Article

The Trump phenomenon: An explanation from sociophysics

Authors:
  • ScencesPo and French National Centre for Scientific Research (CNRS)
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Abstract

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 develops along two successive steps. During a first moment, Trump's statement produces a majority of voters against him. But at the same time, according to the model the shocking character of the statement modifies the prejudice balance. In case the prejudice is present even being frozen among voters, the tipping point is lowered at Trump's benefit. Nevertheless, although the tipping point has been lowered by the activation of frozen prejudices it is instrumental to preserve enough support from openly prejudiced people to be above the threshold. Then, as infuriated voters launch intense debate, occurrence of ties will drive progressively hostile people to shift their voting intention without needing to endorse the statement which has infuriated them. The on going debate does drive towards a majority for Trump. The possible Trump victory at November Presidential election is discussed. In particular, the model shows that to eventually win the Presidential election, Trump must not modify his past shocking attitude but to appeal to a different spectrum of frozen prejudices, which are common to both Democrats and Republicans.

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... Opinion dynamics, being one of the essential branches of sociophysics, studies the statistical physics of collective opinion evolution driven by microscopic rules of individuals [1]. Opinion dynamics models can be broadly classified into two categories concerning the opinion space [2]: the discrete opinion space [3][4][5][6][7][8][9][10][11], and the continuous opinion space [12][13][14][15][16]. The models based on discrete opinion space usually assume two opposing opinions in the system (e.g., +1, −1, or A, B, etc.). ...
... The models based on discrete opinion space usually assume two opposing opinions in the system (e.g., +1, −1, or A, B, etc.). The classic discrete opinion dynamics models include the voter model [3][4][5], the Sznajd model [6][7][8], and the Galam model [9][10][11]. Another class of models is based on continuous opinion space, where an individual's opinion is measured by a real number between 0 and 1, inclusive. ...
Article
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The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent’s opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion’s result influences all participants’ opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent’s opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is more convenient to combine with other higher-order interactions, from the contagion process to evolutionary dynamics.
... Moreover, election results are mostly spot measurement of an unsettled many body system. Strategies and their timings may induce modest shift in the opinions which can change the tipping point or introduce instability [49][50][51], thereby changing the political outcome. ...
... In situations in which the external bias is strong they can tilt the balance of opinions. We also conjecture that this effect is similar to the role of prejudice studied extensively by Galam et al. [49]. ...
Article
Inspired by partisan competitions and contentious elections in democratic countries, we numerically explore the effect of campaign strategies and related factors on the opinion of an electorate. The nature of the electorate is modeled through agents with different behaviors, such as, being conformist, contrarian or inflexible. The agents are assumed to take discrete opinion values that depend on both internal and external influences. The inhomogeneity of external influence on individuals is modeled as a random field. Two types of electorates have been considered. In an electorate with only conformist agents short-duration high impact campaigns are highly effective. These are, however, also sensitive to perturbations at the local level modeled as inflexibles and/or absentees. In electorates with both conformist and contrarian agents and varying level of dominance due to local factors, short-term campaigns are effective only in the case of fragile dominance of a single party. Strong local dominance is relatively difficult to influence and long term campaigns with strategies aimed to impact local level politics are seen to be more effective.
... Opinion dynamics have received great interest in recent years due to its importance in understanding human interactions and reproducing diverse social processes (Fortunato & Castellano, 2007;Galam, 2004Galam, , 2008Galam, , 2016. Humans constitute one of the basic elements of social phenomena, and the most important factors behind the human behavior are those opinions, beliefs, and circumstances that drive their actions (Dong et al., 2018). ...
... Undoubtedly, an influential and representative class of models for opinion dynamics is formed by those based on majority rule (MR) or some of its variants (relative, weighted, qualified, or absolute majority) such as Ising's model with zero-temperature and Glauber kinetics (IG) or Galam's local MR model which, in fact, was applied to describe Trump's effect on past 2016 EU Presidential Elections (Galam, 2000(Galam, , 2004(Galam, , 2016Krapivsky & Redner, 2003). Three basic steps are needed to apply MR: first, count group opinions; second, decide the majority opinion in the group; and finally, assign it to the whole group (Kolbin, 2003, p. 36). ...
Article
This article explores the opinion dynamics of a double coalition opinion against a third opinion under majority rule updates on odd fixed size connected groups. For this purpose, coalition benefit criteria and three opinion formation models which extend the 2-state majority rule model on lattices are introduced. The proposed models focus on the coalition profit of its constituent coalition opinions and cover the possible final scenarios from coalition alliance perspective: either minor opinion or major opinion is favored, or dynamics do not favor to any coalition opinion. Opinion exchanges take place on a torus embedded lattice network of a 3-state system having in consideration tie configurations and two rules to break them: either by random choice or leaving ties unaltered. Models were analyzed in the statistical mechanics spirit through Monte Carlo simulations without node replacement. Estimations for coalition benefits, the growth of coalition ties, and consensus probabilities are reported. The loss of coalition strengths due to coalition ties and its indecision is indicated. In particular, the logistic decay of consensus probability is due to the logistic adaptive growth of coalition ties. Scaling behaviors for consensus time and coalition ties in terms of network size are suggested. The results of numerical simulations are discussed in the context of social influence and social dynamics.
... The best examples of such successful predictions are those made by Serge Galam. He anticipated the rejection of the Treaty establishing a Constitution for Europe in the French referendum in 2005 [64,86,87], or more recently, Trump's victory in the 2016 United States presidential election [88]. Based on the same model, the outcome of the British referendum on leaving the European Union could have been foreseen [87,88]. ...
... He anticipated the rejection of the Treaty establishing a Constitution for Europe in the French referendum in 2005 [64,86,87], or more recently, Trump's victory in the 2016 United States presidential election [88]. Based on the same model, the outcome of the British referendum on leaving the European Union could have been foreseen [87,88]. Another possibility is to compare the model results with some historical data obtained from various sources, like elections [89][90][91], market shares [65], censuses [92], etc. ...
Article
Full-text available
We present a short review based on the nonlinear q-voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: "independence vs. anticonformity" or "personality vs. situation". We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations. Accepted Manuscript: https://arxiv.org/abs/1903.04786
... The best examples of such successful predictions are those made by Serge Galam. He anticipated the rejection of the Treaty establishing a Constitution for Europe in the French referendum in 2005 [64,86,87], or more recently, Trump's victory in the 2016 United States presidential election [88]. Based on the same model, the outcome of the British referendum on leaving the European Union could have been foreseen [87,88]. ...
... He anticipated the rejection of the Treaty establishing a Constitution for Europe in the French referendum in 2005 [64,86,87], or more recently, Trump's victory in the 2016 United States presidential election [88]. Based on the same model, the outcome of the British referendum on leaving the European Union could have been foreseen [87,88]. Another possibility is to compare the model results with some historical data obtained from various sources, like elections [89][90][91], market shares [65], censuses [92], etc. ...
Preprint
Full-text available
We present a short review based on the nonlinear q-voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: "independence vs. anticonformity" or "personality vs. situation". We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations.
... The fact that using my model of opinion dynamics [1] I successfully predicted both Trump victory a few months ahead of the election [6] and the Brexit scenario several years ago [7,8], fueled credibility to my alert, which was quite sound given the then peculiar volatile French political context. My alarming got quite a large media impact echoing to the overall feeling that democratic countries were being swept within a wave of rising populism. ...
... The model also predicted the outcome of the 2005 French referendum on the European constitution which was rejected [31]. Using the same model I also predicted Donald Trump's totally unexpected victory over Hilary Clinton in the 2016 US Presidential election [6]. Earlier, the model also forecasted the scenario of Jean-Marie Le Pen's 2002 breakthrough victory at the first round Presidential election [32]. ...
Article
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I revisit the 2017 French Presidential election which opposed the far right National Front candidate Marine Le Pen against the center candidate Emmanuel Macron. While voting intentions for Le Pen stuck below 50% and polls kept predicting her failure, I warned on the emergence of a novel phenomenon I defined as unavowed abstention, which could suddenly reverse the ranking at Le Pen benefit on the voting day. My warning got a massive media coverage. She eventually lost the runoff at a score worse than predicted by the polls. Using a quantitative mathematical framing, which reveals the existence of tipping points in respective turnouts, I show that the predicted phenomenon of unavowed abstention did happen. But instead of shattering the expected outcome, against all odds it occurred at Le Pen expense, therefore without impact on the final outcome. The results shed a new light on other national cases such as Obama and Trump victories in the US.
... Obviously, consensus states are not observed in real-world political elections, and thus the basic models cannot be plausibly considered as realistic models that are able to describe empirical voting data. Accordingly, more realistic models of opinion dynamics have been proposed that incorporate, among other features, social impact theory [60][61][62], opinion leaders and zealots [18-19, 29-38, 62-63], external influences and fields [2,[18][19][64][65][66][67][68][69][70], individual's biases [71][72], contrarians [73], individual's own current opinion [74][75], wordof-mouth spreading [52], non-overlapping cliques [59], or noisy diffusive process [58]. Below we further elaborate on the themes of opinion leaders and zealots, external influences, and individual's biases-themes that play an important role in our model, and that have been seen empirically by studies of electoral behavior (see Introduction). ...
... The role of external influences (distinct from social imitation) in opinion formation has often been modeled as an external perturbation or modulation acting on all agents in the system, or by some external field or global coupling [3]. These perturbations could account for the effects of propaganda [65], fashion waves [66][67], or the mass media [68][69][70]; but are also driven by individual biases and prejudices [71][72], or level of political awareness [64]. More generally, these perturbations represent the dynamic response of a complex system to an external environment [18][19]63]. ...
