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Processing fragments of data collected on a monitored person to find out whether this person is a would-be terrorist (WT) is very challenging. Moreover, the process has proven to be deceptive, with repeated dramatic failures. To address the issue I suggest a mirror simple model to mimic the process at stake. The model considers a collection of ground items which are labelled either Terrorist Connected (TC) or Terrorist Free (TF). To extract the signal from the ground data items I implement an iterated coarse-grained scheme, which yields a giant unique item with a label TC or TF. The results obtained validate the processing scheme with correct outcomes for the full range of proportions of TC items, beside in a specific sub-range. There, a systematic wrong labelling of the giant item is obtained at the benefit of WT, who are wrongly labeled not would-be terrorist (NWT). This flaw proves to be irremovable because it is anchored within the processing itself in connexion with the treatment of uncertain aggregates, which inevitable appear. The ``natural" allocation of uncertain aggregates to the TF label, in tune with the ethical application of the presumption of innocence in force in democracies, confines the wrong diagnosis systematically to the benefit of some WT, who are labelled NWT. It happens that applying the presumption of guilt, instead of that of innocence, to label the indeterminate aggregates, shifts the systematic errors to another sub-range of proportions of TC items with then zero errors in identifying a WT. But instead, some NWT are wrongly labeled WT. Despite of being quite far from reality, my results suggest that intelligence agencies should investigate the overall effect of seemingly inconsequential "natural" labelling, which are applied locally when data are uncertain with no immediate detectable impact on the data processing., 31 pages, 15 figures

A new approach to the understanding of sociological collective behaviour, based on the framework of critical phenomena in physics, is presented. The first step consists of constructing a simple mean-behaviour model and applying it to a strike process in a plant. The model comprises only a limited number of parameters characteristic of the plant considered and of the society. A dissatisfaction function is introduced with a basic principle stating that the stable state of the plant is a state, which minimizes this function. It is found that the plant can be in one of two phases: the "collective phase" and the "individual phase". These two phases are separated by a critical point, in the neighbourhood of which the system is very sensitive to small changes in the parameters. The collective phase includes a region of parameters for which the system has two possible states: a "work state" and a "strike state". The actual state of the system depends on the parameters and on the "history of the system". The irreversibility of the transition between these two states indicates the existence of metastable states. For these particular states, the effect of small groups of workers or of a small perturbation in the system results in drastic changes in the state of the plant. Other non-trivial implications of the model, as well as possible extensions and refinements of the approach, are discussed., Comment: First paper coining the term sociophysics to launch a new field of research (submitted in 1980, published in 1982), retyped in its original format, 13 pages, 4 figures

Справедливое распределение участия соавторов в публикациях с несколькими авторами представляется многолетней проблемой наукометрии. Например, при подсчете h-индекса всем соавторам присваивается равная степень участия в конкретной публикации независимо от вклада данного автора в работу или общего числа всех соавторов. Предпринимались разные попытки распределить степень участия в более подходящей манере. В своей недавней статье Хирш предложил новый способ присвоения степени участия, фундаментально отличающийся от представленных ранее: все участие в статье с несколькими авторами достается одному автору, так называемому «a-автору», определяемому как лицо с самым высоким имеющимся h-индексом (но не самым высоким h-индексом при публикации статьи) [1]. Набор статей данного автора, которому доверено выступить в качестве a- автора, затем используется для подсчета нового индекса, ha , в соответствии с той же самой процедурой, применяемой для подсчета обычного h-индекса. Целью этого новшества скорее является не более честное распределение степени участия, а определение совершенно иного свойства - степень научного лидерства индивидуума. В статье устанавливается, что с учетом сложной временной зависимости отдельных ученых от h подход использования имеющегося h-значения, а не предыдущих значений, проблематичен, и поэтому утверждается, что целесообразно определять a-автора при публикации статьи. С другой стороны, имеются иные практические соображения, значительно затруд- няющие подсчет предложенного ha . В качестве альтернативы изучаются другие способы приписывания статей одному автору в целях проверки раннего карьерного достижения или научного лидерства.

