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We review a model of sociophysics which deals with democratic voting in bottom up hierarchical systems. 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 frame- work. Using this model a real political event was successfully predicted with the victory of the French extreme right party in the 2000 first round of French presidential elections. The perspectives and the challenges to make sociophysics a predictive solid field of science are discussed.

We study the relations between strategies in game theory and the conformity. The latter is a behavior deemed relevant in social psychology and, as shown in several works, it strongly influences many social dynamics. We consider a population of agents that evolves in accordance with a payoff matrix which embodies two main strategies: cooperation and defection. In particular, agents play a game (e.g., the Prisoner’s Dilemma) by choosing between these two strategies, in order to increase their payoff, i.e., their gain. During the evolution of the system, agents can change strategy according to an update rule, i.e., they can play sometimes as cooperators and sometimes as defectors. Usually, rules to update the strategy are driven by the payoffs of the neighbors of each agent. For instance, an agent imitates its best neighbor, i.e., the one having the highest payoff among the other neighbors. In this context, ‘imitation’ means to adopt the strategy of another agent. In order to study if and how the emergence of cooperation can be affected by a social influence, we provide agents with two different behaviors, i.e., conformity and nonconformity, they use to select their strategy. Numerical simulations show that conformity strongly affects these dynamics, as cooperation emerges in the population, even under conditions of the games that usually lead, almost all agents, to play as defectors.

The emergence and spreading of “extreme opinions” are studied in networks with agents sharing mild opinions. The turning extreme shift is driven by social group meetings. The extremization process is apprehended according to the social psychology phenomenon of group polarization and illustrated in the case of terrorism. In particular the focus is on the dynamics of emergence of “passive supporters” from which terrorists can then be recruited. Becoming a passive supporter being considered as taking an extreme opinion, group polarization is shown to play an important role for increasing the transition probabilities from mild opinion (e.g., anti-western feeling) to its extreme form (e.g., passive supporter or terrorist). Accordingly a simple agent-based model is defined to implement interactions among agents on networks. Three opinions are considered, pro-western opinion, anti-western opinion and extreme anti-western opinion. The latter may lead people to become passive supporters and, potentially, terrorists. Results of simulations show that a substantial fraction of anti-western agents adopt the extreme opinion exhibiting an emergent phenomenon which may shed some new light on real social phenomena of political violence.

Recent years have witnessed the increasing interest of physicists, mathematicians and computer scientists for socio-economic systems. In our view, the many reasons behind this can be summarized by observing that traditional approaches to disciplines as sociology and economics have dramatically shown their limitations.

The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature T(c1) to embody the total landscape of initial conditions at a second critical temperature T(c2), with T(c1)≈1.59 and T(c2)≈2.11 in J/k(B) units. It appears that T(c2) is close to the Onsager result T(c)≈2.27. The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at T(c2), reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at T(c)≈3.09. Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed.

Galam reshuffling introduced in opinion dynamics models is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature T_C \approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different from both values, not reshuffled (T_C=2/arcsinh(1) \approx 2.27 [J/k_B]) and mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as function of 0 \leq p \leq 1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of T_C as function of p is obtained and exhibits a non-linear behavior. The simplest Solomon network realization is noted to reproduce Galam p=1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean-field values., 11 pages, 5 figures in 6 eps files, to appear in IJMPC

We present a general sequential probabilistic frame, which extends a series of earlier opinion dynamics models. In addition, it orders and classifies all of the existing two-state spin systems. The scheme operates via local updates where a majority rule is applied differently in each possible configuration of a local group. It is weighted by a local probability which is a function of the local value of the order parameter, i.e., the majority-to-minority ratio. The system is thus driven from one equilibrium state into another equilibrium state till no collective change occurs. A phase diagram can thus be constructed. It has two phases, one where the collective opinion ends up broken along one opinion, and another with an even coexistence of both opinions. Two different regimes, monotonic and dampened oscillatory, are found for the coexistence phase. At the phase transition local probabilities conserve the density of opinions and reproduce the collective dynamics of the Voter model. The essential behavior of all existing discrete two-state models (Galam, Sznajd, Ochrombel, Stauffer, Krapivsky-Redner, Mobilia-Redner, Behera-Schweitzer, Slanina-Lavicka, Sanchez ...) is recovered and found to depart from each other only in the value of their local probabilities. Corresponding simulations are discussed. It is concluded that one should not judge from the above model results the validity of their respective psycho-social assumptions.