Article
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Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science—elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.
... The interest in sociophysics has greatly increased in the past two decades, mainly when considering the dynamics that are present in social systems or networks [1][2][3][4][5][6][7][8]. Stauffer [5] and Galam [9], who proposed models that use local majority rule arguments, are considered the predecessors of the sociophysics emerging field, also termed as "the dynamics of opinions". In fact, the dynamics of opinions are treated in the same way that researchers treat the usual real world [10]. ...
Article
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A discrete version of opinion dynamics systems, based on the Biswas–Chatterjee–Sen (BChS) model, has been studied on Barabási–Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barabási–Albert networks (DBANs), as well as on Erdös–Rènyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities.
... The formation and dynamics of opinions [1][2][3][4][5][6][7][8][9][10][11] and its spread and propagation [12,13] seem to be a vivid section of sociophysics [14][15][16][17][18][19][20]. Existing models [21,22] may be grouped into two families: with discrete or continuous opinions. ...
Article
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In this paper, the results of computer simulations based on the Nowak–Szamrej–Latané model with multiple (from two to five) opinions available in the system are presented. We introduce the noise discrimination level (which says how small the clusters of agents could be considered negligible) as a quite useful quantity that allows qualitative characterization of the system. We show that depending on the introduced noise discrimination level, the range of actors’ interactions (controlled indirectly by an exponent in the distance scaling function, the larger the exponent, the more influential the nearest neighbors are) and the information noise level (modeled as social temperature, which increases results in the increase in randomness in taking the opinion by the agents), the ultimate number of the opinions (measured as the number of clusters of actors sharing the same opinion in clusters greater than the noise discrimination level) may be smaller than the number of opinions available in the system. These are observed in small and large information noise limits but result in either unanimity, or polarization, or randomization of opinions.
... The models can be employed by plugging an initial proportion into the model and calculating the limit of p n as n goes to infinity. Versions of this model have been used in an attempt to predict election results, such as the French rejection of the European constitution in 2005 [33], the Brexit vote [22], Trump's election for president in 2016 [21], as well as the U.S. presidential election in 2020 [23]. ...
Preprint
We analyse a model of binary opinion dynamics in which iterative discussions take place in local groups of individuals and study the effects of random deviations from the group majority. The probability of a deviation or flip depends on the magnitude of the majority. Depending on the values of the flip parameters which give the probability of a deviation, the model shows a wide variety of behaviour. We are interested in the characteristics of the model when the flip parameters are themselves randomly selected, following some probability distribution. Examples of these characteristics are whether large majorities and ties are attractors or repulsors, or the number of fixed points in the dynamics of the model. Which of the features of the model are likely to appear? Which ones are unlikely because they only present as events of low probability with respect to the distribution of the flip parameters? Answers to such questions allow us to distinguish mathematical properties which are stable under a variety of assumptions on the distribution of the flip parameters from features which are very rare and thus more of theoretical than practical interest. In this article, we present both exact numerical results for specific distributions of the flip parameters and small discussion groups and rigorous results in the form of limit theorems for large discussion groups. Small discussion groups model friend or work groups - people that personally know each other and frequently spend time together. Large groups represent scenarios such as social media or political entities such as cities, states, or countries.
... Парадоксально, але Д. Трамп не намагався здобути підтримку виборців, навпаки, за допомогою своїх прямолінійних виступів він породжував сумніви у думках людей з усталеними цінностями, провокував їх відкинути упередження і долучитися до дебатів з метою пошуку істини, переосмислення поглядів, раціоналізації того, що раніше видавалося неприйнятним. Відтак індивідуальні сумніви виборців, переконаних антитрампістів, з переходом на колективний рівень набували все більшого впливу й активували несвідоме упередження, яке схиляло їх робити вибір на користь Д. Трампа [4]. Іншими словами, експресивною поведінкою та імпульсивністю, самовпевненими висловлюваннями і надихаючими перебільшеннями Д. Трамп не лише привернув увагу, а й спонукав мільйони людей переступити поріг своїх цінностей. ...
... The transition of social discussions leading to consensus building is an old problem, but it is also an important theme in the analysis of various communications on the Internet in modern society. The opinion dynamics of binary opinions (agree and disagree or agree and ignore) have long been studied in analogy with magnetic physics [3][4][5][6][7][8][9]. In addition, since 2000, the Bounded Confidence Model, which analyzes opinions not as binary values but as continuously varying quantities, has been presented, and more precise studies have been conducted [10][11][12][13][14]. ...
Chapter
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This paper introduces the Trust-Distrust Model and its applications, extending the Bounded Confidence Model, a theory of opinion dynamics, to include the relationship between trust and mistrust. In recent years, there has been an increase in the number of cases in which the prerequisites for conventional communication (e.g., the other person’s gender, appearance, tone of voice, etc.) cannot be established without the exchange of personal information. However, in recent years, there has been an increase in the use of personal information, such as letters and pictograms “as cryptographic asset data” for two-way communication. However, there are advantages and disadvantages to using information assets in the form of personalized data, which are excerpts of personal information as described above. In the future, the discussion of trust value in the above data will accelerate in indicators such as personal credit scoring. In this paper, the Trust-Distrust Model will be discussed with respect to theories that also address charismatic people, the effects of advertising, and social divisions. Furthermore, simulations of the Trust-Distrust Model show that 55% agreement is sufficient to build social consensus. By addressing this theory, we hope to use it to discuss and predict social risk in future credit scoring discussions.
... [105,106] ). Sociophysics per se includes the political context as a sub-discipline, with the primarily focus on cross-sectional opinion dynamics (e.g., [13,14,22,34,[36][37][38]44,106] ). Different to the existing literature, the study at hand investigates the multifractal content of politically attached time-series. ...
Article
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This paper studies the long-range dependence and multifractal content of U.S. political time-series to gather a deeper understanding of sociophysic phenomena. Specifically, multifractal detrended fluctuation analysis (MF-DFA) is applied upon data in the context of (i) president approval (polls), (ii) president on- line attention (Google Trends) and (iii) election-win probabilities (prediction markets). All analyzed series are characterized by anti-persistence, which may be interpreted as a nervous and overreacting behavior. We further detect significant multifractality with true non-linear correlation remaining after correcting for spurious sources. Importance from understanding the multifractal behavior arises from the fact that all three data types are used in practice for the prediction of election outcomes. We further argue that variation in local persistence (as implied by multifractality) can be both beneficial and destructive in dif- ferent real-world scenarios. We draw parallels to simple examples like the timing of political campaigns or trading on prediction markets. On the methodological side, the article implements recent improve- ments of MF-DFA such as focus-based regression and overlapping segments.
... [105,106]). Sociophysics per se includes the political context as a sub-discipline, with the primarily focus on cross-sectional opinion dynamics (e.g., [13,14,22,34,[36][37][38]44,106]). Different to the existing literature, the study at hand investigates the multifractal content of politically attached time-series. ...
Preprint
Full-text available
This paper studies the long-range dependence and multifractal content of U.S. political time-series to gather a deeper understanding of sociophysic phenomena. Specifically, multifractal detrended fluctuation analysis (MF-DFA) is applied upon data in the context of (i) president approval (polls), (ii) president online attention (Google Trends) and (iii) election-win probabilities (prediction markets). All analyzed series are characterized by anti-persistence, which may be interpreted as a nervous and overreacting behavior. We further detect significant mul-tifractality with true non-linear correlation remaining after correcting for spurious sources. Importance from understanding the multifractal behavior arises from the fact that all three data types are used in practice for the prediction of election outcomes. We further argue that variation in local persistence (as implied by multifractality) can be both beneficial and destructive in different real-world scenarios. We draw parallels to simple examples like the timing of political campaigns or trading on prediction markets. On the methodological side, the article implements recent improvements of MF-DFA such as focus-based regression and overlapping segments.
... A number of problems have been studied over the course of the last decades using the general setup of the Galam model with suitable modifications. Versions of this model have been used to predict surprising election results, such as the French rejection of the European constitution in 2005 [30], the Brexit vote [20], and Trump's election for president in 2016 [19]. However, the prediction of a second Trump victory in 2020 failed by a short margin [21]. ...
Preprint
We study the effect of local distortions to the majority rule on the dynamics of opinions using an extension of the Galam model. At each iteration of the local updates of opinion, the new model accounts for different probabilities of a local flip against the local majority as a function of the ratio of majority / minority within the discussing group. Depending of those probabilities, the model exhibits a wide variety of patterns which include new features in the topology of the landscape driving the dynamics. In particular, we uncover a rich interplay between attractors and tipping points coupled with both monotonic and alternating dynamics. The cases of group sizes 3 and 5 are investigated in detail, and we find regimes that feature competition between three attractors for size 5. Larger groups are also analysed. The local flip model also applies to the study of bottom-top hierarchical voting, where each group elects a representative at the next higher level according to the local majority in the group. The local flip corresponds to a representative who decides to vote against the choice of their electing group, i.e. a "faithless elector". The results shed a new light on a series of social phenomena triggered by one single individual who acts against the local majority.
... Another approach was proposed by Serge Galam, where a community is divided into some subsets and the opinions initially win in the subsets until a majority is formed. Galam succeeded in explaining with this class of models the victory of Trump in the American elections in 2016 [14]. Different from this approach, where an opinion of the neighbors convinces an individual, was the one proposed by Sznajd-Weron and Sznajd [15]. ...
