Modeling social interactions

Author : Lassaad El Asmi*

* Lassaad El Asmi is Professor of Applied Mathematics, President of the University of Carthage (2011-2017).

This paper presents a study of social interactions based on thermodynamic considerations, in the spirit of providing a general theory of the group. Social interactions are seen in terms of the evolution and adaptation of the human species to its environment. A thesis on the formation of oligarchies is presented by various illustrations and based on the theory of dissipative structures as developed by I. Prigogine. The oligarchy is here coupled with notions of domination, conformism and influences in the group. The example of the social dynamics in Tunisia is presented at the end of the article, with an attempt to explain the phenomena in progress.

Key words : Oligarchy, modeling, social groups, dissipative structure.


In our social life, we are confronted with phenomena that are often repeated and which, each time, surprise us without wondering if these phenomena would not ultimately be natural. It turns out that when a group is composed of individuals who are bound by a common interest, that group does not remain in the initial state in which it was formed. Quite quickly a subgroup stands out to manage its affairs. There is not a class at school that is not dominated by a small group of students, a sports team, where a few players stand out to lead the team. There is no association or organization, intended to be unstructured, that is not ultimately guided by a minority. In any prison, life between prisoners is governed by very strict rules in which a relationship of domination is established and respected without blemish or severe reprisals.

The observations [1] show that the functioning of every social cell generates relationships of influence and conformity and the emergence of a dominant minority of individuals. This minority relies on the resources developed by all individuals to position themselves in such a way as to gather all powers. Those who form this minority are thus placed as leaders to exert their influence and impose their authority on the whole group. They are then seen as representatives of authority. Each member of the rest of the group then becomes a target and receiver of influence. There is no other choice for him than the acceptance of fait accompli or rejection, that is, conformity or refusal. The refusal implies isolation from the group or its exclusion. Once established, this relationship will settle in only one direction, influence of the dominant over the dominated. The social cell thus creates leaders who distinguish themselves from the masses and come out of its influence.
These relations of domination, conformity, submission and war of positions, govern social relations, they govern the world. It seems that the need to dominate, to create a hierarchy, is a matter of instinct in human beings and in animals [2], [3]. Indeed, the human species is not the only species to organize in a hierarchical group. For most animal species, there are dominant and dominated. The work of Thorleif Schjelderup-Ebbe (1920) shows that “at the beginning the chickens fight with each other to determine who will eat first. After a few days, the aggressive behavior decreases considerably. It is then enough for the one who emerges victorious of the first battles to make a small gesture of the head so that the other chickens leave him the free way “[4]. “The Maylandiae zebrae are fishes of the cichlid family that live in Lake Malawi. They present a clear hierarchy “[4]. The hierarchy of groups established during the development of species seems necessary for the survival of groups. This hierarchy is exercised between individuals within a group or between groups themselves. Social groups can be explicit such as organizations, associations, states or implicit, defined by a common characteristic, such as the rich and the poor, urban and rural, members of a trade and others, etc. [5]

The oligarchies:

This phenomenon of the domination of the minority over the whole has been the subject of several studies and publications. This minority is called “oligarchy” [6], [7], [8]. The oligarchy is the distinction of a small group, within a group of people, which is placed or placed by itself in a hierarchical manner in relation to the whole. It can be an institution, an organization, a state or any population of individuals that we will call social group. This oligarchy distinguishes a dominant class for the social group that transforms horizontal relationships between individuals as “democracy” would want in vertical relationships between individuals and that minority. The word is often associated with the absence of democracy or the absence of the state in a country. The phenomenon is however more general. Any social structure, whatever its size, is likely to develop an oligarchy.

The world oligarchies:

Effects of influence and domination on a world scale exist and seem to have always existed. Whatever the historical period, the world’s populations have always been dominated by communities, even very hierarchical.
Today, apart from the dominant institutional oligarchies that make up the world’s powers, such as the United States, China and Russia, it is becoming increasingly common to hear about lobbies influencing the policies of countries, the media and weighing on strategic choices. We are talking about shadow people who are involved in the governance of countries, we talk about parallel powers that are carried out within non-governmental organizations, financial institutions and mega-corporations. They are criticized for influencing countries’ policies, manipulating the media, directing debates and influencing the course of business in the world. These phenomena seem to be growing today, although this mode of operation is not recent. These questions are now being raised with insistence, it is probably because of the financial crisis that is disrupting global relations and the phenomenon of the explosion of information technologies. What is happening in one part of the globe is diffused instantaneously throughout the planet. Information circulates, even those that only circled in closed circles or were classified as secret. With different social networks, different Blogs, the Wikileaks site, Youtube channels and various media, no more information can be hidden. On the contrary, we are overwhelmed with information, which must be disentangled and dissected in order to perceive its meaning. It is becoming more and more difficult to silence the real functioning of business in the world, to silence the anomalies or inequalities that exist here and there. For example, inequalities in the distribution of wealth where 20% of the richest people in the world would monopolize more than 94% of the world’s wealth and 80% of the world’s population would share 5.5% of the world’s heritage. We also know that the race for wealth benefits only an overwhelming minority [9]. This race, which involves the exploitation of nature and man and which leads to the destruction of the world’s resources, does not benefit the entire world population, but the dominant minorities. It is a race which on the world scale responds to the same principles of hierarchization of social groups, which are observable at the level of individuals. It is also shown that the representative mode of governance in all the States of the world is not really the expression of the population but of the groups of influences that hold the wealth and the keys to the economy. Martin Gilens et al. [10] show by a statistical study that the majority does not govern in the United States. On the contrary, economic elites and organized groups representing financial interests have the greatest impact on US government policy. In Latin America, the notion of oligarchy is part of the political vocabulary [11], “graofino” in Brazil, “rosca” in Bolivia, “oligarquia” in Peru. The Latin American oligarchy operates as a closed and welded clan, completely separated from the masses. “The Latin American oligarchy thus appears as a rigidly closed elite, a” clan, “a clique (…), and this elite is unproductive, not only greedy and gluttonous, but sterile, and to borrow from Saint-Simon its famous antithesis, between hornets and bees, it is composed only of consumers, of jouissance, who live off the work of the exploited “masses.” “[11]. South Africa is an example where the country seems to be under the influence of a particularly powerful Indian industrial group [12].
This can easily be extrapolated to the majority of the countries of the globe. The world is governed by informal oligarchies.

Airain law of the oligarchy [13]: “[…] The so-called organization is a tendency to oligarchy. In every organization, whether it be a party, a union of trade, etc., the aristocratic tendency manifests itself in a very pronounced manner. The mechanism of organization, at the same time as it gives it a solid structure, causes serious changes in the organized mass. He completely reversed the respective positions of the chiefs and the masses. The effect of the organization is to divide any party or trade union into a ruling minority and a controlled majority. “

Modeling the oligarchy:

It is proposed here to study these phenomena which appear in the context of social life, to understand the intrinsic mechanisms that lead to the hierarchization of groups and the appearance of an oligarchy. These phenomena of social behavior, which occur within the dynamics of groups and which are otherwise well described by psychosociology [1], seem to have scientific interpretations. Social conformity is a phenomenon described by the experience of psychologist Solomon Asch [14]. Ash shows that the influence of the entourage on the individual pushes him to respect the norms established for the sake of affiliation to the group. This concern for belonging to the group would respond to the same mechanism that leads spiders to live in colony [15], driven by the survival instinct. Milgram [16] also shows the power of authority over the individual.

The experience of Salomon Asch (1956-1971) [17]

It demonstrates the tendency of the human being to conform to the opinion of a group. In this experiment, a test of visual perception is announced to the guinea pig, and he does not know that he participates in it alongside 7 actors. Each one is asked to compare a line segment with 3 other segments and find which one has the same length as the first. The actors all give the same wrong answer, the guinea pig quickly ranks with them, disturbed to be the only one to give another answer (yet the right one!). With false answers given unanimously and consistently, 33% of guinea pigs conform to the group’s answers, going against their own perception. Thus, 33% of our behavior is conformist in nature.

The Stanley Milgram experiment (1956-1974) [18]

It demonstrates the tendency of the human being to submit to authority. In this experiment, we consider 3 individuals, the monitor (naive subject of the experiment), the pupil, an accomplice actor of the Professor and the authoritative Professor, recognized and accepted by the subject. The student is placed on a chair with straps on the arm and an electrode on the wrist. He must learn a list of pairs of words; the errors will be sanctioned by electric discharges of increasing intensity. The teacher then invites the instructor to pass the learning test. When the answer is correct it must pass to the next couple of words. If he is mistaken, he must give an electric shock to him, starting with the lowest voltage, and gradually increase. 62.5% of the subjects are obedient and administer the discharge of 450 volts as long as the authority appears homogeneous.