We generalize Galam's model of opinion spreading by introducing three competing choices. At each update, the population is randomly divided in groups of three agents, whose members adopt the opinion of the local majority. In the case of a tie, the local group adopts opinion A, B or C with probabilities alpha, beta and (1-alpha-beta) respectively. We derive the associated phase diagrams and dynamics by both analytical means and simulations. Polarization is always reached within very short time scales. We point out situations in which an initially very small minority opinion can invade the whole system., To appear in European Physical Journal B. A few errors corrected, some figures redrawn from the first version

The origins of Sociophysics are discussed from a personal testimony. I trace back its history to the late seventies. My twenty 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., 7 pages, no figure, Proceedings of the XVIII Max Born Symposium on Statistical Physics outside Physics, Ladek, Poland, September 2003

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.

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 a c = 1 6 , 0.23, 0.30… 1 2 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.

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 don't 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., 17 pages, 7 figures, Proceedings of the International Workshop Randomness And Complexity in honor of Shlomo Havlin's 60th birthday held in January 2003, Eilat, Israel

The recent astonishing wide adhesion of french people to the rumor claiming `No plane did crash on the Pentagon on September the 11", is given a generic explanation in terms of a model of minority opinion spreading. Using a majority rule reaction-diffusion dynamics, a rumor is shown to invade for sure a social group provided it fulfills simultaneously two criteria. First it must initiate with a support beyond some critical threshold which however, turns out to be always very low. Then it has to be consistent with some larger collective social paradigm of the group. Othewise it just dies out. Both conditions were satisfied in the french case with the associated book sold at more than 200 000 copies in just a few days. The rumor was stopped by the firm stand of most newspaper editors stating it is nonsense. Such an incredible social dynamics is shown to result naturally from an open and free public debate among friends and colleagues. Each one searching for the truth sincerely on a free will basis and without individual biases. The polarization process appears also to be very quick in agreement with reality. It is a very strong anti-democratic reversal of opinion although made quite democratically. The model may apply to a large range of rumors.

The dynamics of majority rule voting in hierarchical structures is studied using concepts from collective phenomena in physics. In the case of a two-party competition a very simple model to a democratic dictatorship is presented. For each running group, a critical threshold (in the overall support) is found to ensure full and total power at the hierarchy top. However, the respective value of this threshold may vary a lot from one party to the other. It is this difference which creates the dictatorian nature of the democratic voting system. While climbing up the hierarchy, the initial majority-minority ratio can be reversed at the profit of actual running party. Such a reversal is shown to be driven by the natural inertia of being in power. The model could shed light on last century Eastern European Communist collapse.

A model of the dynamics of appearance of a new collective feeling, in addition and opposite to an existing one, is presented. Using percolation theory, the collective feeling of insecurity is shown to be able to coexist with the opposite collective feeling of safety. Indeed this coexistence of contradictory social feelings result from the simultaneous percolation of two infinite clusters of people who are respectively experiencing a safe and unsafe local environment. Therefore opposing claims on national debates over insecurity are shown to be possibly both valid.