Article
The world’s population suffers a COVID-19 pandemic. By September 2020 nearly 1 million people had died. These are official numbers. The real cases might be much higher, due to under-reporting in many countries. Different strategies were adopted by national governments. Neglecting what was defined by sanitarian authorities, some politicians, at the beginning of the pandemic, declared that it would be a little flu, without consequences, lighter than seasonal flues. Some politicians propagated medicines with no scientific support. In many countries and regions, people became confused. The population’s reactions to these political positions may facilitate or block the virus spread. In this paper, we propose a model connecting the spreading of opinions with the propagation of a pandemic. We discuss how conflicting opinions can diffuse in the pandemic environment and the influence it has on the population’s behavior; how it may cause a greater or smaller number of infected individuals.
... Among those models stands the seminal Galam model [22][23][24][25][26], which combines local majority rule updates with local symmetry breaking driven by unconscious prejudices and cognitive biases in case of an even-size group at a tie. The model has revealed some heuristic capacity with the successful predictions of a few political events such as 2016 Brexit victory [24,27], Trump election [28], and 2005 French rejection of the European constitution project [29]. It has been subsequently extended to incorporate heterogeneous populations with three different psychological traits, which are heterogeneous prejudices, inflexibility or stubbornness [30][31][32][33][34][35][36][37], and contrarianism [38][39][40][41]. ...
Article
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A universal formula is shown to predict the dynamics of public opinion including eventual sudden and unexpected outbreaks of minority opinions within a generic parameter space of five dimensions. The formula is obtained by combining and extending several components of the Galam model of opinion dynamics, otherwise treated separately, into one single update equation, which then deploys in a social space of five dimensions. Four dimensions account for a rich diversity of individual traits within a heterogeneous population, including differentiated stubbornness, contrarianism, and embedded prejudices. The fifth dimension is the size of the update groups being discussed. Having one single formula allows one to explore the complete geometry of the underlying landscape of opinion dynamics. Attractors and tipping points, which shape the topology of the different possible dynamics flows, are unveiled. Driven by repeated discussion among small groups of people during a social or political public campaign, the phenomenon of minority spreading and parallel majority collapse are thus revealed ahead of their occurrence. Accordingly, within the opinion landscape, unexpected and sudden events such as Brexit and Trump victories become visible within a forecast time horizon, making them predictable. Despite the accidental nature of the landscape, evaluating the parameter values for a specific case allows one to single out which basin of attraction is going to drive the associate dynamics, and thus, a prediction of the outcome becomes feasible. The model may apply to a large spectrum of social situations including voting outcomes, market shares, and societal trends, allowing us to envision novel winning strategies in competing environments.
... For example, Braha and de Aguiar [20] and Fern\' andez-Gracia et al. [33] combined voter models with data on election results to comment on vote-share distributions and correlations across U.S. counties. In a series of papers (e.g., [35,36]), Galam used a``sociophysics"" approach (without reliance on polls or fundamental data) to suggest race outcomes and shed light on the dynamics that may underlie various election results. Very recently, Top\{\i} rceanu [80] developed a temporal attenuation model for U.S. elections with a basis in national polling data. ...
... Among those models stands the seminal Galam model [22][23][24][25][26], which combines local majority rule updates with local symmetry breaking driven by unconscious prejudices and cognitive biases in case of an even-size group at a tie. The model has revealed some heuristic capacity with the successful predictions of a few political events such as 2016 Brexit victory [24,27], Trump election [28], and 2005 French rejection of the European constitution project [29]. It has been subsequently extended to incorporate heterogeneous populations with three different psychological traits, which are heterogeneous prejudices, inflexibility or stubbornness [30][31][32][33][34][35][36][37], and contrarianism [38][39][40][41]. ...
Article
Full-text available
A universal formula is shown to predict the dynamics of public opinion including eventual sudden and unexpected outbreaks of minority opinions within a generic parameter space of five dimensions. The formula is obtained combining and extending several components of Galam model of opinion dynamics, otherwise treated separately, into one single update equation, which then deploys in a social space of five dimensions. Four dimensions account for a rich diversity of individual traits within a heterogeneous population, including differentiated stubbornness, contrarianism, and embedded prejudices. The fifth dimension is the size for the discussing update groups. Having one single formula allows exploring the complete geometry of the underlying landscape of opinion dynamics. Attractors and tipping points, which shape the topology of the different possible dynamics flows, are unveiled. Driven by repeated discussions among small groups of people during a social or political public campaign, the phenomenon of minority spreading and parallel majority collapse are thus revealed ahead of their occurrence. Accordingly, within the opinion landscape, unexpected and sudden events like Brexit and Trump victories become visible within a forecast time horizon making them predictable. Despite the accidental nature of the landscape, evaluating the parameter values for a specific case allows to single out which basin of attraction is going to drive the associate dynamics and thus a prediction of the outcome becomes feasible. The model may apply to a large spectrum of social situations including voting outcomes, market shares and societal trends, allowing to envision novel winning strategies in competing environments.
... One such technique was the Ising model, a model used to explain critical phase transitions where very simple interactions can lead to qualitative changes on a macroscopic scale (Sznajd-Weron 2005). Models have explored group decision making in various contexts including firms and small committees (Galam 1997), voting behaviour (González et al. 2004;Bernardes et al. 2002), how to convince others (Stauffer 2003), making political predictions (Galam 2017), modelling the impact of social influence on the prices of options (Oster and Feigel 2015) and the modelling of industrial strikes in big companies (Galam et al. 1982). Across sociology, psychology, politics, public policy and business, there have been a number of relevant studies including: experiments to explore the effect of social influence on judgment shifts (Moussaïd et al. 2013), understanding the psychological factors affecting opinion formation with an application to American politics (Duggins 2017), the initiation of smoking amongst adolescents (Sun and Mendez 2017) and consensus reaching in social network group decision making (Dong et al. 2018(Dong et al. , 2017. ...
Article
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This paper explores the influence of two competing stubborn agent groups on the opinion dynamics of normal agents. Computer simulations are used to investigate the parameter space systematically in order to determine the impact of group size and extremeness on the dynamics and identify optimal strategies for maximizing numbers of followers and social influence. Results show that (a) there are many cases where a group that is neither too large nor too small and neither too extreme nor too central achieves the best outcome, (b) stubborn groups can have a moderating, rather than polarizing, effect on the society in a range of circumstances, and (c) small changes in parameters can lead to transitions from a state where one stubborn group attracts all the normal agents to a state where the other group does so. We also explore how these findings can be interpreted in terms of opinion leaders, truth, and campaigns.
... In contrast, using a model of opinion dynamics [1] I have been developing for a few decades within sociophysics [1][2][3][4][5], I did predict Trump coming victory against all odds [6]. It is worth to notice that I myself did not believe my prediction could be right but the model was yielding Trump victory. ...
Preprint
In 2016, Trump was unanimously seen as the loser in the November 8 election. In contrast, using a model of opinion dynamics I have been developing for a few decades within the framework of sociophysics, I predicted his victory against all odds. According to the model, the winning paradoxical martingale of 2016, has been Trump capability to activate frozen prejudices in many voters by provoking their real indignation. However, four year later, Trump shocking outings do not shock anymore, they became devitalized, losing their ability to generate major emotional reactions. Does this mean that this time around he will lose the 2020 election to Biden, as nearly all analysts, pundits and commentators still predict? No, because although frozen prejudices will remain frozen, this time the spontaneously activated prejudices are benefiting to both Biden and Trump. The main ones are the fear of the other candidate policy and the personal stand facing a danger. In addition, since Trump presidency having polarized a large part of American voters into narrow-minded anti-Trump and narrow-minded pro-Trump, those I designate in my model as inflexibles, will also drive the dynamics. Both effects, prejudices and inflexibles can either compete or cooperate making their combination within each state, to determine the faith of the state election. Tiny differences can make the outcome. Based on my rough estimates of associated proportions of inflexibles and prejudices, the model predicts Trump victory in the 2020 November election.
... These models have applications in real life. At least two studies used binary opinion models to explain Trump's 2016 victory [36,37]. ...
Preprint
Full-text available
Opinion dynamics have attracted the interest of researchers from different fields. Local interactions among individuals create interesting dynamics for the system as a whole. Such dynamics are important from a variety of perspectives. Group decision making, successful marketing and constructing networks (in which consensus can be reached or prevented) are a few examples of existing or potential applications. The invention of the Internet has made the opinion fusion faster, unilateral, and on a whole different scale. Spread of fake news, propaganda, and election interferences have made it clear there is an essential need to know more about these dynamics. The emergence of new ideas in the field has accelerated over the last few years. In the first quarter of 2020, at least 50 research papers have emerged, either peer-reviewed and published or on pre-print outlets such as arXiv. In this paper, we summarize these groundbreaking ideas and their fascinating extensions, and introduce newly developed concepts.
... Averaging over large societal groups washes away individual particularities while retaining shared characteristics that affect conflict outcomes. We have used this approach to analyze concrete situations such as the Brexit referendum [18,19], the US election in 2016 [18][19][20][21], and the Serbia-Herzegovina-Croatia election in 2018 [22,23]. We have generated anticipatory scenarios for these conflicts. ...