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., Comment: 24 pages, 7 figures, 9 tables

Using a new opinion dynamics using the polarity analysis of measured data of Twitter about "toilet paper" and "COVID-19", we analyzed the chain of fear that people feel for the rumor of lack of toilet paper and COVID-19 itself. We use opinion dynamics for the analysis of the fears, and we obtain the opinion distribution of the fear calculated using the opinion dynamics and the observed distribution. By comparing the two distribution, we found that the opinion distribution for the fear is consisted with the mixture of trust and distrust.

A fair assignment of credit for multi-authored publications is a long-standing issue in scientometrics. In the calculation of the $h$-index, for instance, all co-authors receive equal credit for a given publication, independent of a given author's contribution to the work or of the total number of co-authors. Several attempts have been made to distribute the credit in a more appropriate manner. In a recent paper, Hirsch has suggested a new way of credit assignment that is fundamentally different from the previous ones: All credit for a multi-author paper goes to a single author, the called ``$\alpha$-author'', defined as the person with the highest current $h$-index not the highest $h$-index at the time of the paper's publication) (J. E. Hirsch, Scientometrics 118, 673 (2019)). The collection of papers this author has received credit for as $\alpha$-author is then used to calculate a new index, $h_{\alpha}$, following the same recipe as for the usual $h$ index. The objective of this new assignment is not a fairer distribution of credit, but rather the determination of an altogether different property, the degree of a person's scientific leadership. We show that given the complex time dependence of $h$ for individual scientists, the approach of using the current $h$ value instead of the historic one is problematic, and we argue that it would be feasible to determine the $\alpha$-author at the time of the paper's publication instead. On the other hand, there are other practical considerations that make the calculation of the proposed $h_{\alpha}$ very difficult. As an alternative, we explore other ways of crediting papers to a single author in order to test early career achievement or scientific leadership., Comment: 6 pages, 4 figures

The dynamics of rumor spreading is investigated using a model with three kinds of agents who are, respectively, the Seeds, the Agnostics, and the Others. While Seeds are the ones who start spreading the rumor being adamantly convinced of its truth, Agnostics reject any kind of rumor and do not believe in conspiracy theories. In between, the Others constitute the main part of the community. While Seeds are always Believers and Agnostics are always Indifferents, Others can switch between being Believer and Indifferent depending on who they are discussing with. The underlying driving dynamics is implemented via local updates of randomly formed groups of agents. In each group, an Other turns into a Believer as soon as m or more Believers are present in the group. However, since some Believers may lose interest in the rumor as time passes by, we add a flipping fixed rate 0

Asymmetry in contrarian behavior is investigated within the Galam model of opinion dynamics using update groups of size 3 with two competing opinions A and B. Denoting $x$ and $y$ the respective proportions of A and B contrarians, four schemes of implementations are studied. First scheme activates contrarians after each series of updates with probabilities $x$ and $y$ for agents holding respectively opinion A and B. Second scheme activates contrarians within the update groups only against global majority with probability $x$ when A is majority and $y$ when B is majority. Third scheme considers in-group contrarians acting prior to the local majority update against both local majority and minority opinions. Last scheme activates in-group contrarians prior to the local majority update but only against the local majority. The main result is the loss of the fifty-fifty attractor produced by symmetric contrarians. Producing a bit less contrarians on its own side than the other side becomes the key to win a public debate, which in turn can guarantee an election victory. The associated phase diagram of opinion dynamics is found to exhibit a rich variety of counterintuitive results., Comment: 13 pages LaTeX with numerous figs; ver 2 updated with new bibliographic refeernces and corrections to figure references

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., Comment: LaTeX 14 pages, 9 figures

The substantial turmoil created by both 2000 dot-com crash and 2008 subprime crisis has fueled the belief that the two classical paradigms of economics, which are the invisible hand and the rational agent, are not appropriate to describe market dynamics and should be abandoned at the benefit of alternative new theoretical concepts. At odd with such a view, using a simple model of choice dynamics from sociophysics, the invisible hand and the rational agent paradigms are given a new legitimacy. Indeed, it is sufficient to introduce the holding of a few intermediate mini market aggregations by agents sharing their own private information, to recenter the invisible hand and the rational agent at the heart of market self regulation including the making of bubbles and their subsequent crashes. In so doing, an elasticity is discovered in the market efficiency mechanism due to the existence of agents anticipation. This elasticity is found to create spontaneous bubbles, which are rationally founded, and at the same time, it provokes crashes when the limit of elasticity is reached. Although the findings disclose a path to put an end to the bubble-crash phenomena, it is argued to be rationality not feasible., 20 pages, 7 figures

