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Serge Galam

Publications and source records attributed to Serge Galam.

At least 19 recordsLinked to original sources
arXiv2026

Contrarian Majority Dynamics: Violation of Detailed Balance and Nonequilibrium Steady States

I revisit the Galam Majority Model (GMM) with contrarian agents from a statistical-mechanics perspective, revealing three fundamental features. First, in addition to the GMM simultaneous-update of small discussion groups, I construct a related single-agent stochastic dynamics, providing a Markovian microscopic representation, which is found to yield the same evolution equation. Second, I show that, contrary to what is often stated in the literature, the GMM closed evolution equation for the opinion density is not the result of a mean-field approximation. Indeed, I derive the conventional mean-field dynamics associated with majority-rule interactions and show that it yields a distinct, probabilistic evolution equation contrary the deterministic GMM equation. I therefore identify the GMM as an iterated mean-field dynamics. Third, I investigate the thermodynamic nature of the dynamics obtained from both single-agent and simultaneous updates. Both are shown to violate detailed balance. However, while Kolmogorov's cycle condition is satisfied for single-agent updates, it is violated for simultaneous updates, making the departure from equilibrium stronger in the latter case. I then compute the probability flux in the stationary state and show that it is non-vanishing, confirming the absence of an effective Hamiltonian and establishing that the stationary state is a genuine nonequilibrium steady state.These results clarify the statistical-mechanical foundations of the GMM and establish contrarian majority dynamics as an intrinsically non-equilibrium process with distinct regimes of irreversibility. Contrarians are not thermal noise.

cond-mat.stat-mech↗
arXiv2026

Ratio-Dependent Contrarian Activation in Opinion Dynamics

I study the impact of mixed contrarians on the opinion dynamics of an heterogenous population with conformists using Galam Majority Model. Activation of contrarians is a function of the ratio majority/minority in the local groups of discussion. Restricting the group size to 3, two types of contrarians are included in respective proportions $c_{3,0}$ for configurations with ratio 3 to 0 and $c_{2,1}$ for ratio 2 to 1. I then derive the explicit update Equation and obtained analytically the fixed points, their stability, and the resulting full two-dimensional landscape of the dynamics of opinion. Setting $c_{3,0} =c_{2,1} = c$ recovers the original results obtained with uniform contrarians. The findings allow for considering a wide spectrum of new disruptive strategies to secure either a majority/minority ending ensuring the opinion having the larger initial support to win, or a single attractor dynamics at fifty/fifty, which implies a random winner regardless of initial supports.

physics.soc-ph↗
arXiv2026

Two stroke Pumping Technique for Many-Body Systems

I introduce a new analytical framework for estimating critical temperatures in interacting many-body systems, focusing on the Ising model. Combining the Bethe cluster setting, the Metropolis update, and the Galam Majority Model developed in sociophysics, I build a two stroke pumping technique (TSP). Applied to the Ising model in dimensions d=2, 3, 4, TSP yields values of T_c which are all at an excess of +0.03 from exact estimates. At d=1 the exact value T_c=0 is obtained. In addition, TSP indicates analytically the practical impossibility to reach full symmetry breaking at T=0. The results are thus found in good agreement with numerical findings while requiring significantly fewer computational resources than Monte Carlo sampling. Calculations are computationally efficient and transparent. The framework is general and can be extended to a broad class of discrete spin models. This positions TSP as an intermediate yet scalable tool for studying cooperative behavior in many body interacting systems.

cond-mat.stat-mech↗
arXiv2025

Spontaneous Symmetry Breaking, Group Decision Making and Beyond 2. Distorted Polarization and Vulnerability

This paper extends previous work on echo chambers modeled by an Ising-like system at zero temperature (1. Echo Chambers and random Polarization, Symmetry 2024, 16(12), 1566). There, polarization emerged as a spontaneous symmetry-breaking process with a randomly selected direction. Here using a mean-field analysis and Monte Carlo simulations I show that this mechanism is highly vulnerable to minimal distortions. An external symmetry-breaking field, even vanishingly small, suffices to impose a global direction and suppress opposite domains, producing distorted full polarization. In contrast, a handful of quenched local fields with zero average do not erase polarization but reorganize it into opposing domains. Remarkably, as few as two opposed fields, if placed at tipping sites, can redirect the entire system. These fragile sites, indistinguishable from others, act as hidden tipping points that amplify microscopic biases into macroscopic outcomes. Difference in local field proportions is found to be instrumental to guarantee a winning majority. The results highlight how minimal, strategically placed interventions can override autonomous self-organization. The results could, if applicable on social media platforms, question their presumed democratic nature of consensus.

physics.soc-ph↗
arXiv2025

Ambiguities, Built-in Biases and Flaws in Big Data Insight Extraction

I address the challenge of extracting reliable insights from large datasets using a simplified model that illustrates how hierarchical classification can distort outcomes. The model consists of discrete pixels labeled red, blue, or white. Red and blue indicate distinct properties, and white represents unclassified or ambiguous data. A macro-color is assigned only if one color holds a strict majority among the pixels. Otherwise, the aggregate is labeled white, reflecting uncertainty. This setup mimics a percolation threshold at fifty percent. Assuming direct access of the various proportions of colors is infeasible from the data, I implement a hierarchical coarse-graining procedure. Elements (first pixels, then aggregates) are recursively grouped and reclassified via local majority rules, producing ultimately a single super-aggregate whose color represents the inferred macro-property of the collection of pixels as a whole. Analytical results, supported by simulations, show that the process introduces additional white aggregates beyond white pixels, which could be initially present. These arise from groups lacking a clear majority, requiring arbitrary symmetry-breaking decisions to attribute a color to them. While each local resolution may appear minor and inconsequential, their repetitions introduce a growing systematic bias. Even with complete data, unavoidable asymmetries in local rules are shown to skew outcomes. This study highlights a critical limitation of recursive data reduction. Insight extraction is shaped not only by data quality, but by how local ambiguity is handled. That results in built-in biases. Thus, the related flaws are not due to the data, but due to structural choices made during local aggregations. Though based on a simple model, the findings expose the high likelihood of inherent flaws in widely used hierarchical classification techniques.

physics.soc-ph↗
arXiv2025

Democratic Thwarting of Majority Rule in opinion dynamics: 1. Unavowed Prejudices versus Contrarians

I study the conditions under which a democratic dynamics of a public debate drives a Minority-to-Majority transition. A landscape of the opinion dynamics is thus built using the Galam Majority Model (GMM) in a 3-dimensional parameter space for three different sizes r=2, 3, 4 of local discussing groups. The related parameters are (p_0, k, x), the respective proportions of initial agents supporting opinion A, unavowed tie prejudices breaking in favor of opinion A, and contrarians. Combining k and x yields unexpected and counterintuitive results. In most part of the landscape the final outcome is predetermined with a single attractor dynamics independently of the initial supports for the competing opinions. Large domains of (k, x) values are found to lead an initial minority to turn majority democratically without any external influence. A new alternating regime is also unveiled in narrow ranges of extreme proportions of contrarians. The findings indicate that the expected democratic character of free opinion dynamics is indeed rarely satisfied. The actual values of (k, x) are found to be instrumental to predetermine the final winning opinion. Therefore, the conflicting challenge for the predetermined opinion to loose, is to modify these values appropriately to become the winner. However, developing a model which could help manipulating public opinion rises ethical questions. The issue is discussed in the conclusion.

physics.soc-ph↗
arXiv2024

Spontaneous Symmetry Breaking, Group Decision Making and Beyond 1. Echo Chambers and Random Polarization

Starting from a symmetrical multiple choice individual I build a sociophysics model of decision making. Reducing the choices to two and interactions to pairs recover the Ising model from physics at zero temperature. The associated equilibrium state is a spontaneous symmetry breaking with the whole group sharing a unique choice selected at random. However, my focus departs from physics, which aims at identifying the true equilibrium state discarding any possible impact of the initial conditions, the size of the sample and the used update algorithm. Any memory of the past history is erased. In contrast, I claim that dealing with a social system, the history of the system must be taken into account in identifying the relevant social equilibrium state. Using Monte Carlo simulations I explore the spectrum of non universal equilibrium states of the Ising model at zero temperature. I show that different initial conditions with the same value of the order parameter lead to different equilibrium states. The same applies for different sizes and different update algorithms. The results indicate that in the presence of a social network composed of agents sharing different initial opinions, it is their interactions that lead them to share a unique choice and not their mere membership in the network. This finding sheds a new light on the emergence of echo chambers, which appear to be the end of a dynamical process of opinion update and not its beginning with a preferential attachment. Furthermore, polarization is obtained as a side effect of the random selection of the respective unanimous choices of the various echo chambers within a social community. The study points to social media exchange algorithms, which are purely technical levers independent of the issue and opinions at stake, to tackle polarization by either hindering or accelerating the completion of symmetry breaking between agents.

