A two state model for opinion forming, which has proven heuristic power, is reviewed with a novel emphasis on the existence or absence of a threshold for the dynamics. Monitored by repeated small groups discussions floater agents update their opinion according to a local majority rule. A threshold makes the initial supports to flow towards eitheir one of two opposite attractors with only one single opinion. While odd sizes yield a threshold at fifty percent even sizes, which allow the inclusion of doubt at an opinion tie, produces a threshold shift toward either 0 or 1 giving rise to minority opinion spreading. Considering heterogeneous agents like contrarians and inflexibles turn the dynamics threshold less beyond sone critical values. One unique attractor at fifty-fifty drives then the dynamics. In addition inflexibles can generate asymmetry and if one sided they erase the threshold ensuring the associated opinion to eventually gain the all population support. It may shed a new and counter intuitive light on some social aspect of the global warming phenomenon.
No abstract given. Contents: I. Definition and Introduction II. Schelling Model III. Opinion Dynamics IV. Languages, Hierarchies and Football V. Future Directions
Individuals have opinions but can change them under the influence of others. The recent models of Sznajd (missionaries), of Deffuant et al. (negotiators), and of Krause and Hegselmann (opportunists) are reviewed here, while the voter and Ising models, Galam's majority rule and the Axelrod multicultural model were dealt with by other lecturers at this 8th Granada Seminar.
In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability $p$ of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for $p>\sim 0.18$. Another effect of the probability $p$ is to decrease the average relaxation times $τ$, that are log-normally distribute…
Most of the opinion dynamics models in sociophysics have their historic origin in studies two-dimensional magnetization phenomena. This metaphor has proven quite useful, as it allowed to use well known techniques, relating individual behaviours of single spins and their interactions, to large scale properties, such as magnetization or magnetic domains creation. These physical properties were then ``mapped'' to social concepts: spin orientation to a person's views on a specific issue, magnetization to global opinion on the issue, etc. During the past 20 years, the models were significantly expa…
Consensus formation and difference of opinion have long been the subject of research. However, relevant laws and systems within society are being updated to reflect the changes in information networks. Online environment has come to fulfill a major role as a real and concrete place of opposing opinions and consensus formation. In the future, quantitative findings on consensus formation, and findings on relevant trends, must be summarized, and quantitative research related to trends likely to give rise to social and economic risk is required. Thus, the potential for comparing research related t…
The study of opinions $-$ e.g., their formation and change, and their effects on our society $-$ by means of theoretical and numerical models has been one of the main goals of sociophysics until now, but it is one of the defining topics addressed by social psychology and complexity science. Despite the flourishing of different models and theories, several key questions still remain unanswered. The aim of this paper is to provide a cognitively grounded computational model of opinions in which they are described as mental representations and defined in terms of distinctive mental features. We al…
The Trump phenomenon is argued to depart from current populist rise in Europe. According to a model of opinion dynamics from sociophysics the machinery of Trump's amazing success obeys well-defined counter-intuitive rules. Therefore, his success was in principle predictable from the start. The model uses local majority rule arguments and obeys a threshold dynamics. The associated tipping points are found to depend on the leading collective beliefs, cognitive biases and prejudices of the social group which undertakes the public debate. And here comes the sesame of the Trump campaign, which deve…
We expect that democracy enables us to utilize collective intelligence such that our collective decisions build and enhance social welfare, and such that we accept their distributive and normative consequences. Collective decisions are produced by voting procedures which aggregate individual preferences and judgments. Before and after, individual preferences and judgments change as their underlying attitudes, values, and opinions change through discussion and deliberation. In large groups, these dynamics naturally go beyond the scope of the individual and consequently might show unexpected sel…
In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account Indifferent voters: {\it i)} the Sznajd model with symmetry Pro-Contra, {\it ii)} the outflow one move voter model, where Contra's are converted to Indifferent by their Pro neighbours. Our results on the Sznajd model are in an overall agreement with the results of the mean field approach and with those known from the initial model formulation. The simulation …
There are several opinion dynamics models where extremism is defined as part of their characteristics. However, the way extremism is implemented in each model does not correspond to equivalent definitions. While some models focus on one aspect of the problem, others focus on different characteristics. This paper shows how each model only captures part of the problem and how Bayesian inspired opinion models can help put those differences in perspective. That discussion suggests new ways to introduce variables that can represent the problem of extremism better than we do today. Keywords: Extremi…
Formation of a lightning within a cloud, between clouds and towards the earth is studied as an application of sociophysics. The three dimensional society is sky or cloud, which has members as electrically charged clouds (in sky) or patches (in cloud). Members interact with the neighboring ones and all are convinced to average their charges (opinion). Yet, big external drives (mass media) as winds and turbulences may load new charges or may force the present ones to accumulate temporally at a site. For a lightning towards the earth, similarly charged clouds in sky (patches carrying big charges …
In 2000 we proposed a sociophysics model of opinion formation, which was based on trade union maxim "United we Stand, Divided we Fall" (USDF) and latter due to Dietrich Stauffer became known as the Sznajd model (SM). The main difference between SM compared to voter or Ising-type models is that information flows outward. In this paper we review the modifications and applications of SM that have been proposed in the literature.