Coalition forming is investigated among countries, which are coupled with short range interactions, under the influence of externally-set opposing global alliances. The model extends a recent Natural Model of coalition forming inspired from Statistical Physics, where instabilities are a consequence of decentralized maximization of the individual benefits of actors. In contrast to physics where spins can only evaluate the immediate cost/benefit of a flip of orientation, countries have a long horizon of rationality, which associates with the ability to envision a way up to a better configuration even at the cost of passing through intermediate loosing states. The stabilizing effect is produced through polarization by the global alliances of either a particular unique global interest factor or multiple simultaneous ones. This model provides a versatile theoretical tool for the analysis of real cases and design of novel strategies. Such analysis is provided for several real cases including the Eurozone. The results shed a new light on the understanding of the complex phenomena of planned stabilization in the coalition forming.

The dynamics of opinion about the controversy of abnormal death of bees is studied among French speaking journalists using a corpus of 1467 articles published in newspapers during the period 1998–2010. From a systematic textual analysis, each article is tagged to either one of three stances to explain the phenomenon, a uni-factor cause, namely the use of pesticides, a multi-factor cause, or the absence of an understanding. On this basis, evolutions of the respective proportions of each category are obtained over the 13 consecutive years, exhibiting a series of broken lines. Assuming journalists are either flexible or inflexible about their respective views, their associated proportions are extracted from the data applying Galam Unifying Frame (GUF) of opinion dynamics. The variation of inflexibles along each view is thus obtained as a function of years for the 13 years of the corpus. From those distributions the possible pressure applied on journalists from lobbying or other externalities can be inferred. In addition, the results highlight the critical advantage gained by the first whistle-blowers and underline opinion inertia in the debate.

Controversial public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam Unifying Frame (GUF) of opinion dynamics . It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant the value of initial support. On the contrary focusing on open-minded agents may be useless given some topologies. Accordingly, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate. The cases of global warming is briefly discussed.

Majority rule voting in a multi-level system is studied using tools from the physics of disorder. We are not dealing with nation-wide general elections but rather with hierarchical organisations made of small committees. While in theory, for a two candidate election, the critical threshold to absolute power is , the usual existence of some local and reasonable bias makes it asymmetric, transforming a democratic system in effect to a dictatorship. The underlying dynamics of this democratic self-elimination is studied using a simulation which visualizes the full process. In addition the effect of non-voting persons (abstention, sickness, apathy) is also studied. It is found to have an additional drastic effect on the asymmetry of the threshold value to power. Some possible applications are mentioned.

The effect of majority rule voting in hierarchical structures is studied using the basic concepts from real space renormalization group. It shows in particular that a huge majority can be self-eliminated while climbing up the hierarchy levels. This majority democratic self-elimination articulates around the existence of fixed points in the voting flow. An unstable fixed point determines the critical threshold to full and total power. It can be varied from 50% up to 77% of initial support. Our model could shed new light on the last century eastern European communist collapse.

A new model of evolution is presented for finite size systems. Conditions under which a minority species can emerge, spread and stabilize to a macroscopic size are studied. It is found that space organization is instrumental in addition to a qualitative advantage. Some peculiar topologies ensure the overcome of the initial majority species. However the probability of such local clusters is very small and depend strongly on the system size. A probabilistic phase diagram is obtained for small sizes. It reduces to a trivial situation in the thermodynamic limit, thus indicating the importance of dealing with finite systems in evolution problems. Results are discussed with respect to both Darwin and punctuated equilibria theories.

The concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures. It is found that democratic voting can lead to totalitarianism by keeping in power a small minority. Conditions of this paradox are analyzed and singled out. Indeed majority rule produces critical thresholds to absolute power. Values of these thresholds can vary from 50% up to at least 77%. The associated underlying mechanism could provide an explanation for both former apparent eternity of communist leaderships as well as their sudden collapse., Comment: Proceedings of the NATO Advanced Research Workshop, Budapest (May 1999) Eds: A. Gadomski et al

A simple stochastic cellular automaton model is proposed for ripples and dunes formation. Saltation and avalanches are the unique ingredients of the model. The dynamics of ripple formation is found to be logarithmic in time while the ripple merging as well as the dune growth is faster and occurs by bursts. The ripple state turns out to be metastable.