We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the proportions of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases, in which majority-preserving and regime-changing limit cycles are respectively dominant, is found, and also the transition between them is observed., LaTeX, 14 pages, 7 figues, Critical typographical errors in eqs. (4), (5) and (6) corrected

Gerald Bronner : Je ne suis pas un specialiste de l’islam, j’interviens comme specialiste des croyances. L’ideologie djihadiste presente des elements narratifs classiques dans le monde des croyances comme le millenarisme, la posture victimaire et les theories du complot, mais aussi des specificites. C’est le propre de la sociologie de travailler sur l’hybridation entre les invariances des phenomenes sociaux et les variables. Il y a plusieurs points a preciser sur les meca­nismes et les expre...

This chapter shows that a referendum, whatever the issue at stake, is a mechanism to turn our prejudices and fears into rational choices. To predict the outcome requires identifying the prejudices and fears which are prominent at the moment the referendum takes place. The question of identifying which are the leading active beliefs and prejudices in case of a local debate is instrumental in understanding the unexpected machinery of public debate in driving the opinion dynamics against the initial majority of individually made choices. The chapter gives an overview of what sociophysics is. It presents the Galam model of opinion dynamics in detail. The chapter discusses the concept and effect of having a dynamic driven by a tipping point. It illustrates the counterintuitive features of the model and thus provides a basis to explain unexpected voting outcomes. The chapter contains some remarks about future developments of the sociophysics approach.

The methodological approach proposed here combines textual statistical analysis and agent-based simulations. The controversy concerning the unusual disappearance of pollinating bees (Apis mellifera) covered in the French press over a period of 13 years was chosen to describe the different stages of this heuristic framework. First, the articles are categorized according to the origin they attribute to the phenomenon as a univariate cause, a multivariate cause or a lack of understanding. Then, the different proportions of agents supporting either of these causes are obtained and reproduced from a dynamic opinion model, which shows the existence of agents with pre-determined choices. The change in the proportions over time leads to questionning the consistency of the data concerning the independence of all agents. In particular, it becomes possible to assume the existence of networks of influence, a hypothesis that could be verified by other techniques such as qualitative, ethnographic or interview methods. L’ approche méthodologique proposée combine analyse statistique textuelle et simulation par agents. La controverse autour de la disparition inhabituelle des abeilles pollinisatrices (apis mellifera) traitée dans la presse francophone sur une période de 13 ans est choisie pour décrire les différentes étapes de ce cadre heuristique. Premièrement, les articles sont catégorisés selon l’origine qu’ils attribuent au phénomène : soit une cause unifactorielle, soit une cause multifactorielle, soit une absence de compréhension du phénomène. Ensuite, les différentes proportions d’agents soutenant l’une ou l’autre de ces causes sont obtenues et reproduites à partir d’un modèle de dynamique d’opinion, ce qui fait apparaître l’existence d’agents pré-déterminés dans leur choix. La variation de leurs proportions au cours du temps amène à questionner la cohérence des données quant à l’indépendance de tous les agents. En particulier il devient envisageable de supposer l’existence de réseaux d’influence. Hypothèse qui pourrait être vérifiée à partir d’autres techniques comme des méthodes qualitatives, ethnographiques ou par entretien.

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., Comment: 24 pages, 9 figures, to appear in International Journal of Modern Physics B

