Call for PhD applications in the framework of the Labex MME-DII
Opinion Dynamics models: Heterogeneous agents in heterogeneous media.


The ubiquity of communication devices in our everyday activities, changes the way in which we interact with each other, for example, by allowing very different people, who would not have been able to share a discussion or support a common cause before, to converge on a particular action. These changes seem to affect the very notion of social interaction.

Furthermore, an increasing number of our common actions leave digital traces that are collected by different kinds of agents such as governments, scientific societies, commercial firms and NGOs, etc. The fact that the activities of human society can be massively monitored and stored is a new feature in history, and the impact of this fact on our behavior is far from trivial.

The present pandemic crisis provides an unexpected large scale terrain to study the modifications that arrive when the dynamics of social relations is suddenly modified. Regarding public opinion, it is therefore essential to understand the rules that govern its formation and diffusion, according to the different channels that connect the individuals in the society.

Opinion formation, a recurrent subject of study in social sciences, is often addressed through statistical analyses of data collected by the means of surveys or polls. By following the evolution of the statistical outcomes over time, it is possible to obtain some information about the dynamical processes underlying this phenomenon.

What we call the opinion of a society is a global property that characterises the society as a whole and has emerged from the repeated interactions among their agents. Defined in this way, opinion may be studied statistically. This approach is the mathematical realization of the ideas introduced more than one century ago by E. Durkheim[1] , who coined the notion of social fact. This concept refers to a property characterizing the whole society instead of the individuals, which emerges as an outcome of the dynamics governed by the interactions among them. Once the social fact is created, it is imposed on the members of the society who will find it very difficult to change it.

Early opinion dynamics studies mainly assumed a fully mixed population, which means that every agent may potentially interact with any other in the population, in other words, the interactions among agents were supposed to be long range. This approach, equivalent to a mean-field approximation, neglects the structure of the interactions. However, if social opinion emerges from the interactions between the agents, their structure may be relevant.

In fact, the key role of interactions had been recognized long ago by social scientists, who collected detailed data about social interactions in very small societies, using graph theory to represent them. J. Scott [2] gives a nice historical overview of network development in social sciences. With the development computing power and of Network Theory different models of social interactions have been proposed by physicists, applied mathematicians and computer scientists, thus setting a bridge between two different scientific communities[3] .

In spite of all these efforts studies taking into account the fact that the members of a society are intrinsically heterogeneous and so are their interactions are rare. In a very recent work [4] we have shown that when agent’s heterogeneities are taken into account, the outcomes of the very well-known Hagselmann-Krause dynamics are drastically changed.

In this project the selected candidate, will study the influence of heterogeneity in agents’ properties, in their interaction network, and the interplay between them. To do so she/he will combine both theoretical and data based models, and will apply concepts and methods issued from the study of Dynamical Systems, Statistical Mechanics, Agent Based Models and Network Theory.

1. Durkheim, E. Les Règles de la Méthode Sociologique (Les Presses universitaires Paris, France, 1967). URL
2. Scott, J. Social network analysis: developments, advances, and prospects. SOCNET 1, 21–26 (2011).
3. Castellano, C., Fortunato, S. & Loreto, V. Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009).
4. Schawe H. Hernández L, When open mindedness hinders consensus. Nature SciRep (to be published 2020), arXiv:2001.06877.

Working environment and conditions

The selected candidate will work under the supervision of Dr Laura Hernández at the Laboratoire de Physique Théorique et Modélisation (LPTM) UMR8089 CNRS-CYU, Paris-Seine University, France. She/he will also integrate an international and interdisciplinary team, composed by physicists, computer scientists, linguists, and human scientists, which are part of the OpLaDyn project, awardee of the 4th round of the TransAtlantic Platform, Digging into Data Challenge. , and will benefit of its activities.

The contract should start on September 2020 for a duration of 3 years. The basic gross salary (before taxes) is 1758 €/month. A teaching assistant mission may be assigned which involves 64h/year teaching assistant duties (typically one course each semester), and involves a supplement to the basic salary.


Interested candidates should hold a Master in Physics or Mathematics. The application of those completing their master in 2019-2020, is possible provided they graduate before September 2020.

Applicants are expected to have modeling and programming skills, and a marked interest in both theoretical modeling and data analysis.

This is a competitive program, so high records are expected, in particular a good knowledge of Dynamical systems theory, Statistical Physics of phase transitions, and Network Theory would be highly appreciated.

The application should contain:

  • A curriculum vita.
  • An official certificate with the marks obtained at the Bachelor and the Master. Applicant who have not completed the master yet should provide a certified list of the marks obtained until now.
  • A statement of purpose, explaining the applicant’s interest in the project
  • Two recommendation letters of her/his professors or internship supervisors.

These documents should be sent by e-mail to Dr Laura Hernández before May 14th 2020 to: