Quantitative models of social solidarity

Mathematical models of human cooperation and the transformation of human capital into social capital

Part 2. Quantitative models of social solidarity (asabiya) and social capital at the level of groups of people and society



Pavel Barseghyan, PhD

Texas and Armenia




One of the main issues in the mathematical theory of human systems is the influence of the size of a group of people on the characteristics of the system, which is otherwise represented as the non-linear scaling problem of human systems.

In the history of mankind there were many cases when stable state unions were created from the unity of tribal communities with a low level of development, and at the same time there are many cases when powerful statehood with a high level of development collapsed in a very short period of time.

In the general theory of systems, these and related questions unite around a common scientific problem, namely, how systems with certain characteristics (in this case, human systems, including: states, societies, organizations, parties, and so on) can be constructed from elements with known properties (in this case, from people) so that they are stable and prosperous.

From this point of view, the simplest case is the formation of groups of people of different scale with given properties, taking into account the nonlinear transformations accompanying such scaling.

The second part of this article is devoted to the study of such integral characteristics of human groups as the energy for their cooperation, social solidarity and social capital.


Creating viable social groups of individuals is one of the most important problems of building a social hierarchy in society, a problem on whose solution the stability of society and the quality of life of people depend.

The energy model of interaction at the human level, presented in the first part of the work, makes it possible to evaluate a person’s contribution to creating an atmosphere of solidarity or asabiya in society and the formation of social capital [1].

If we approach the problem of contacts and interaction between people from a quantitative point of view, we will see that a widely used field approach in physics can also be useful for describing people’s behavior and activities.

The fact is that each person has contacts and connections with the human environment and creates around himself a certain sphere of influence and corresponding social fields.

These contacts and connections can have different physical, material, financial, informational, psychological and other expressions, which can also be measured in various ways.

The social fields created by man and a group of people are as realistic as the electric, magnetic and thermal fields in physics, and therefore classical field approaches and methods from the realm of physics can be widely used to describe them quantitatively.

The various ways in which people interact and communicate make society a continuous medium of their interaction, an idealized representation of which allows us to consider many aspects of people’s social life, including social solidarity and social capital, as part of an quantitative approach.

For the purposes of mathematical modeling, human life and activities are divided into corresponding action flows, which allows each of the above flows to be represented as a separate equation of state, which, in turn, is related to equations of state representing other flows of human actions.

That is, as a result, it turns out that human life and activities as a whole are represented as an algebraic system of equations of state.

In particular, such an approach can be used for the quantitative consideration of such an urgent problem for any statehood as the problem of the relationship between personal interests and public interests of citizens.

If people do not have a rational attitude to this problem, which can be expressed by the absence of even a small but sacrificial act in this direction, this will indicate the weakness of the public thinking of people, and as a result the state itself will also not be effective.

The same applies to the economic development of a country, the effectiveness of its judicial system and other features and indicators of a country at a system level that directly depend on the level of activity of an ordinary citizen.

The basis of all these state-building efforts is human capital, which, with its ability to unite and pursue common goals, creates social capital and an appropriate environment for the successful development of statehood.

The egoistic tendencies of people and their desire for cooperation and conflict play a central role in this process, which quantitative analysis is the main topic of the present work.

A quantitative representation of these phenomena and processes in the form of mathematical models and equations allows us to create a whole set of qualitative and structural patterns aimed at the effective management of society.


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How to cite this paper: Barseghyan, P. (2019). Mathematical models of human cooperation and the transformation of human capital into social capital. Part 2. Quantitative models of social solidarity (asabiya) and social capital at the level of groups of people and society; PM World Journal, Vol. VIII, Issue IV (May). Available online at https://pmworldlibrary.net/wp-content/uploads/2019/05/pmwj81-May2019-Barseghyan-math-models-of-human-cooperation-part2-social-solidarity.pdf



About the Author

Pavel Barseghyan, PhD

Yerevan, Armenia
Plano, Texas, USA



Dr. Pavel Barseghyan is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 45 years’ experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia).  Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/.  Pavel can be contacted at terbpl@gmail.com