An alternative voting scheme is proposed to fill the democratic gap between a president elected democratically via universal suffrage (deterministic outcome, the actual majority decides), and a president elected by one person randomly selected from the population (probabilistic outcome depending on respective supports). Moving from one voting agent to a group of r randomly selected voting agents reduces the probabilistic character of the outcome. Building r such groups, each one electing its president, to constitute a group of the groups with the r local presidents electing a higher-level president, does reduce further the outcome probabilistic aspect. Repeating the process n times leads to a n-level bottom-up pyramidal structure. The hierarchy top president is still elected with a probability but the distance from a deterministic outcome reduces quickly with increasing n. At a critical value n_{c,r} the outcome turns deterministic recovering the same result a universal suffrage would yield. The scheme yields several social advantages like the distribution of local power to the competing minority making the structure more resilient, yet preserving the presidency allocation to the actual majority. An area is produced around fifty percent for which the president is elected with an almost equiprobability slightly biased in favor of the actual majority. However, our results reveal the existence of a severe geometric vulnerability to lobbying. A tiny lobbying group is able to kill the democratic balance by seizing the presidency democratically. It is sufficient to complete a correlated distribution of a few agents at the hierarchy bottom. Moreover, at the present stage, identifying an actual killing distribution is not feasible, which sheds a disturbing light on the devastating effect geometric lobbying can have on democratic hierarchical institutions., Comment: 52 pages, 22 figures, to appear in Mathematical Models and Methods in Applied Sciences

We are investigating a paradigm of instability in coalition forming among countries, which indeed is intrinsic to any collection of individual groups or other social aggregations. Coalitions among countries are formed by the respective attraction or repulsion caused by the historical bond propensities between the countries, which produced an intricate circuit of bilateral bonds. Contradictory associations into coalitions occur due to the independent evolution of the bonds. Those coalitions tend to be unstable and break down frequently. The model extends some features of the physical theory of Spin Glasses. Within the frame of this model, the instability is viewed as a consequence of decentralized maximization processes searching for the best coalition allocations. In contrast to the existing literature, a rational instability is found to result from forecast rationality of countries. Using a general theoretical framework allowing to analyze the countries' decision making in coalition forming, we feature a system where stability can eventually be achieved as a result of the maximization processes. We provide a formal implementation of the maximization principles and illustrate it in the multi-thread simulation of the coalition forming. The results shed a new light on the prospect of searches for the best coalition allocations in the networks of social, political or economical entities., 24 pages, 12 Figures

This paper reviews a sociophysics two-state model for opinion forming that has proven heuristic power. The dynamics are driven by repeated small-group discussions; within each group, a local majority rule is applied to update the opinions of agents. Iterating the dynamics leads towards one of two opposite attractors at which every agent shares the same opinion. The successful attractor is a function of the initial support with respect to a certain threshold, the value of which depends on the size distribution of the local update groups. While odd-sized groups yield a threshold at fifty percent, even-sized groups, which allow the inclusion of doubt in the case of an opinion tie, produce a threshold shift toward either one of the two attractors, giving rise to minority opinion spreading. In addition, agents can be heterogeneous in their cognitive nature, obeying different rules to update their opinion. While floater agents are open to changing their mind, contrarians chose to oppose whatever opinion was held by the majority of agents in their vicinity, and inflexibles never change their mind. Contrarians and inflexibles have drastic and counter-intuitive effects on the opinion dynamics. Beyond certain critical proportions, contrarians trigger an upside change of the dynamics, making it threshold-less with only one attractor at precisely 50/50 regardless of the initial conditions. Inflexibles produce the same threshold-less dynamics, except with an asymmetric single attractor that favors a specific opinion, even when they start with very low support. The results are used to shed new and unexpected light on controversial issues such as global warming.

Most models of opinion dynamics are threshold-like. For two competing opinions the dynamics is one-dimensional and the associated opinion flow is shaped by at least two attractors separated by a tipping threshold, not necessarily located at 50 %. Initial supports are thus instrumental to determine the final debate outcome. In contrast, the absence of a tipping threshold implies a unique attractor making the initial conditions irrelevant. One of the opinions is predetermined to become the majority whatever initial support it has. Accordingly, to make a threshold dynamics non threshold appears to be an instrumental strategic option. An illustration of the possibility of such a reshaping of the opinion dynamics geometry is given using the Galam sequential opinion dynamics model. The key parameters are pair interactions and inflexible or stubborn agents. A new and counter intuitive light is shed on the design of winning strategies in public issues. However the findings pose ethical issues. The case of global warming is discussed.