Article
We present our research on the application of statistical physics techniques to multi-group social conflicts. We identify real conflict situations of which the characteristics correspond to the model. We offer realistic assumptions about conflict behaviors that get factored into model-generated scenarios. The scenarios can inform conflict research and strategies for conflict management. We discuss model applications to two-and three-group conflicts. We identify chaotic time evolution of mean attitudes and the occurrence of strange attractors. We examine the role that the range of interactions plays with respect to the occurrence of chaotic behavior.
... Everyday, we encounter a variety of situations in which we have to make decisions following our opinions, typical examples including political campaigns [1,2]. Human society could be free of conflicts if all agents share the same opinion on issues they encounter. ...
Preprint
Full-text available
In this work, we study a nonlocal opinion dynamics in a ring of agents with circular opinion in the presence of both attractive and repulsive interactions. We identified three types of consensus in this model, including global consensus, local consensus, and chimera consensus. In global consensus, both local agreement among adjacent agents and global agreement among all agents are achieved. In local consensus, local agreement is satisfied but global agreement fails. There are two domains in chimera consensus, one preserves local agreement and the other breaks the local agreement. The relation between the opinion difference between adjacent agents and the interaction radius is investigated and a scaling law is found. The transitions between local consensus and chimera consensus are exemplified.
... Moreover, a local majority decision model using the concept of renormalization groups from theoretical physics is also binary, consisting of approval and disapproval [20,21]. Utilizing this theory, Galam published a study on the analysis of the referendum of Britain's EU withdrawal (BREXIT) [22] and the election of US President Trump [23]. ...
Conference Paper
Full-text available
Consider the problem of socially isolated people who are not trusted by the people around them. This can be not only in the real world, but also in human relations on SNS. Using a new theory of opinion dynamics that can handle both trust and distrust among people, we perform simulations related to isolated person. We found that a charismatic popular person could be saved by having a relationship with an isolated person. However, on the other hand, the charismatic population is weakened.
... [15,16] Utilizing this theory, Galam published a study on the analysis of the referendum of Britain's EU withdrawal (BREXIT) [17] and the election of US President Trump. [18] Meanwhile, representative examples of the theory of opinions as consecutive values include the Deffuant-Weisbuch Model and the Bounded Confidence Model known as the Heselmann-Krause Model. [19,20,21] Although there have been attempts to deal with bipolarization resulting from conflicting opinions as an expansion of the Deffuant-Weisbuch Model, [22,23,24] the Hegselmann-Krause Model considers only consensus building. ...
Conference Paper
Full-text available
New opinion dynamics theory is presented where both trust and distrust are included in interpersonal relationship. Using this theory, we do not obtain consensus building if half of the human relationship are distrust. We also try to measure opinion distribution to compare with obtained opinion distribution obtained by this theory using the data of comments to news program on YouTube
... Galam [115] and Biswas et al. [116] both attempted, with different approaches, to explain Trump's victory in the US presidential election. ...
Preprint
Full-text available
In this age of Facebook, Instagram and Twitter, there is a rapidly growing interest in understanding network-enabled opinion dynamics in large groups of autonomous agents. The phenomena of opinion polarization, the spread of propaganda and fake news, and the manipulation of sentiment are of interest to large numbers of organizations and people, some of whom are resource rich. Whether it is the more nefarious players such as foreign governments that are attempting to sway elections or large corporations that are trying to bend sentiment – often quite surreptitiously, or it is more open and above board, like researchers that want to spread the news of some finding or some business interest that wants to make a large group of people aware of genuinely helpful innovations that they are marketing, what is at stake is often significant. In this paper we review many of the classical, and some of the new, social interaction models aimed at understanding opinion dynamics. While the first papers studying opinion dynamics appeared over 60 years ago, there is still a great deal of room for innovation and exploration. We believe that the political climate and the extraordinary (even unprecedented) events in the sphere of politics in the last few years will inspire new interest and new ideas. It is our aim to help those interested researchers understand what has already been explored in a significant portion of the field of opinion dynamics. We believe that in doing this, it will become clear that there is still much to be done.
... When the evolution of opinions is involved, we are facing opinion dynamics. Opinion dynamics has been a popular topic, in social physics [3][4][5][6][7][8][9][10], mathematics [11,12], to name but a few. Opinions can be described by discrete variables as well as continuous ones. ...
Article
In opinion dynamics with continuous opinion, bounded confidence is a critical parameter. Agents can interact with each other only when the opinion difference between them is less than the bounded confidence. Larger bounded confidence always leads to fewer opinion clusters. Stubbornness characterizing the insistence of an agent on her own opinion is thought to only affect the transition time. In this work, a modified Hegselmann–Krause model with heterogeneous population is investigated, where agents in different/same subpopulation have different/same bounded confidence and stubbornness. We find that, due to the interaction among subpopulations, increasing the stubbornness of agents in the subpopulation with the largest bounded confidence favors fewer opinion clusters and the expansion of the largest cluster. We also find that increasing the bounded confidence of a subpopulation leads to fewer clusters and a larger largest cluster provided that all the others have large bounded confidence. While one subpopulation is with a small bounded confidence, there exist an optimal bounded confidence of another subpopulation for the smallest number of opinion clusters and that for the largest size of the largest cluster.
... Models of opinion dynamics are among the most studied models of complex systems [1][2][3][4]. This is not surprising, because they can be treated as a zero-level approach to various more complex social processes, including polarization of opinion [5][6][7], diffusion of innovation [8][9][10], or political voting [11][12][13]. In most of these models, public opinion is formed as an outcome from individual opinions of mutually interacting agents. ...
Article
Full-text available
We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and possesses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q -voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q -voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed if the threshold r=0.5 , which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r>0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.
... Models of opinion dynamics are among the most studied models of complex systems [1][2][3][4]. This is not surprising, because they can be treated as a zero-level approach to various more complex social processes, including polarization of opinion [5][6][7], diffusion of innovation [8][9][10] or political voting [11][12][13]. In most of these models public opinion is formed as an outcome from individual opinions of mutually interacting agents. ...
Preprint
We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and posses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, namely the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via mean-field approach, which gives exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally we provide a heuristic reasoning, which explains observed phenomena. We show that indeed, if the threshold r = 0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r > 0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.
... Among the numerous existing models of opinion dynamics [5][6][7][8][9][10][11][12][13][14][15] stands the earlier Galam model [16][17][18][19][20][21], which has established a promising frame leading to a unifying frame [22]. Galam model has yielded several successful predictions of unexpected events like 2016 Brexit victory [18,19,23] and Trump election [24]. it also has predicted the 2005 French rejection of the European constitution project [25]. ...
Preprint
Sudden and unexpected disruptive phenomena like current French "gilets jaunes" movement, Arab springs, Trump and Brexit victories, put at stake the feasibility of their eventual forecasting. Here we claim that such unpredictable social events are indeed predictable, provided one can build the opinion landscape to identify the underlying dynamics. We derive a universal mathematical formula for the temporal evolution of opinion distribution among a heterogeneous population. It allows identifying the various tipping points and attractors triggering opinion flows thus unveiling the hidden mechanisms behind sudden upheavals like minority spreading and majority collapse. With our formula, the final outcome of an opinion dynamics can be predicted with substantial flexibility in the parameters evaluations, if the proper identification of relevant attractors are made. This opens the path to a large spectrum of real applications including voting outcomes, market shares and societal trends. This positioning provides a new ground to predict opinion dynamics outcomes and envision competing strategies to win a public debate.
... We are here interested in the dynamics of a specific kind of social contagion: the influences among politicians in a parliament. The dynamics of politics has already been studied considering a number of different approaches 21,22,23,24,25,26,27 . In those works, the interest ranges from theoretical aspects, like the emergence of phase transitions, to more practical aspects, like the reproduction of real results or the making of predictions. ...
Article
Full-text available
In this work, we study a simple model of social contagion that aims to represent the dynamics of social influences among politicians in an artificial corrupt parliament. We consider an agent-based model with three distinct types of artificial individuals (deputies), namely honest deputies, corrupt deputies and inflexible corrupt deputies. These last agents are committed to corruption, and they never change their state. The other two classes of agents are susceptible deputies, that can change state due to social pressure of other agents. We analyze the dynamic and stationary properties of the model as functions of the frozen density of inflexible corrupt individuals and two other parameters related to the strength of the social influences. We show that the honest individuals can disappear in the steady state, and such disappearance is related to an active-absorbing nonequilibrium phase transition that appears to be in the directed percolation universality class. We also determine the conditions leading to the survival of honesty in the long-time evolution of the system, and the regions of parameters for which the honest deputies can be the either the majority or the minority in the artificial parliament.
... Obviously, consensus states are not commonly observed in real-world applications. Accordingly, more realistic models of opinion dynamics have been proposed that incorporate, among other features, social impact theory [1,19,20], opinion leaders and zealots [7,13,[20][21][22][23][24][25][26][27][28][29][30][31], external influences and fields [6,7,13,[32][33][34][35][36][37][38], individual's biases [39,40], contrarians [41], individual's own current opinion [42][43][44], word-of-mouth spreading [45], non-overlapping cliques [46], or noisy diffusive process [18]. ...
Article
Full-text available
We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The random heterogeneities in the external perturbations are shown to affect the critical behavior of the network relative to networks without disorder. The size of the shift in the critical behavior essentially depends on the total fluctuation of the external influence disorder. Furthermore, the external perturbation disorder also has the surprising effect of amplifying the expected support of an already biased opinion. We show analytically that the vote-share variability is directly related to the external influence fluctuations. We extend our analysis by considering a fat-tailed multivariate lognormal disorder, and present numerical simulations that confirm our analytical results. Simulations for other network topologies demonstrate the generalizability of our findings. Understanding the dynamic response of complex systems to disordered external perturbations could account for a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.