physics.soc-ph↗
arXiv2024

Asymmetric games on networks: mapping to Ising models and bounded rationality

We investigate the dynamics of coordination and consensus in an agent population. Considering agents endowed with bounded rationality, we study asymmetric coordination games using a mapping to random field Ising models. In doing so, we investigate the relationship between group coordination and agent rationality. Analytical calculations and numerical simulations of the proposed model lead to novel insight into opinion dynamics. For instance, we find that bounded rationality and preference intensity can determine a series of possible scenarios with different levels of opinion polarization. To conclude, we deem our investigation opens a new avenue for studying game dynamics through methods of statistical physics.

physics.soc-ph↗
arXiv2024

Measuring the Subjective Passage of Time

I address the question of measuring the subjective perception of the passage of time at the individual level in relation to its objective duration using a physicist-type treatment. A simple model is thus built in terms of a very small number of equations, which is found to yield a quantitative framework for individual subjective perception of time. Given an objective unit of time like the year, the hypothesis is to introduce a subjective unit of time for each person, which is inversely proportional to the number of objective units already experienced by that person. A power law is also considered. The model is then implemented by stacking individual clocks, each being linked to social rituals, which mark and shape the specific time of an individual throughout their life. For each person, the first of these events is their own birth. A future horizon, as well as an origin of the past, are then defined, along with a speed of subjective passage of time. The model shows that the price for the first ritualized socialization is to exit eternity in terms of a future to be lived with the simultaneous reward of experiencing a moment of infinity analogous to that of birth. The results recover common feelings about the passage of time over a lifetime. In particular, the fact that time passes more quickly with age.

physics.soc-ph↗
arXiv2024

Fake news: No ban, No spread -- with Sequestration

Fake news is today a major threat to free and democratic making of public opinion. To curb their spread, all efforts by institutions and policy makers rely mainly on imposing restriction, prohibition and fact checking sites, which end up to an effective limitation of freedom of speech. This policy of prohibition, supported by a wide consensus, has been recently broken by the controversial policy applied by Elon Musk to regulate the social media X, with a backlash accusing him of promoting hate speech. Here, notwithstanding these two policies, I explore another avenue denoted ``No ban, No spread - with Sequestration", which amounts at the same time preserving full freedom of speech and neutralization of fake news impact. To investigate the feasibility of my proposal, I tackle the issue within the Galam model of opinion dynamics. In addition to the basic ingredients of the model, I explore for the first time the effect on the dynamics of opinion of a simultaneous activation of prejudice tie breaking and contrarian behavior. The results show that indeed most pieces of fake news do not propagate beyond small groups of people and thus pose no global threat. However, I have unveiled some peculiar sets of parameters for which fake news, even if initially shared by only a handful of agents, spreads ``naturally" to invade a whole community with no resistance. Based on these findings, I am able to outline a path to neutralize such invasive fake news by blocking "naturally" its spread, effectively sequestering it in very small social networks of people. The scheme relies on reshaping the social geometry of the landscape in which fake news evolves. No prohibition is required with fake news left free to prosper but being sequestrated. Next challenging step will be designing measures to implement the model's findings into the real world of social media.

physics.soc-ph↗
arXiv2023

Contrarian Majority rule model with external oscillating propaganda and individual inertias

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda, in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with other three random agents and takes the majority opinion among the agents with probability $p(t)$ (majority behavior) or the opposite opinion with probability $1-p(t)$ (contrarian behavior). The probability of following the majority rule $p(t)$ varies with the temperature $T$ and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as $T$ is varied. A transition temperature $T_c$ separates a bimodal oscillatory regime for $T T_c$ in which $m$ oscillates around zero. These regimes are characterized by the distribution of residence times that exhibits a unique peak for a resonance temperature $T^*$, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that $T^*$ and $T_c$ are closely related.