A model of diluted random field sustained by quenched volume deformations is shown to reproduce puzzling physical features found in X(CN)_{x}Y_{1-x} mixed cyanide crystals. X is an alkali metal (K, Na or Rb) and Y is a spherical halogen ion (Br, Cl or I). Critical thresholds x_c at which associated first order ferroelastic transitions disappear are calculated exactly. The diluted random field is shown to compete with compressibility in making the transition first order. Transitions are then found to remain first order down to x_c except in the case of bromine dilution where they become continuous. All the results are in excellent agreement with available experimental data., Comment: 10 pages, latex

This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: "Upset" (U), "Violent" (V), "Sensitive" (S), "Immune" (I), and "Relaxed" (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed a new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent world violent events are discussed., Comment: 22 pages, 9 figures

Competing bimodal coalitions among a group of actors are discussed. First, a model from political sciences is revisited. Most of the model statements are found not to be contained in the model. Second, a new coalition model is built. It accounts for local versus global alignment with respect to the joining of a coalition. The existence of two competing world coaltions is found to yield one unique stable distribution of actors. On the opposite a unique world leadership allows the emergence of unstable relationships. In parallel to regular actors which have a clear coalition choice, ``neutral" ``frustrated" and ``risky" actors are produced. The cold war organisation after world war II is shown to be rather stable. The emergence of a fragmentation process from eastern group disappearance is explained as well as continuing western group stability. Some hints are obtained about possible policies to stabilize world nation relationships. European construction is analyzed with respect to european stability. Chinese stability is also discussed., 14 pages, latex, no figures, to appear in Physica A

The interplay between disorder and compressibility in Ising magnets is studied. Contrary to pure systems in which a weak compressibility drives the transition first order, we find from a renormalization group analysis that it has no effect on disordered systems which keep undergoing continuous transition with rigid random-bond Ising model critical exponents. The mean field calculation exhibits a dilution-dependent tricritical point beyond which, at stronger compressibility the transition is first order. The different behavior of XY and Heisenberg magnets is discussed., Comment: 16 pages, latex, 2 figures not included

This paper further develops a new theory of power advanced by the authors in two previous papers (Galam and Moscovici, 1991, 1994). According to this theory power results from the build up of conflicts within a group, these conflicts requiring a degree of organizational complexity which is itself a decreasing function of group size. Within this approach, power appears to be a composite of three qualitatively different powers, institutional, generative and ecological. Levels and relationships among these forms of power are considered as a function of the diversity of the group. There exist also three states of organization associated with power evolution. At the group initial stage is the paradigmatic state. Creation and inclusion of conflicts are accomplished in the transitional state through the building of complexity. At a critical value of diversity, the group moves into the agonal state in which institutional power vanishes simultaneously with the fusion of generative and ecological powers

We consider the phase diagram of two randomly coupled Ising models to mimic the successive phase transitions in plastic crystals. Detailed mean-field calculations are performed. Depending on the strength of the couplings, the phase diagrams display three ordered phases and some multicritical points. A tetracritical point is found to turn bicritical as the strength of the couplings increases. The nature of this multicritical point is then analyzed by means of a momentum-space renormalization-group calculation. Using the replica trick, we obtain an effective n-component spin Hamiltonian. The random coupling is found to be relevant and shown to have drastic effects on the multicritical behavior. The lower critical dimension is estimated to be ${\mathit{d}}_{\mathit{l}}$=2. In the n=0 limit, to first order in the parameter \ensuremath{\epsilon}=4-d, a system of seven recursion relations is obtained. Although there is a stable fixed point, it cannot be reached from physically acceptable initial conditions. We give arguments to support a runaway of the flow lines associated with a fluctuation-induced first-order transition.