... Not only are these models becoming more complex internally, but they begin to bring results relevant to a deeper understanding of what makes us change our opinions (individually and in groups), such as the successful predictions of social behavior in concrete cases, such as elections or popular campaigns. Just as an example, two predictions of political elections in which the results were far from obvious (Sobkowicz 2016;Galam 2016) have shown that ABM may have not only descriptive but also predictive power, with all the associated risks. Other examples of works related to real world issues include Fortunato and Castellano (2007), Zhang et al. (2016) and Duggins (2017). ...
Article
Full-text available
Computational models of group opinion dynamics are one of the most active fields of sociophysics. In recent years, advances in model complexity and, in particular, the possibility to connect these models with detailed data describing individual behaviors, preferences and activities, have opened the way for the simulations to describe quantitatively selected, real world social systems. The simulations could be then used to study ‘what-if’ scenarios for opinion change campaigns, political, ideological or commercial. The possibility of the practical application of the attitude change models necessitates that the research community working in the field should consider more seriously the moral aspects of their efforts, in particular the potential for their use for unintended goals. The paper discusses these issues, and offers a suggestion for a new research direction: using the attitude models to increase the awareness and detection of social manipulation cases. Such research would offer a scientific challenge and meet the ethical criteria.
Preprint
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In this paper, the results of the computer simulations based on Nowak--Szamrej--Latan\'e model with multiple (from two to five) opinions available in the system are presented. We introduce the noise discrimination level as a quite useful quantity that allows qualitative characterization of the system. We show that depending on the introduced noise discrimination level, the range of actors' interactions and the information noise level, the ultimate number of the opinions (measured as the number of clusters of actors sharing the same opinion in clusters greater than the noise discrimination level) may be smaller than the number of opinions available in the system. These are observed in small and large information noise limits but result in either unanimity, or polarization, or randomization of opinions. We also show that the larger the range of interaction, the more influential the nearest neighbors are.
Article
The rapid development of the Internet and networking technologies greatly facilitates the interactions among heterogeneous agents, while it also causes problems, such as the breakout of rumors and online bullying. Thus, it is critical to study the strategy evolution process in complex networks, that is, how heterogeneous agents interact with each other, update their opinions, and make decisions. In the literature, there have been numerous works on the modeling and analysis of decision making and opinion dynamics in social networks. However, most works assume that agents are homogeneous or only consider one single attribute in agent heterogeneity. In complex social networks, agents differ in many attributes and they constantly influence each other's decisions. How strategy evolves in complex networks with heterogeneous agents remains unknown. In this work, we consider three different attributes of agents: influence, susceptibility, and interest. We use graphical evolutionary game theory to theoretically analyze the impact of different attributes on the strategy evolution process and the evolutionary stable states (ESS). Both theoretical analysis and simulation results show that the influence attribute alone cannot change the ESS of the strategy evolution, while super agents who are both influential and stubborn have the largest impact on the ESS. Furthermore, real data validation shows that our proposed model can effectively model the information diffusion process in online social networks. This study is critical to the better understanding of agents' decision making process, and provides important guidelines on the management of social networks.
Article
The phase transition of a discrete version of the non-equilibrium Biswas–Chatterjee–Sen model, defined on Erdös–Rényi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs), has been studied. The mutual interactions (or affinities) can be both positive and negative, depending on the noise parameter value. Through extensive Monte Carlo simulations and finite-size scaling analysis, the continuous phase transitions and the corresponding critical exponent ratios have been obtained for several values of the average connectivity z. The effective dimensionality of the system has been found to be Deff≈1.0 for all values of z, which is similar to the one obtained on Barabási–Albert networks. The present results show that kinetic models of discrete opinion dynamics belong to a different universality class as the corresponding equilibrium Ising and Potts, and non-equilibrium majority-vote models on the same ERRGs and DERRGs. It is also noticed that the kinetic model here studied on ERRGs and DERRGs is in different universality classes for connectivities z<20, while for z≥20 the critical exponents are the same for both random graphs.
Article
We study the effect of probabilistic distortions to the local majority rules used in the Galam model of opinion dynamics and bottom-up hierarchical voting. A different probability for a flip against the local majority within the discussion group is associated with each ratio of majority/minority. The cases of groups of sizes 3 and 5 are investigated in detail. For hierarchical voting, the local flip corresponds to a ‘faithless elector’, a representative who decides to vote against the choice of their electing group. Depending on the flip probabilities, the model exhibits a rich variety of patterns for the dynamics, which include novel features in the topology of the landscape. In particular, for size 5, we uncover for the first time an interplay between five fixed points, which split into either three attractors and two tipping points or two attractors and three tipping points, depending on the flip probabilities. Larger groups are also analysed. These features were absent in the former versions of the Galam model, which has at maximum three fixed points for any group size. The results shed a new light on a series of social phenomena triggered by one single individual who acts against the local majority.
Chapter
Passing through tremendous catastrophes, tragedies, and unbelievable achievements, an optimistic philosophy of history could say that the technical and scientific developments are means to the noble end of human emancipation. This end, in the midst of many problems and contradictions, seemed to have led us irreversibly from tribes to humanity. A global universalism based on the values stated by the Universal Declaration of Human Rights (1948) calls for the cardinal principles of human dignity. Principles and values which have been increasingly embedded into most of the national constitutional laws, as well as the goals of liberation from poverty and disease, have been shared at the global level. Even the growing awareness of the sustainability standard seemed to be increasingly accepted by industry, business, politics, people.
Article
Most of opinion models focus on consensus induced by assimilation effects (attractive interaction). The roles of backfire effects (repulsive interaction dependent upon opinion difference) on non-consensus states are less paid attentions on. In this work, we introduce circular opinion which is defined on a circle with a circumference of 1. We study a circular opinion model on a ring with the backfire effect. The interplay between circular opinions and repulsive interaction leads to rich opinion dynamics. We identify six types of opinion states according to their profiles in opinion space and their spatial organizations: three opinion states without spatial structure including disordered state, fragment state with several opinion clusters, and polarized state with only two opinion clusters; three opinion states with spatial structure, travelling polarized state which is a tilted polarized state in space, clustered polarized states and clustered, and travelling clustered polarized state. The stability diagrams of different opinion states have been explored on the parameter plane and we find the coexistence among different opinion states is prevalent.
Chapter
The purpose of this paper is to interpret the diffusion of innovation (transfer of opinions to the adoption category) from the simulation of opinion dynamics with five adapter categories set as agents, and to provide a computational social science method useful for marketing and mass media research. In the simulation, we observed the impact on the spread of innovation by manipulating variables such as the Initial Distribution of Opinions, the Confidence Coefficient between agents, the Mass Media Effects, and the Network Connection Probabilities of the random network. Simulation results show that when the media has a uniform impact on the market, the distribution of people's opinions is distorted in the direction that the media takes the lead. We also observed that by manipulating the initial values of the opinions of the initial adopters, the reliability coefficient, and the connection probability between the nodes of the random network, the market is affected, and the spread of innovation is affected.
Article
This paper predicting Trump victory has been submitted before the election and revised after, allowing to add a Foreword and Node Added in Revision to discuss in details the causes of the failure of the prediction. In 2016, Trump was unanimously seen as the loser in the November 8 election. In contrast, using a model of opinion dynamics I have been developing for a few decades within the framework of sociophysics, I predicted his victory against all odds. According to the model, the winning paradoxical martingale of 2016, has been Trump capability to activate frozen prejudices in many voters by provoking their real indignation. However, four year later, Trump “shocking” outings do not shock anymore, they became devitalized, losing their ability to generate major emotional reactions. Does this mean that this time around he will lose the 2020 election against Biden, as nearly all analysts, pundits and commentators still predict? No, because with frozen prejudices remaining frozen, the spontaneous prejudices will be activated but this time they will benef to both Biden and Trump. The main ones are the fear of the other candidate policy and the personal stand facing a danger. In addition, Trump presidency having polarized a large part of American voters into narrow-minded anti-Trump and narrow-minded pro-Trump, those I denote in my model as inflexibles, will be driving the dynamics of choices. Both effects, prejudices and inflexibles can either compete or cooperate making their local combination within each state, decisive to determine the faith of the state election. As a result, tiny differences can make the outcome. Based on my rough estimates of associated proportions of inflexibles and prejudices, the model predicts Trump victory in the 2020 November election.
Chapter
We simulated the effects of mass media in society using a new theory of opinion dynamics that incorporated both trust and distrust into human relationships. We calculated not only the case where the media works uniformly for the people of society, but also the case of microtargeting where the media works only for those who have weak opinions. We also calculated the mass media effect that drives people to a particular opinion. The network of people is a random network, the coefficient of trust between people is determined by random numbers, and half of human relationships are untrusted.
Article
Opinion dynamics have attracted the interest of researchers from different fields. Local interactions among individuals create interesting dynamics for the system as a whole. Such dynamics are important from a variety of perspectives. Group decision making, successful marketing, and constructing networks (in which consensus can be reached or prevented) are a few examples of existing or potential applications. The invention of the Internet has made the opinion fusion faster, unilateral, and on a whole different scale. Spread of fake news, propaganda, and election interferences have made it clear there is an essential need to know more about these dynamics. The emergence of new ideas in the field has accelerated over the last few years. In the first quarter of 2020, at least 50 research papers have emerged, either peer-reviewed and published or on preprint outlets such as arXiv. In this paper, we summarize these ground-breaking ideas and their fascinating extensions and introduce newly surfaced concepts.