The Mexican Ola [19]

The most spectacular phenomenon of group movement is the Mexican Ola, which is a particular mode of crowd phenomenon. The Mexican wave, or the Ola, appeared during the football world cup in Mexico in 1986. The spectators, sitting in a stadium, step from one bleach to the other to jump on their feet with the arms up, then sitting down again. The next step stands to repeat the movement. They create a wave that spreads along the rostrum. To interpret and quantify this behavior, I. Farkas et al. [20] used a variant of the models originally developed to describe excitable media such as heart tissue. The modeling of the reaction of the shed with respect to the triggering of the wave shows how the phenomenon is stimulated and what is the minimum size necessary for triggering. This phenomenon may represent the simplest spontaneous and reproducible behavior of an immense crowd with a surprisingly high degree of coherence and co-operation. In addition, La Ola raises the question on the ways in which a crowd can be stimulated to perform a particular pattern of behavior.
This modeling of the movement of groups shows that the scientific principles that have allowed the modeling of physical phenomena can very well be applied to social phenomena. Despite the highly evolved and complex form of its constitution as living matter, the human being seems to behave as an ordinary component of physical matter and to respond to the same basic principles of functioning of matter, namely the principles of the thermodynamics of irreversible phenomena. Indeed, human societies are complex systems and these are the object of irreversible phenomena, which with the arrow of time, lead irreducibly to aging. These phenomena are governed by the principles of thermodynamics and in particular by the notion of dissipative structure, introduced in 1969 by I. Prigogine [21], [22].

Dissipative structures [23]:

The most important notions in living systems are undoubtedly the notion of entropy and the notion of dissipative structures. Entropy measures the degree of energy dispersal within a system. The dissipative structures as described by Prigogine appear in systems that are traversed by matter and energy flows, far from thermodynamic equilibrium. These dissipative structures self-organize to maximize the rate at which energy dissipates in the universe. This is the maximum production law of the Entropy Production (MEP) entropy [24], which we will call MEP.
This MEP principle allows us to explain the role of natural selection in biology [25]. Living organisms dissipate energy and natural selection selects organisms that dissipate energy in the best way [26]. Human societies are complex systems, which are both subject to the arrow of time and to the creative chaos. The arrow of time is associated with the evolution of entropy, and the creative chaos is associated with enthalpic tendencies or “negentropy”. The latter, which is the opposite of entropy, is the possibility for complex systems to self-organize and produce a potential energy. It is on this basis that we will try to understand the behavior of social cells, which are composed of individuals, these being essentially dissipative structures capable of producing spontaneously order. They organize themselves to diminish their entropies by increasing the entropy of their environment.
The social cell that we are studying here behaves like a dissipative structure, which tends to self-organize itself to diminish its entropy at the expense of its environment. This cell is composed of a group of individuals, each one behaving in its turn as a dissipative structure which tends to consume order on the external environment.
Thus the formation with time of subcells in any social cell constitutes a phase change responding to the MEP principle. The social cell being a dissipative structure, under the effect of flows of energy and matter coming from outside, tends to self-organize and to favor the development of dominant structures in order better to preserve oneself. The creation of an oligarchy within a social cell is therefore a phenomenon of self-organization of the cell in order to best respond to external solicitations. The oligarchy is thus created spontaneously from the mother cell to respond to the same tendency of self-organization of the dissipative structure far from the equilibrium as it was described by Ilya Prigogine. The formation of an oligarchy can therefore be interpreted as a natural phenomenon, inherent in the evolution of species.

Mechanisms of formation of the oligarchy:

It seems that what drives the formation of an oligarchy within a group is the survival instinct, when it is triggered in the face of an external stimulus. As Stephen Gartlan shows [4], primates in captivity are better hierarchized than those in freedom. This suggests a correlation between environmental conditions and hierarchy. In addition, Richard Wrangham, Elizabeth Sterck and Carel van Schaik have “correlated the concentration of food in space with the hierarchy of the group. When food is concentrated, all members of the group struggle to gain access to it. In order to avoid these combats, the animals have the advantage of establishing an order of passage. On the other hand, when the food is distributed over a large area, the animals do not have to fight and therefore do not establish a hierarchy “[4].
A social cell subjected to a constraint tends to self-organize by creating a hierarchy. The group is structured in a hierarchical way to better defend itself against external threats, it organizes itself in order to survive better.
Jean-Philippe Fouquet [27] shows how the road transport business is reorganized hierarchically in the face of threats brought from outside. It shows that the transformation of working conditions, whether at political, economic or technical level, leads to hierarchical recompositions.
In general, we know that all trades are self-organizing, creating trade unions to better defend the trade.

Is this hierarchical organization of social groups a fate? can there not be a more consensual model of organization? Animal species are not, however, always organized in a hierarchical way. Indeed, there is a strong current literature on the issues of the formation of birds, fish bands, herds and their movement, which shows the emergence of consensual groups [12], [28], [29] ].