The drastic effect of local alliances in three-party competition is investigated in democratic hierarchical bottom-up voting. The results are obtained analytically using a model which extends a sociophysics frame introduced in 1986 (Galam in J. Math. Phys. 30:426, 1986) and 1990 (Galam in J. Stat. Phys. 61:943, 1990) to study two-party systems and the spontaneous formation of democratic dictatorship. It is worth stressing that the 1990 paper was published in the Journal of Statistical Physics, the first paper of its kind in this journal. It was shown how a minority in power can preserve its leadership using bottom-up democratic elections. However such a bias holds only down to some critical value of minimum support. The results were used latter to explain the sudden collapse of European communist parties in the nineties. The extension to three-party competition reveals the mechanisms by which a very small minority party can get a substantial representation at higher levels of the hierarchy when the other two competing parties are big. Additional surprising results are obtained, which enlighten the complexity of three-party democratic bottom-up voting. In particular, the unexpected outcomes of local voting alliances are singled out. Unbalanced democratic situations are exhibited with strong asymmetries between the actual bottom support of a party and its associated share of power at the top leadership. Subtle strategies are identified for a party to maximize its hold on the top leadership. The results are also valid to describe opinion dynamics with three competing opinions.

The combined effects of collective beliefs and individual inflexibility in the dynamics of a public debate are investigated using the Galam sequential probabilistic model of opinion dynamics. The study is focused on pair interactions for which the bias produced by collective beliefs is the decisive factor to win the debate. The current value of that bias is a fixed external parameter. It is a constant of the problem not given to change. In contrast, inflexibility is an individual property. It results from external ingredients, which are susceptible to be modified during the debate. More precisely, giving some beliefs we determine the required inflexibility to oppose its associated bias in the debate outcome. The results shed a new and counter intuitive light on paradoxical outcomes of sensitive issues, which are discussed in the public. The cases of global warming issue and debate over evolution are discussed.

The dynamics of wine purchasing behavior is studied focusing on the respective impacts of the word-to-mouth versus wine expert judgements and reputations. To investigate the problem we apply the Galam model of opinion dynamics to agents who have to select a preference about which type of wine to buy given expert judgements, individual preferences and wine reputations. It could be, for instance, a preference between Bordeaux and Burgundy. The main novelty of the work is not about the building of a new model but indeed the construction of a scheme to confront the Galam model to a specific problem of the real world. Accordingly we design a commercial strategy to hold on to a share of the wine market. It provides a novel understanding on how, given some established reputation, the competitive interplay between social interactions and expert judgments affects the market shares distribution. The financial implications of the practical implementation of these results are discussed. In particular it is found that sample distribution of bottles could be drastically reduced from the usual levels practiced by producers. We hope our results will convince some wine producers to test our predictions.

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

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–Schroder, then the 2005 Schroder–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 2004 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.

The phenomenon of radicalization is investigated within a mixed population composed of core and sensitive subpopulations. The latest includes first to third generation immigrants. Respective ways of life may be partially incompatible. In case of a conflict core agents behave as inflexible about the issue. In contrast, sensitive agents can decide either to live peacefully adjusting their way of life to the core one, or to oppose it with eventually joining violent activities. The interplay dynamics between peaceful and opponent sensitive agents is driven by pairwise interactions. These interactions occur both within the sensitive population and by mixing with core agents. The update process is monitored using a Lotka-Volterra-like Ordinary Differential Equation. Given an initial tiny minority of opponents that coexist with both inflexible and peaceful agents, we investigate implications on the emergence of radicalization. Opponents try to turn peaceful agents to opponents driving radicalization. However, inflexible core agents may step in to bring back opponents to a peaceful choice thus weakening the phenomenon. The required minimum individual core involvement to actually curb radicalization is calculated.It is found to be a function of both the majority or minority status of the sensitive subpopulation with respect to the core subpopulation and the degree of activeness of opponents. The results highlight the instrumental role core agents can have to hinder radicalization within the sensitive subpopulation. Some hints are outlined to favor novel public policies towards social integration., Comment: 15 pages, 3 figures. Published on PloS ONE

We revisit the deduction of the exit probability of the one dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008)]. This approximation is peculiar in that in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), A. M. Timpanaro and C. P. C. Prado, 89, 052808 (2014)] the hypothesis about the correlation lenghts behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd and "United we Stand, Divided we Fall" (USDF) models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975), K. Sznajd-Weron and J. Sznajd, Int. Journ. Mod. Phys. C 11, 1157 (2000)] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with $10^3$ sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability., 6 pages, 5 figures. To be submitted to Physical Review E