Chapter
We extend the theory of opinion dynamics, which introduces trust and distrust in human relationships in society, to multiple components. The theory is made up of N components, and in particular, here, two components are treated. In this paper, we show the calculation for real opinion and official stance as the two components of opinions.
Article
In this work, we study a nonlocal opinion dynamics in a ring of agents with circular opinion in the presence of both attractive and repulsive mechanisms. We identify three types of consensus in this model, including global consensus, local consensus and chimera consensus. In global consensus, both local agreement among adjacent agents and global agreement among all agents are achieved. In local consensus, local agreement is satisfied but global agreement fails. There are two domains in chimera consensus, one preserves local agreement and the other breaks the local agreement. The relation between the opinion difference between adjacent agents and the interaction radius is investigated and a scaling law is found. The transitions between local consensus and chimera consensus are exemplified.
Chapter
The problem of socially isolated people who are not trusted by the people around them is considered using a new opinion dynamics theory that can handle both trust and distrust among people. This can be not only in the real world, but also in human relations on SNS. Using the new theory of opinion dynamics, we perform simulations related to isolated persons. We found that a charismatic popular person could be saved by having a relationship with an isolated person. However, on the other hand, the charismatic population is weakened. The best way is to resolve distrust of themselves by everyone before using the popularity of the charismatic person.
Article
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In this work, we study a continuous opinion dynamics model considering 3-agent interactions and group pressure. Agents interact in a fully-connected population, and two parameters govern the dynamics: the agents’ convictions [Formula: see text] that are homogeneous in the population, and the group pressure [Formula: see text]. Stochastic parameters also drive the interactions. Our analytical and numerical results indicate that the model undergoes symmetry-breaking transitions at distinct critical points [Formula: see text] for any value of [Formula: see text], i.e. the transition can be suppressed for sufficiently high group pressure. Such transition separates two phases: for any [Formula: see text], the order parameter [Formula: see text] is identically null ([Formula: see text], a symmetric, absorbing phase), while for [Formula: see text], we have [Formula: see text], i.e. a symmetry-broken phase (ferromagnetic). The numerical simulations also reveal that the increase of group pressure leads to a wider distribution of opinions, decreasing the extremism in the population.
Article
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Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a "carrot and stick" approach towards symbionts with a stabilizing effect on their symbiosis. In open human societies, a mutualistic relationship arises when a native insider population attracts outsiders with benevolent incentives in hope that the additional labor will improve the standard of all. A lingering question, however, is the extent to which insiders are willing to tolerate outsiders before mutualism slips into antagonism. To test the assertion by Karl Popper that unlimited tolerance leads to the demise of tolerance, we model a society under a growing incursion from the outside. Guided by their traditions of maintaining the social fabric and prizing tolerance, the insiders reduce their benevolence toward the growing subpopulation of outsiders but do not invoke punishment. This reduction of benevolence intensifies as less tolerant insiders (e.g., "radicals") openly renounce benevolence. Although more tolerant insiders maintain some level of benevolence, they may also tacitly support radicals out of fear for the future. If radicals and their tacit supporters achieve a critical majority, herd behavior ensues and the relation between the insider and outsider subpopulations turns antagonistic. To control the risk of unwanted social dynamics, we map the parameter space within which the tolerance of insiders is in balance with the assimilation of outsiders, the tolerant insiders maintain a sustainable majority, and any reduction in benevolence occurs smoothly. We also identify the circumstances that cause the relations between insiders and outsiders to collapse or that lead to the dominance of the outsiders.
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Simmering debates leading to polarization are observed in many domains. Although empirical findings show a strong correlation between this phenomenon and modularity of a social network, still little is known about the actual mechanisms driving communities to conflicting opinions. In this paper, we used an agent-based model to check if the polarization may be induced by a competition between two types of social response: conformity and anticonformity. The proposed model builds on the q-voter model~\citep{CAS:MUN:PAS:09} and uses a double-clique topology in order to capture segmentation of a community. Our results indicate that the interplay between intra-clique conformity and inter-clique anticonformity may indeed lead to a polarized state of the entire system. We have found a dynamic phase transition controlled by the fraction $L$ of cross-links between cliques. In the regime of small values of $L$ system is able to reach the total positive consensus. If the values of $L$ are large enough, anticonformity takes over and the system always ends up in a polarized stated. Putting it the other way around, the segmentation of the network is not a sufficient condition for the polarization to appear. A suitable level of antagonistic interactions between segments is namely required to arrive at a polarized steady state within our model.
Article
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We investigate opinion formation against authority in an authoritarian society composed of agents with different levels of authority. We explore a (symbolically) "right" opinion, held by lower-ranking, obedient, less authoritative people, spreading in an environment of a "wrong" opinion held by authoritative leaders. The mental picture would be that of a corrupt society where the ruled people revolts against authority, but it could be argued to hold in more general situations. In our model, agents can change their opinion depending on the relative authority to their neighbors and their own confidence level. In addition, with a certain probability, agents can override the authority to take the right opinion of a neighbor. Based on analytic derivation and numerical simulations, we observe that both the network structure and heterogeneity in authority, and their correlation significantly affect the possibility of the right opinion to spread in the population. In particular, the right opinion is suppressed when the authority distribution is very heterogeneous and there is a positive correlation between the authority and number of neighbors of people. Except for such extreme cases, the spreading of the right opinion from the obedient agents takes place when there exist a tendency to override the authority to take the right opinion, but it can take a long time depending on the model parameters. We argue that the underlying social structure of agents sets the time scale of reaching consensus, based on the analysis of the underlying social relations.
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We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field $p_c$ such that for a weak external field ($p$$<$$p_c$), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large ($p$$>$$p_c$), there is only one (stable) fixed point which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasi-stationary distribution and is found to be in agreement with the results obtained by numerical simulations.
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A continuous-time Markov process is proposed to analyze how a group of humans solves a complex task, consisting in the search of the optimal set of decisions on a fitness landscape. Individuals change their opinions driven by two different forces: (i) the self-interest, which pushes them to increase their own fitness values, and (ii) the social interactions, which push individuals to reduce the diversity of their opinions in order to reach consensus. Results show that the performance of the group is strongly affected by the strength of social interactions and by the level of knowledge of the individuals. Increasing the strength of social interactions improves the performance of the team. However, too strong social interactions slow down the search of the optimal solution and worsen the performance of the group. In particular, we find that the threshold value of the social interaction strength, which leads to the emergence of a superior intelligence of the group, is just the critical threshold at which the consensus among the members sets in. We also prove that a moderate level of knowledge is already enough to guarantee high performance of the group in making decisions.
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In this work we study opinion formation in a population participating of a public debate with two distinct choices. We considered three distinct mechanisms of social interactions and individuals' behavior: conformity, non-conformity and inflexibility. The conformity is ruled by the majority-rule dynamics, whereas the non-conformity is introduced in the population as an independent behavior, implying the failure to 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 performed numerical simulations for distinct population sizes, and our results suggest that the different formulations of the model undergo order-disorder phase transitions in the same universality class of the Ising model. Some of our results are complemented by analytical calculations.
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We here present a model of the dynamics of extremism based on opinion dynamics in order to understand the circumstances which favour its emergence and development in large fractions of the general public. Our model is based on the bounded confidence hypothesis and on the evolution of initially anti-conformist agents to extreme positions. Numerical analyses demonstrate that a few anti-conformists are able to drag a large fraction of conformists agents to their position provided that they express their views more often than the conformists. The most influential parameter controlling the outcome of the dynamics is the uncertainty of the conformist agents; the higher their uncertainty, the higher is the influence of anti-conformists. Systematic scans of the parameter space show the existence of two regime transitions, one following the conformists uncertainty parameter and the other one following the anti-conformism strength.
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We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean field approximation and on small-world and scale-free networks. In the mean field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.
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Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator-prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor nodes after their long inactivity. However, due to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.
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We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement in one- and two-dimensional arrays. In both cases, the probability of reaching full consensus exhibits well-defined scaling properties as a function of the system size. Two-dimensional systems, in particular, possess nontrivial exponents and critical points. The dynamical rules of our models, which emphasize the interaction between small groups of agents, should be considered as complementary to the imitation mechanisms of traditional opinion dynamics.
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Background Agent-based models (ABM) are believed to be a very powerful tool in the social sciences, sometimes even treated as a substitute for social experiments. When building an ABM we have to define the agents and the rules governing the artificial society. Given the complexity and our limited understanding of the human nature, we face the problem of assuming that either personal traits, the situation or both have impact on the social behavior of agents. However, as the long-standing person-situation debate in psychology shows, there is no consensus as to the underlying psychological mechanism and the important question that arises is whether the modeling assumptions we make will have a substantial influence on the simulated behavior of the system as a whole or not. Methodology/Principal Findings Studying two variants of the same agent-based model of opinion formation, we show that the decision to choose either personal traits or the situation as the primary factor driving social interactions is of critical importance. Using Monte Carlo simulations (for Barabasi-Albert networks) and analytic calculations (for a complete graph) we provide evidence that assuming a person-specific response to social influence at the microscopic level generally leads to a completely different and less realistic aggregate or macroscopic behavior than an assumption of a situation-specific response; a result that has been reported by social psychologists for a range of experimental setups, but has been downplayed or ignored in the opinion dynamics literature. Significance This sensitivity to modeling assumptions has far reaching consequences also beyond opinion dynamics, since agent-based models are becoming a popular tool among economists and policy makers and are often used as substitutes of real social experiments.
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This study considers a simple variation of the voter model with two competing parties. In particular, we represent the case of political elections, where people can choose to support one of the two candidates or to remain neutral. People operate within a social network and their opinions depend on those of the people with whom they interact. Therefore, they may change their opinions over time, which may mean supporting one particular candidate or none. Candidates attempt to gain people's support by interacting with them, whether they are in the same social circle (i.e. neighbors) or not. In particular, candidates follow a strategy of interacting for a time with people they do not know (that is, people who are not their neighbors). Our analysis of the proposed model sought to establish which network strategies are the most effective for candidates to gain popular support. We found that the most suitable strategy depends on the topology of the social network. Finally, we investigated the role of charisma in these dynamics. Charisma is relevant in several social contexts, since charismatic people usually exercise a strong influence over others. Our results showed that candidates' charisma is an important contributory factor to a successful network strategy in election campaigns.
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This paper is concerned with the bottom-up hierarchical system and public debate model proposed by Galam (2008), as well as a spatial version of the public debate model. In all three models, there is a population of individuals who are characterized by one of two competing opinions, say opinion −1 and opinion +1. This population is further divided into groups of common size s . In the bottom-up hierarchical system, each group elects a representative candidate, whereas in the other two models, all the members of each group discuss at random times until they reach a consensus. At each election/discussion, the winning opinion is chosen according to Galam's majority rule: the opinion with the majority of representatives wins when there is a strict majority, while one opinion, say opinion −1, is chosen by default in the case of a tie. For the public debate models we also consider the following natural updating rule that we call proportional rule: the winning opinion is chosen at random with a probability equal to the fraction of its supporters in the group. The three models differ in term of their population structure: in the bottom-up hierarchical system, individuals are located on a finite regular tree, in the nonspatial public debate model, they are located on a complete graph, and in the spatial public debate model, they are located on the d -dimensional regular lattice. For the bottom-up hierarchical system and nonspatial public debate model, Galam studied the probability that a given opinion wins under the majority rule and, assuming that individuals' opinions are initially independent, making the initial number of supporters of a given opinion a binomial random variable. The first objective of this paper is to revisit Galam's result, assuming that the initial number of individuals in favor of a given opinion is a fixed deterministic number. Our analysis reveals phase transitions that are sharper under our assumption than under Galam's assumption, particularly with small population size. The second objective is to determine whether both opinions can coexist at equilibrium for the spatial public debate model under the proportional rule, which depends on the spatial dimension.
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When the full stock of a new product is quickly sold in a few days or weeks, one has the impression that new technologies develop and conquer the market in a very easy way. This may be true for some new technologies, for example the cell phone, but not for others, like the blue-ray. Novelty, usefulness, advertising, price, and fashion are the driving forces behind the adoption of a new product. But, what are the key factors that lead to adopt a new technology? In this paper we propose and investigate a simple model for the adoption of an innovation which depends mainly on three elements: the appeal of the novelty, the inertia or resistance to adopt it, and the interaction with other agents. Social interactions are taken into account in two ways: by imitation and by differentiation, i.e., some agents will be inclined to adopt an innovation if many people do the same, but other will act in the opposite direction, trying to differentiate from the "herd". We determine the conditions for a successful implantation of the new technology, by considering the strength of advertising and the effect of social interactions. We find a balance between the advertising and the number of anti-herding agents that may block the adoption of a new product. We also compare the effect of social interactions, when agents take into account the behavior of the whole society or just a part of it. In a nutshell, the present model reproduces qualitatively the available data on adoption of innovation.
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Motivated by the dynamics of cultural change and diversity, we generalize the three-species constrained voter model on a complete graph introduced in [J. Phys. A 37, 8479 (2004)]. In this opinion dynamics model, a population of size N is composed of "leftists" and "rightists" that interact with "centrists": a leftist and centrist can both become leftists with rate (1+q)/2 or centrists with rate (1-q)/2 (and similarly for rightists and centrists), where q denotes the bias towards extremism (q>0) or centrism (q<0). This system admits three absorbing fixed points and a "polarization" line along which a frozen mixture of leftists and rightists coexist. In the realm of Fokker-Planck equation, and using a mapping onto a population genetics model, we compute the fixation probability of ending in every absorbing state and the mean times for these events. We therefore show, especially in the limit of weak bias and large population size when |q|~1/N and N>>1, how fluctuations alter the mean field predictions: polarization is likely when q>0, but there is always a finite probability to reach a consensus; the opposite happens when q<0. Our findings are corroborated by stochastic simulations.
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The connection between contradictory public opinions, heterogeneous beliefs, and the emergence of majority- or minority-induced extremism is studied, extending our former two-state dynamic opinion model. Agents are attached to a social-cultural class. At each step they are distributed randomly in different groups within their respective classes to evolve locally by majority rule. In case of a tie the group adopts one or another opinion with respective probabilities k and (1-k) . The value of k accounts for the average of individual biases driven by the existence of heterogeneous beliefs within the corresponding class. It may vary from class to class. The process leads to extremism with a full polarization of each class along one opinion. For homogeneous classes the extremism can be along the initial minority making it minority induced. In contrast, heterogeneous classes exhibit more balanced dynamics, which results in a majority-induced extremism. Segregation among subclasses may produce a coexistence of opinions at the class level, thus averting global extremism. Insight into the existence of contradictory public opinions in similar social-cultural neighborhoods is given.
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The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.
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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-Schr\H{o}der, then the 2005 Schr\H{o}der-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 margin for the predicted winner. While all these events were perceived as accidental and isolated, our model suggests that indeed they are deterministic and obey to one single universal phenomena associated to the effect of contrarian behavior on the dynamics of opinion forming. The not hung Bush-Kerry 2005 presidential election is shown to belong to the same universal frame. To conclude, the existence of contrarians hints at the repetition of hung elections in the near future.
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We review a series of models of sociophysics introduced by Galam and Galam et al in the last 25 years. The models are divided in five different classes, which deal respectively with democratic voting in bottom up hierarchical systems, decision making, fragmentation versus coalitions, terrorism and opinion dynamics. For each class the connexion to the original physical model and technics are outlined underlining both the similarities and the differences. Emphasis is put on the numerous novel and counterintuitive results obtained with respect to the associated social and political framework. Using these models several major real political events were successfully predicted including the victory of the French extreme right party in the 2000 first round of French presidential elections, the voting at fifty - fifty in several democratic countries (Germany, Italy, Mexico), and the victory of the no to the 2005 French referendum on the European constitution. The perspectives and the challenges to make sociophysics a predictive solid field of science are discussed. Comment: 17 pages, 20 figures
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We introduce a statistical physics model for opinion dynamics on random networks where agents adopt the opinion held by the majority of their direct neighbors only if the fraction of these neighbors exceeds a certain threshold, p_u. We find a transition from total final consensus to a mixed phase where opinions coexist amongst the agents. The relevant parameters are the relative sizes in the initial opinion distribution within the population and the connectivity of the underlying network. As the order parameter we define the asymptotic state of opinions. In the phase diagram we find regions of total consensus and a mixed phase. As the 'laggard parameter' p_u increases the regions of consensus shrink. In addition we introduce rewiring of the underlying network during the opinion formation process and discuss the resulting consequences in the phase diagram. Comment: 5 pages, eps figs
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A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria. Comment: 7 pages, latex, 2 figures included
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We discuss a cellular automata model to study the competition between an emergent better fitted species against an existing majority species. The model implement local fights among small group of individual and a synchronous random walk on a 2D lattice. The faith of the system, i.e. the spreading or disappearance of the species is determined by their initial density and fight frequency. The initial density of the emergent species has to be higher than a critical threshold for total spreading but this value depends in a non-trivial way of the fight frequency. Below the threshold any better adapted species disappears showing that a qualitative advantage is not enough for a minority to win. No strategy is involved but spatial organization turns out to be crucial. For instance at minority densities of zero measure some very rare local geometries which occur by chance are found to be killer geometries. Once set they lead with high probability to the total destruction of the preexisting majority species. The occurrence rate of these killer geometries is function of the system size. This model may apply to a large spectrum of competing groups like smoker-non smoker, opinion forming, diffusion of innovation setting of industrial standards, species evolution, epidemic spreading and cancer growth. Comment: 11 pages, 8 figures
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A model for terrorism is presented using the theory of percolation. Terrorism power is related to the spontaneous formation of random backbones of people who are sympathetic to terrorism but without being directly involved in it. They just don't oppose in case they could. In the past such friendly-to-terrorism backbones have been always existing but were of finite size and localized to a given geographical area. The September 11 terrorist attack on the US has revealed for the first time the existence of a world wide spread extension. It is argued to have result from a sudden world percolation of otherwise unconnected and dormant world spread backbones of passive supporters. The associated strategic question is then to determine if collecting ground information could have predict and thus avoid such a transition. Our results show the answer is no, voiding the major criticism against intelligence services. To conclude the impact of military action is discussed. Comment: 12 pages, 4 figures
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The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo.Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation. Comment: 11 pages, 2 figures
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Article
We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement in one- and two- dimensional arrays. In both cases, the probability of reaching full consensus exhibits well-defined scaling properties as a function of the system size. Two-dimensional systems, in particular, possess nontrivial exponents and critical points. The dynamical rules of our models, which emphasize the interaction between small groups of agents, should be considered as complementary to the imitation mechanisms of traditional opinion dynamics. © 2014, Instituto de Fisica de Liquidos y Sistemas Biologicos. All rights reserved.