physics.soc-ph↗
arXiv2023

Unanimity, Coexistence and Rigidity: Three Sides of Polarization

Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant democratic society, namely the open and informal discussions among agents. Indeed, within a homogeneous social community with floaters, the dynamics leads gradually toward unanimity (zero entropy). Polarization can eventually appear as the juxtaposition of non-mixing social groups sharing different prejudices about the issue at stake. On the other hand, the inclusion of contrarian agents produces a polarization within a community that mixes when their proportion $x$ is beyond a critical value $x_c=\frac{1}{6}\approx 0.167$ for discussing groups of size 3 and 4. Similarly, the presence of stubborn agents produces also a polarization of a community that mixes when the proportion of stubborns is greater than some critical value. For equal proportions of stubborns $a$ along each opinion, $a_c=\frac{2}{9}\approx 0.22$ for group size 4 against $a_c=\frac{1}{4}= 0.25$ for group size 3. However, the evaluation of the proportion of individual opinion shifts at the attractor $\frac{1}{2}$ indicates that the polarization produced by contrarians is fluid with a good deal of agents who keep shifting between the two opposed blocks (high entropy). That favors a coexistence of opposite opinions in a divided community. In contrast, the polarization created by stubborn agents is found to be frozen with very few individuals shifting opinion between the two opinions (low entropy). That yields a basis for the emergence of hate between the frozen opposed blocks.

physics.soc-ph↗
arXiv2023

Identifying a would-be terrorist: An ineradicable error in the data processing?

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.

physics.soc-ph↗
arXiv2022

Sociophysics: a new approach of sociological collective behaviour. I. Mean-behaviour description of a strike

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.

physics.soc-ph↗
arXiv2022

Opinion Dynamics and Unifying Principles: A Global Unifying Frame

I review and extend the set of unifying principles, which allow comparing all models of opinion dynamics within one single frame. Within the Global Unifying Frame (GUF), any specific update rule chosen to study opinion dynamics for discrete individual choices is recast into a probabilistic update formula. The associated dynamics is deployed using a general probabilistic sequential process, which is iterated via the repeated reshuffling of agents between successive rounds of local updates. The related driving attractors and tipping points are obtained with non-conservative regimes featuring both threshold and threshold-less dynamics. Most stationary states are symmetry broken, but fifty-fifty coexistence may also occur. A practical procedure is exhibited for several versions of Galam and Sznajd models when restricted to the use of three agents for the local updates. Comparing these various models, some are found to be identical within the GUF. Possible discrepancies with numerical simulations are discussed together with the difference between the GUF procedure and a mean field approach.

physics.soc-ph↗
arXiv2022

Physicists, Non Physical Topics, and Interdisciplinarity

Defining interdisciplinary physics today requires first a reformulation of what is physics today, which in turn calls for clarifying what makes a physicist. This assessment results from my forty year journey arguing and fighting to build sociophysics. My view on interdisciplinary physics has thus evolved jumping repeatedly to opposite directions before settling down to the following claim: today physics is what is done by physicists who handle a problem the "physicist's way". However the training of physicists should stay restricted to inert matter. Yet adding a focus on the universality of the physicist approach as a generic path to investigate a topic. Consequently, interdisciplinary physics should become a cabinet of curiosities including an incubator. The cabinet of curiosities would welcome all one shots papers related to any kind of object provided it is co-authored at least by one physicist. Otherwise the paper should uses explicitly technics from physics. In case a topic gets many papers, it would be moved to the incubator to foster the potential emergence of a new appropriate subfield of physics. A process illustrated by the subsection social physics in Frontiers in physics.

physics.soc-ph↗
arXiv2022

Deviations from the Majority: A Local Flip Model

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.

physics.soc-ph↗
arXiv2022

Radicalism: The asymmetric stance of Radicals versus Conventionals

We study the conditions of propagation of an initial emergent practice qualified as extremist within a population adept at a practice perceived as moderate, whether political, societal or religious. The extremist practice is carried by an initially ultra-minority of Radicals (R) dispersed among Conventionals (C) who are the overwhelming majority in the community. Both R and C are followers, that is, agents who, while having arguments to legitimize their current practice, are likely to switch to the other practice if given more arguments during a debate. The issue being controversial, most C tend to avoid social confrontation with R about it. They maintain a neutral indifference assuming it is none of their business. On the contrary, R aim to convince C through an expansion strategy to spread their practice as part of a collective agenda. However, aware of being followers, they implement an appropriate strategy to maximize their expansion and determine when to force a debate with C. The effect of this asymmetry between initiating or avoiding an update debate among followers is calculated using a weighted version of the Galam model of opinion dynamics. An underlying complex landscape is obtained as a function of the respective probabilities to engage in a local discussion by R and C. It discloses zones where R inexorably expand and zones where they get extinct. The results highlight the instrumental character of above asymmetry in providing a decisive advantage to R against C. It also points to a barrier in R initial support to reach the extension zone. In parallel, the landscape reveals a path for C to counter R expansion pushing them back into their extinction zone. It relies on the asymmetry of C being initially a large majority which puts the required involvement of C at a rather low level.

physics.soc-ph↗