Example: Case of the Tunisian Revolution

We can try to explain why, the multiplication of social cells presents itself in a climate of great social freedom. We take here as an example the one that occurred in Tunisia after the revolution of January 14, 2011, when we saw a spontaneous creation of more than 200 political parties, more than ten thousand associations and the multiplication of union structures at all levels and in all sectors. Explaining this phenomenon makes it possible to understand certain mechanisms of social interactions which can give several useful information to political and economic forecasts. The in-depth analysis requires a good appreciation of the social situation prevailing prior to the period covered by our study. It is therefore necessary to go back to the history of this country. The Tunisian people is the product of a mixture of several civilizations and populations dating back several millennia. A succession of civilizations that have left deep traces in the Tunisian identity heritage. This plural civilization is expressed through dialogue and consultation, practices that date back to the time of the first traders came by way of sea. A spirit of dialogue and consultation which gradually forged a unique identity which define today the Tunisian identity heritage.
After independence, Tunisia lived several peaceful years, building a modern society, emancipated and cultivated. Unfortunately, over the years the single regime that had imposed, becoming increasingly authoritarian and paternalistic, feeding the population of a continuous propaganda praising the great works of the father of the nation, eventually lost its credibility and of the trust capital obtained through his struggle against the French occupation (1881-1956). This pushed society into an explosive situation, quickly recovered by the man who at the time had control of the powers. Tunisia suddenly found itself, in 1987, under a dictatorial, stifling and affairist regime. Subjected to 23 years of domination by a single person and his family in an almost mafia-like manner, Tunisia began to sink into the abyss.
The events of 17 December to 14 January 2011, were a new turning point for Tunisia. The flight of the dictator allowed Tunisia to find, overnight, absolute freedom. This abruptly regained freedom has created a vacuum that has quickly filled with an incredible number of social structures and oligarchies. Here we have an example of a dissipative structure that has been used to maximize energy dissipation, according to the MEP principle. The feeling of absence of the state and weakness of its institutions, as it was foreseen by the population, generated a feeling of insecurity which led the populations to react to this insidious threat by a self-organization and the creation of structures that allow them to better defend themselves.
Currently, Tunisia is in an unprecedented phase of social dynamics. It seems that a social disharmony is spreading in a continuous and diffuse way. The evolution of this system could lead it to a bifurcation point, the outcome of which is not necessarily negative. Our society, which is an open system and which is experiencing freedom, is the seat of a growing disorder and could be the object of unexpected self-organization and structuring. Indeed, as any dissipative structure that is installed in an internal and external imbalance and in a chaotic position, it can progress to a bifurcation point, where two things can happen, collapse and disappear, or self organization and structuring. This last possibility, which is the most probable, is the resilience, the appearance of negentropy. The bifurcation to one state or to the other depends on the type of social interaction. Our remarks are inspired by thermodynamics and even if the analogy can not be applied directly, it is useful to remember that the dynamics of phase change of a supercooled liquid to a solid, which can occur homogeneous or heterogeneous nucleation depends on interactions between molecules [28]. For human societies, several publications show on the basis of statistical studies and mathematical modeling of dynamic systems [29] that interactions between individuals are very determinant of the close interactions between agents and the mode of evolution of society. Will this change of phase in the evolution of Tunisian society mark a stage of rebirth for the whole Arab world? The revival in Europe was marked by a questioning of the dominant institutions in the Middle Ages. The rebirth of our society may require changes in the oligarchies.


The study carried out here on the phenomena of social dynamics, oligarchies, their nature and the conditions of their formation, is an attempt to better understand these phenomena from the scientific point of view. This approach is based on intuition and would require more rigorous development. We hope that this essay will give rise to mathematical formulations. We hope that through this study, it will be possible to better understand the social interactions, which would make it possible to better manage them. Knowing that every social cell tends to develop an oligarchy in an almost systematic way will help to better understand certain situations, to anticipate some of them and to manage them better.


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[14] Daniela Ovadia, Solomon Asch et la force du conformisme, Cerveau&Psycho N° 79 – Juillet – Août 2016,


[16] Bernard Dantier, “Organisation sociale et dépendance hiérarchique : Stanley Milgram, Soumission à l’autorité.” Extrait de: Edward Stanley Milgram, Soumission à l’autorité. Paris, Calmann-Lévy, Éditeur, 1974, pp. 169-190.

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[18] Wikipedia, S., Contrôle Mental: Expérience de Milgram, Stanley Milgram, Implant Cerebral, la Troisième, University-Press Org, 2013,

[19] « La Ola de Mexico » Guinness World Record,

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[24] Rod Swenson, Thermodynamics, Evolution, and Behavior,

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[27] Jean-Philippe Fouquet, « Configurations spatiales et hiérarchisation professionnelle : le cas des conducteurs de poids lourds», Journal des anthropologues [En ligne], 77-78 | 1999, mis en ligne le 01 juin 2000, consulté le 03 octobre 2016. URL :

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[29] Motsch, Sebastien; Tadmor, Eitan, Heterophilious dynamics enhances consensus. SIAM Rev. 56 (2014), no. 4, 577–621.

[30] François Feuillebois, personal communication.


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