Book
Using tricks to handle coupled nonlinear dynamical many-body systems, several advancements have already been made in understanding the behavior of markets/economic/social systems and their dynamics. The book intends to provide the reader with updated reviews on such major developments in both econophysics and sociophysics, by leading experts in the respective fields. This is the first book providing a panoramic view of these developments in the last decade.
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People are often challenged to select one among several alternatives. This situation is present not only in decisions about complex issues, e.g. political or academic choices, but also about trivial ones, such as in daily purchases at a supermarket. We tackle this scenario by means of the tools of statistical mechanics. Following this approach, we introduce and analyse a model of opinion dynamics, using a Potts-like state variable to represent the multiple choices, including the ‘undecided state’, which represents the individuals who do not make a choice. We investigate the dynamics over Erdös–Rényi and Barabási–Albert networks, two paradigmatic classes with the small-world property, and we show the impact of the type of network on the opinion dynamics. Depending on the number of available options q and on the degree distribution of the network of contacts, different final steady states are accessible: from a wide distribution of choices to a state where a given option largely dominates. The abrupt transition between them is consistent with the sudden viral dominance of a given option over many similar ones. Moreover, the probability distributions produced by the model are validated by real data. Finally, we show that the model also contemplates the real situation of overchoice, where a large number of similar alternatives makes the choice process harder and indecision prevail.
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We introduce a novel type of contrarian agent, the balancer, to the Galam model of opinion dynamics, which features group-majority update, in order to account for the existence of social skepticism over one-sidedness. We find that, along with majoritarian floaters and single-sided inflexibles, the inclusion of balancers, who normally act as floaters but oppose inflexibles in their presence, brings about the emergence of a critical point on parametric plane of the dynamical system. Around the critical point, three distinct phases of opinion dynamics separated by discontinuous changes are found.
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This paper proposes a systems approach to social sciences based on mathematical tools derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a large living evolving ensemble of individuals, who express specific strategies, cooperate, compete, and might aggregate into groups, which pursue a common interest. A critical analysis on the complexity features of social system is developed and a general differential structure is derived to provide a general framework toward modeling. Such a structure is deemed to capture the aforesaid complexity features and provide the time evolution of a probability distribution over the microscopic state of individual entities, by means of which social systems are described.
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Defending a confined territory from a surprise attack is seldom possible. We use molecular dynamics and statistical physics inspired agent-based simulations to explore the evolution and outcome of such attacks. The study suggests robust emergent behavior, which emphasizes the importance of accurate surveillance, automated and powerful attack response, building layout, and sheds light on the role of communication restrictions in defending such territories.
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An alternative model of the formation of pyramidal structures is presented in the framework of social systems. The population is assumed to be distributed between two social orientations G and H with respective probabilities p 0 and (1-p 0 ). Instead of starting the hierarchy with a given H-orientation at the top and then going downwards in a deterministic way, the hierarchy is initiated randomly at the bottom from the surrounding population. Every level is then selected from the one underneath using the principle of majority rule. The hierarchy is thus self-oriented at the top. It is shown how such self-oriented hierarchies are always H-oriented provided they have a minimal number of levels which is determined by the values of p 0 . Their stability is studied against increases in p 0 . An ideal transition to G-self-oriented hierarchies is obtained.
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The September 11 attack on the US has revealed an unprecedented terrorism with worldwide range of destruction. It is argued to result from the first worldwide percolation of passive supporters. They are people sympathetic to the terrorism cause but without being involved with it. They just do not oppose it in case they could. This scheme puts suppression of the percolation as the major strategic issue in the fight against terrorism. Acting on the population is shown to be useless. Instead a new strategic scheme is suggested to increase the terrorism percolation threshold and in turn suppress the percolation. The relevant associated space is identified as a multi-dimensional social space including both the ground earth surface and all various independent flags displayed by the terrorist group. Some hints are given on how to shrink the geographical spreading of terrorism threat. The model apply to a large spectrum of clandestine activities including guerilla warfare as well as tax evasion, corruption, illegal gambling, illegal prostitution and black markets.
Article
A model for the dynamics of opinion forming in democratic public debate is presented. Using concepts and techniques from the physics of disorder the dynamics of social refusal spreading is studied within a perfect world, where the minority holds neither better arguments nor lobbying backing. The one-person-one-vote rule, together with local majority rules, are used to determine the outcome of local group discussions. In case of a local tie, the group decides on keeping the Status Quo. The geometry of social life shaped by offices, houses, bars, and restaurants is shown to determine the distribution size of these discussion groups. It is found to yield very asymmetric unstable thresholds to the total spreading of one opinion at the benefit of the refusal one. The associated dynamics is rather quick and completed within few days. This democratic paradox of public debate driven majority opinion reversal is discussed in light of some European construction issues. The model may apply to rumor and fear propagation.
Article
We study the effects of contrarians on the dynamics of opinion forming using the 2-state Galam opinion dynamics model. In a single update step, groups of a given size are defined and all agents in each group adopt the state of the local majority. In the absence of contrarians, the dynamics is fast and leads to a total polarization always along the initial majority (for groups of odd sizes). The introduction of contrarians is then shown to give rise to interesting new dynamics properties. First, at low concentration a, a new mixed phase is stabilized with a coexistence of both states. This is an ordered phase with a clear cut majority–minority splitting (non zero order parameter). Second, there is a phase transition into a new disordered phase at , 0.23, for groups of respective sizes 3, 5, 9 and infinite. For a⩾ac the disordered phase has no opinion dominating with both state densities equal (zero order parameter). In this phase agents keep shifting states but no global symmetry breaking, i.e., the appearance of a majority, takes place. Our results may shed a new light on the phenomenon of “hung elections” as occured in the 2000 American presidential elections and that of the 2002 German parliamentary elections.
Article
The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight against terrorism. Accordingly the world density of passive supporters should be reduced below the percolation threshold. In terms of solid policy, it means to neutralize millions of random passive supporters, which is contrary to ethics and out of any sound practical scheme. Given this impossibility we suggest instead a new strategic scheme to act directly on the value of the terrorism percolation threshold itself without harming the passive supporters. Accordingly we identify the space hosting the percolation phenomenon to be a multi-dimensional virtual social space which extends the ground earth surface to include the various independent terrorist-fighting goals. The associated percolating cluster is then found to create long-range ground connections to terrorism activity. We are thus able to modify the percolation threshold pc in the virtual space to reach p<pc by decreasing the social space dimension, leaving the density p unchanged. At once that would break down the associated world terrorism network to a family of unconnected finite-size clusters. The current world terrorism threat would thus shrink immediately and spontaneously to a local geographic problem. There, military action would become limited and efficient.
Article
In this paper we analyze the stochastic model proposed by Galam in [S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Physica A 320 (2003), 571–580], for information spreading in a ‘word-of-mouth’ process among agents, based on a majority rule. Using the communications rules among agents defined in the above reference, we first perform simulations of the ‘word-of-mouth’ process and compare the results with the theoretical values predicted by Galam’s model. Some dissimilarities arise in particular when a small number of agents is considered. We find motivations for these dissimilarities and suggest some enhancements by introducing a new parameter dependent model. We propose a modified Galam’s scheme which is asymptotically coincident with the original model in the above reference. Furthermore, for relatively small values of the parameter, we provide a numerical experience proving that the modified model often outperforms the original one.
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The origins of Sociophysics are discussed from a personal testimony. I trace back its history to the late 1970s. My 20 years of activities and research to establish and promote the field are reviewed. In particular, the conflicting nature of Sociophysics with the physics community is revealed from my own experience. Recent presentations of a supposed natural growth from Social Sciences are criticized.
Article
Understanding the emergence of extreme opinions and in what kind of environment they might become less extreme is a central theme in our modern globalized society. A model combining continuous opinions and observed discrete actions (CODA) capable of addressing the important issue of measuring how extreme opinions might be has been recently proposed. In this paper I show extreme opinions to arise in a ubiquitous manner in the CODA model for a multitude of social network structures. Depending on network details reducing extremism seems to be possible. However, a large number of agents with extreme opinions is always observed. A significant decrease in the number of extremists can be observed by allowing agents to change their positions in the network.
Les mathématiques sinvitent dans le débat européen (interview S. Galam), Le Monde
  • P Lehir
P. Lehir, Les mathématiques sinvitent dans le débat européen (interview S. Galam), Le Monde 26/02 (2005) 23.
Sociophysics: A Physicist's Modeling of Psycho-political Phenomena
  • S Galam
S. Galam, Sociophysics: A Physicist's Modeling of Psycho-political Phenomena (Springer, 2012).
Agent based modeling of a surprise attack by intruders: can the defenders win?
  • L Shanahan
  • S Sen
L. Shanahan and S. Sen, Agent based modeling of a surprise attack by intruders: can the defenders win?, Mod. Phys. Lett. B 25 (2011) 2279-2287.
  • S Galam
  • Crier
  • Pourquoi
S. Galam, Crier, mais pourquoi, Libération 17/04 (1998) 6.
Role of the plurality rule in multiple choices
  • A M Calvo
  • M Ramos
  • C Anteneodo
A. M. Calvo, M. Ramos and C. Anteneodo, Role of the plurality rule in multiple choices, J. Stat. Mech. 2016 (2016) 023405.