Two models of opinion dynamics are entangled in order to build a more realistic model of inflexibility. The first one is the Galam Unifying Frame (GUF), which incorporates rational and inflexible agents, and the other one considers the combination of Continuous Opinions and Discrete Actions (CODA). While initially in GUF, inflexibility is a fixed given feature of an agent, it is now the result of an accumulation for a given agent who makes the same choice through repeated updates. Inflexibility thus emerges as an internal property of agents becoming a continuous function of the strength of its opinion. Therefore an agent can be more or less inflexible and can shift from inflexibility along one choice to inflexibility along the opposite choice. These individual dynamics of the building up and falling off of an agent inflexibility are driven by the successive local updates of the associated individual opinions. New results are obtained and discussed in terms of predicting outcomes of public debates., 16 pages, 7 figures

It is found that a simple renormalization scheme may apply to spin glasses, provided time is added to real space coordinates among scaling variables. The model suggests that the critical slowing in spin glasses results not from a hierarchy but from a diffusion process among eigenstates available to the spin system in phase space.

Using a very simple renormalized site percolation model, the rich phase diagram exhibited by ACNxMn1−x mixtures, where A stands for K, Na or Rb while Mn represents Br, Cl or I, is obtained as function of cyanide concentration, x. From a steric hindrance argument, some cyanides are found to be randomly frozen at low temperatures being thus prevented from propagating long range orientational order. Actual cyanide density x should then be divided into a frozen-in part, xf, and a free-to-reorient part, xr, making only the last term relevant to quadrupolar ordering. The first term xf can indeed be calculated from microscopic characteristics of the molecules involved. This leads to the existence of two critical thresholds, xc and xd. While the former is associated to the disappearance of the ferroelastic transition, the latter defines the concentration extension range for the existence of ferroelastic domains. When available, experimental data for the critical thresholds are in excellent agreement with our calculated values. Predictions are made for a large variety of mixtures.

A new theory of power is presented using the concept of symmetry breakdown in small and large groups. Power appears to result from the building up of conflicts within the group. Introduction and support of these conflicts requires an internal organization of the group. The organization-associated complexity is a decreasing function of group size. Thus small groups have more difficulties in generating internal conflicts than large ones. This group dynamic is characterized by two states which are different in their nature. The group is first built within the paradigmatic state aimed to determine and reproduce group conformity The group challenge is then to reach the transitional state which enriches the group possibilities through the inclusion and stabilization of internal conflicts.

This overview of my salient models of sociophysics exhibits the potential power of sociophysics with respect to a very large spectrum of social, political, economical, and strategic applications as seen in Fig. 11.1

The origins of Sociophysics are discussed from personal testimony. I trace back its history to the late 1970s. The first steps of my 30 years of activities and research to establish and promote the field are reviewed. In particular, the decades long strong opposition from the physics community is emphasized, together with the almost total absence of contributors. During these years of rejection, only a very few and scarce papers were published in the field. However, in the mid-1990s, quite suddenly the number of contributions started to increase.

The analogy, if any, between men and atoms is discussed to single out what can be the contribution from physics to the understanding of human behavior. The basic assumptions of the approach of sociophysics are formulated together with the methodology used to tackle a given problem taken from the social and political worlds [1, 2].

The use of bottom-up democratic voting in hierarchical structures was shown to produce some major and unexpected biases which in turn might drive toward the stable establishment of democratic dictatorships. However, this demonstration was performed in the case of two competing parties A and B.

That’s it; we have reached the end point of our journey through the wonderful world of sociophysics, which I hope, you have found beautiful and enlightening. It is time to say goodbye (see Fig. 18.1) but before parting, I would like to reassess the particularities of this book.

Although the question of the democratic legitimacy of leadership is not the main focus of this book, it is also included here to make the overview complete. Whatever is the political organization of a social, economic, or political group, hierarchies are present in most of the cases. Two main extreme hierarchies are found: authoritarian and democratic. In the first one, everything starts from the top and proceeds down towards the bottom while in the second case it is the reverse.