We investigate the opinion evolution of outflow dynamics based on the Sznajd model on a complete graph involving contrarian and independence behaviors. We consider a group of four spins representing the social agents with the following scenarios: (1) scenario two-two with contrarian agents or independence agents and (2) scenario three-one with contrarian or independence agents. All of them undergo a second-order phase transition according to our simulation. The critical point decreases exponentially as $λ$ and $f$ increases, where $λ$ and $f$ are contrarian and flexibility factors, respectivel…
A sociophysical model for opinion dynamics is shown to embody a series of recent western hung national votes all set at the unexpected and very improbable edge of a fifty-fifty score. It started with the Bush-Gore 2000 American presidential election, followed by the 2002 Stoiber-Schrőder, then the 2005 Schrőder-Merkel German elections, and finally the 2006 Prodi-Berlusconi Italian elections. In each case, the country was facing drastic choices, the running competing parties were advocating very different programs and millions of voters were involved. Moreover, polls were given a substantial ma…
The q-voter model, a variant of the classic voter model, has been analyzed by several authors: while allowing to study opinion dynamics, this model is also believed to be one of the most representative among the many defined in the wide field of sociophysics. Here, we investigate the consequences of conformity on the consensus reaching process, by numerically simulating a q-voter model with agents behaving either as conformists or non-conformists, embedded on heterogeneous network topologies (as small-world and scale-free). In fact, although it is already known that conformity enhances the rea…
Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines as physics, mathematics, computer science, social psychology and philosophy. Agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to eac…
We consider a general class of three--state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a fraction of individuals (zealots) maintain unshakably their opinion, one of four qualitatively distinct kinds of collective dynamics arise, depending on the specific rules governing the social interactions. Unsurprisingly, when their density is high, zealots drive the whole population to consensus on their opinion. For low densities a rich phase diagram emerges: a…
Modern societies face the challenge that the time scale of opinion formation is continuously accelerating in contrast to the time scale of political decision making. With the latter remaining of the order of the election cycle we examine here the case that the political state of a society is determined by the continuously evolving values of the electorate. Given this assumption we show that the time lags inherent in the election cycle will inevitable lead to political instabilities for advanced democracies characterized both by an accelerating pace of opinion dynamics and by high sensibilities…
In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion may convince their neighbors with probability $p$, which induces an increase of the group's reputation. On the other hand, there is always a probability $q=1-p$ of the neighbors to keep their opinions, which induces a decrease of the group's reputation. These rules describe a competition between groups with high reputation and hesitant agents, which makes th…
A model of opinion formation on a Small World type topology is studied to observe qualitatively its difference with one is own conviction versus the opinion of others. It is possible to observe that the relation between conviction to copy the agent with whom it interacts and this agent is an undecided agent who leaves decisions to chance becomes outstanding since the probability of undecided agents is greater than 0.1 and is maintained until 0.7 so that in the border regions, it is only a transition towards this predictive.
We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation-a mechanism limiting the agents' persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents' reputation increases for each persuaded neighbor, and case 2, in which the agents' reputation increases for each persuasion and decreases when a neigh…
Recent technological changes have increased connectivity between individuals around the world leading to higher frequency interactions between members of communities that would be otherwise distant and disconnected. This paper examines a model of opinion dynamics in interacting communities and studies how increasing interaction frequency affects the ability for communities to retain distinct identities versus falling into consensus or polarized states in which community identity is lost. We also study the effect (if any) of opinion noise related to a tendency for individuals to assert their in…
We investigate the emergence of extreme opinion trends in society by employing statistical physics modeling and analysis on polls that inquire about a wide range of issues such as religion, economics, politics, abortion, extramarital sex, books, movies, and electoral vote. The surveys lay out a clear indicator of the rise of extreme views. The precursor is a nonlinear relation between the fraction of individuals holding a certain extreme view and the fraction of individuals that includes also moderates, e.g., in politics, those who are "very conservative" versus "moderate to very conservative"…
We consider a dual model of decision making, in which an individual forms its opinion based on contrasting mechanisms of imitation and rational calculation. The decision making model (DMM) implements imitating behavior by means of a network of coupled two-state master equations that undergoes a phase transition at a critical value of a control parameter. The evolutionary spatial game (EGM), being a generalization of the Prisoner's dilemma game, is used to determine in objective fashion the cooperative or anti-cooperative strategy adopted by individuals. Interactions between two sources of dyna…
We present an extensive study of the foreshock and aftershock signatures accompanying peaks of book sales. The time series of book sales are derived from the ranking system of Amazon.com. We present two independent ways of classifying peaks, one based on the acceleration pattern of sales and the other based on the exponent of the relaxation. They are found to be consistent and reveal the co-existence of two types of sales peaks: exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous sale peaks occur after a progressively accelerating power law growth follow…
Bounded confidence models of opinion dynamics have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations of the Deffuant-Weisbuch (DW) bounded confidence, relative agreement model, we propose the Mixed model that takes into account two psychological types of individuals. Concord agents (C-agents) are friendly people; they interact in a way that their opinions get closer always. Agents of the other psychological type show partial antagonism in their interaction…
Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge. An earlier model could explain the formation of such factions if reputations were assumed to be symmetric. We show this is not the case for non-symmetric reputations, and propose an alte…
We present a simple agent-based model to study the development of a bubble and the consequential crash and investigate how their proximate triggering factor might relate to their fundamental mechanism, and vice versa. Our agents invest according to their opinion on future price movements, which is based on three sources of information, (i) public information, i.e. news, (ii) information from their "friendship" network and (iii) private information. Our bounded rational agents continuously adapt their trading strategy to the current market regime by weighting each of these sources of informatio…