We propose a novel approach framed in terms of information theory and entropy to tackle the issue of conspiracy theories propagation. We start with the report of an event (such as 9/11 terroristic attack) represented as a series of individual strings of information denoted respectively by two-state variable Ei=+/-1, i=1,..., N. Assigning Ei value to all strings, the initial order parameter and entropy are determined. Conspiracy theorists comment on the report, focusing repeatedly on several strings Ek and changing their meaning (from -1 to +1). The reading of the event is turned fuzzy with an increased entropy value. Beyond some threshold value of entropy, chosen by simplicity to its maximum value, meaning N/2 variables with Ei=1, doubt prevails in the reading of the event and the chance is created that an alternative theory might prevail. Therefore, the evolution of the associated entropy is a way to measure the degree of penetration of a conspiracy theory. Our general framework relies on online content made voluntarily available by crowds of people, in response to some news or blog articles published by official news agencies. We apply different aggregation levels (comment, person, discussion thread) and discuss the associated patterns of entropy change., 21 page, 14 figures

According to the classic Galam model of opinion dynamics, each agent participates at each update of an opinion interaction. While the scheme gives everyone the same chance to in- fluence others, in reality, social activity and influence vary considerably from one agent to another. To account for such a feature, we introduce a new individual attribute – ‘‘active- ness’’ – which makes some agents more inclined than others at engaging in local discus- sions. To enhance the corresponding effect, opinion updates are shifted from all-out agent interaction cycles to few agent interaction cycles. Using dynamic analysis and simulations the resulting model is found to exhibit a ‘‘Minority Counteroffensive’’ phenomenon, which under some initial conditions makes the minority to win the opinion competition despite a threshold tipping point at fifty percent. The associated probabilistic phenomenon persists in the case ‘‘activeness’’ is held equal for all agents. The effect of ‘‘opinion leaders’’ is also investigated. Indeed, a leader is an inflexible agent, i.e., an agent who does not change opin- ion. The results reveal that two opinion leaders with moderate social influence may have a stronger effect than one opinion leader with a strong social influence. The model may shed a new light to the understanding of opinion formation and public voting.

We present in this paper an approximation that is able to give an analytical expression for the exit probability of the $q$-voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large networks [A. M. Timpanaro and C. P. C. do Prado, Phys. Rev. E 89, 052808 (2014)] and as such departs from the expression $\frac{{\ensuremath{\rho}}^{q}}{{\ensuremath{\rho}}^{q}+{(1\ensuremath{-}\ensuremath{\rho})}^{q}}$ found in papers that investigated small networks only [R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); P. Przyby\l{}a et al., Phys. Rev. E 84, 031117 (2011); F. Slanina et al., Europhys. Lett. 82, 18006 (2008)]. The approximation consists in assuming a large separation on the time scales at which active groups of agents convince inactive ones and the time taken in the competition between active groups. Some interesting findings are that for $q=2$ we still have $\frac{{\ensuremath{\rho}}^{2}}{{\ensuremath{\rho}}^{2}+{(1\ensuremath{-}\ensuremath{\rho})}^{2}}$ as the exit probability and for $qg2$ we can obtain a lower-order approximation of the form $\frac{{\ensuremath{\rho}}^{s}}{{\ensuremath{\rho}}^{s}+{(1\ensuremath{-}\ensuremath{\rho})}^{s}}$ with $s$ varying from $q$ for low values of $q$ to $q\ensuremath{-}\frac{1}{2}$ for large values of $q$. As such, this work can also be seen as a deduction for why the exit probability $\frac{{\ensuremath{\rho}}^{q}}{{\ensuremath{\rho}}^{q}+{(1\ensuremath{-}\ensuremath{\rho})}^{q}}$ gives a good fit, without relying on mean-field arguments or on the assumption that only the first step is nondeterministic, as $q$ and $q\ensuremath{-}\frac{1}{2}$ will give very similar results when $q\ensuremath{\rightarrow}\ensuremath{\infty}$.