The democratic majority rule voting in democratic bottom-up hierarchical structures is shown to produce under certain conditions dictatorship effects by keeping a minority in power against a huge increase of the opposition. No coercion is necessary, only democratic voting. This result sheds new light in particular on the internal strength of former communist organizations. It also provides a scheme to assess the conditions by which a minority extremist group can quickly get into power by democratic means and without any intermediate step. In turn, it also defines the conditions by which to avoid such a danger.

While we have shown up several democratic advantages in the use of bottom-up voting hierarchies, we can now undertake the deconstruction of the “beautiful world of democracy” to account for some very specific and inherent features of human behavior, and in particular, spontaneous wise “cheating.”

From our current level of investigation of the use of majority rule voting in bottom-up hierarchical structures, we are now in a position to touch on one of the most fascinating features of the “life” of inert matter; the phase transition of a given system from one global organization into another. An example in matter would be going from a liquid to a gas or from a conductor to a super-conductor. The mechanisms at work in such a metamorphosis are universal, which means that they obey the same restricted set of laws whatever the physical nature of the matter undergoing the phase transition. The most salient signature of a phase transition is the divergence of the so-called correlation length.

In the study of group decision making, I introduce the Ising ferromagnetic model, which assumes that interactions amongst agents tend to align themselves along the same opinion. It is inspired from the existence of ferromagnetism in inert matter. However, nature is rather rich and usually covers the whole spectrum of symmetries. Therefore, anti-ferromagnetism, i.e., a material in which interactions force the coupled spins to be anti-parallel. Accordingly, it was natural to explore this feature and to introduce within the social models couplings amongst agents, which push them apart in regards to their respective choices.

In this chapter, I review the series of rather different models that I have been developing over the past three decades (1980–2010). They go in several directions, and focus on five different sociopolitical phenomena. To have these subjects accepted by the physics community was a long and tedious fight[1].

In order not to discourage any impatient readers, we outline here the main steps of our investigation together with some of the major findings [1–19]. It has to be read “a la maniere” of a research physical paper. In other words, not many details are given. Explanations are limited and no backward motivation is given. It should be an incentive to plunge into the heart of the work contained in the following chapters.

Anyone familiar with the so-called Ising ferromagnetic model of modern statistical physics would certainly be tempted to make a connection with the behavior of people. Its major feature relies on its incredible universality. Many situations in the world are governed by the emergence of a global order from local interactions. It has proven very powerful in explaining the properties of many different physical systems. It is therefore a very appealing universal model, which could certainly also apply to a large spectrum of social situations. Any book on statistical mechanics will provide an introduction to the Ising model. Among them, I recommend the books by Pathria, Reif, and Ma [1, 2, 3].

Another meaningful representation of the evolution of the respective proportions in voting for A and B agents is to draw the proportions p n as a function of n as shown in Fig. 14.1 for various sizes ofvoting groups as illustrated in the figure. Starting from a certain initial value p o , the series p1, p2,..., p n is plotted for several values of r. Increasing r reduces the number of levels necessary to reach the democratic balance within a fixed precision.

Dealing with terrorism is extremely delicate. Too much sorrow, passion, hate, and death are at stake. But that should not prevent us from trying to model the issue to try to single out its bare mechanisms and to eventually be able to curb its destructive capacity. The use of equations combined with what could look a priori like a simplistic viewpoint, but in fact is inspired from the physics of disorder, may indeed provide a new insight, which could eventually open unexpected paths to help in reducing terrorism. Any improvement is urged and should be welcomed. But modeling does not mean discovering the one and only “truth”. The problem is multi-fold, difficult, complex, emotional, and operated by archaic passions. This is precisely why the use of “nonhuman” frames and concepts could turn out to be quite productive in providing us with a different paradigm for encompassing the phenomenon, which may lead to useful solid steps in curbing terrorism.