting the fragmentation points.

Non-Bayesian social learning

We develop a dynamic model of opinion formation in social networks when the information required for learning a parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors. We show that, as long as individuals take their personal signals into account in a Bayesian way, repeated interactions lead them to successfully aggregate information and learn the true parameter. This result holds in spite of the apparent naïveté of agentsʼ updating rule, the agentsʼ need for information from sources the existence of which they may not be aware of, worst prior views, and the assumption that no agent can tell whether her own views or those of her neighbors are more accurate.

THE POLITICS OF MOTIVATION

Taber and Lodge offer a powerful case for the prevalence of directional reasoning that aims not at truth, but at the vindication of prior opinions. Taber and Lodge's results have far-reaching implications for empirical scholarship and normative theory; indeed, the very citizens often seen as performing “best” on tests of political knowledge, sophistication, and ideological constraint appear to be the ones who are the most susceptible to directional reasoning. However, Taber and Lodge's study, while internally beyond reproach, may substantially overstate the presence of motivated reasoning in political settings. That said, focusing on the accuracy motivation has the potential to bring together two models of opinion formation that many treat as competitors, and to offer a basis for assessing citizen competence.

Estimation of an agent-based model of investor sentiment formation in financial markets

We use weekly survey data on short-term and medium-term sentiment of German investors to estimate the parameters of a stochastic model of opinion formation governed by social interactions. The bivariate nature of our data set also allows us to explore the interaction between the two hypothesized opinion formation processes, while consideration of the simultaneous weekly changes of the stock index DAX enables us to study the influence of sentiment on returns. Technically, we extend the maximum likelihood framework for parameter estimation in agent-based models introduced by Lux (2009a) by generalizing it to bivariate and tri-variate settings. As it turns out, our results are consistent with strong social interaction in short-run sentiment. While one observes abrupt changes of mood in short-run sentiment, medium-term sentiment is a more slowly moving process in which the influence of social interaction seems to be less pronounced. The tri-variate model entails a significant effect from short-run sentiment on prices in-sample, but its out-of-sample predictive performance does not beat the random walk benchmark.

DISTRIBUTION OF VOTES AND A MODEL OF POLITICAL OPINION FORMATION FOR MAJORITY ELECTIONS

We study the behavior of the number of votes cast for different electoral subjects in majority elections, and in particular, the Albanian elections of the last 10 years, as well as the British, Russian, and Canadian elections. We report the frequency of obtaining a certain percentage (fraction) of votes versus this fraction for the parliamentary elections. In the distribution of votes cast in majority elections we identify two regimes. In the low percentiles we see a power law distribution, with exponent about -1.7. In the power law regime we find over 80% of the data points, while they relate to 20% of the votes cast. Votes of the small electoral subjects are found in this regime. The other regime includes percentiles above 20%, and has Gaussian distribution. It corresponds to large electoral subjects. A similar pattern is observed in other first past the post (FPP) elections, such as British and Canadian, but here the Gaussian is reduced to an exponential. Finally we show that this distribution can not be reproduced by a modified "word of mouth" model of opinion formation. This behavior can be reproduced by a model that comprises different number of zealots, as well as different campaign strengths for different electoral subjects, in presence of preferential attachment of voters to candidates.