Mathematical models of human cooperation

and the transformation of human capital into social capital

Part 1. The individual energy field of human interaction with social environment and the formation of social solidarity (asabiya) and social capital



Pavel Barseghyan, PhD

Texas and Armenia



Different societies, along with other features, differ from each other in the degree of cooperation between people, mutual understanding and their social solidarity.

As early as the 14th century, Ibn Khaldun described this group of features of human society with the term asabiya, which indicates the degree of social solidarity and the ability of people to organize coordinated and successful joint activities.

These qualities of groups of people of different size and scale, in turn, are directly related to such a concept, reflecting the internal forces of society, as social capital.

The above features also largely determine the cohesion of society around the ideas of stability and development of countries.

In such conditions, the understanding and control of the internal dynamics of the development of society require a comprehensive study of the problems associated with it, along with other approaches, using the methods of mathematical modeling.

The first part of this work is devoted to the development of mathematical models of interaction between people and their internal harmony (asabiya) at the level of an individual from an energy point of view, meaning the interrelationship and assessment of energy consumed by a person for his/her own vital needs and for the vital needs associated with interactions with other people.

In the second part of the study, mathematical models of social cohesion or asabiya and the social capital of society will be considered, depending on the relevant characteristics of the people that make up society.

Key words: Collaboration, social solidarity, mathematical model, human capital, social capital, asabiya, institutional structure of society

Introduction: Collaboration of people and their solidarity as the cornerstones of sustainable social life

Even the most simple and superficial observation of people’s lives can clearly show that cooperation and solidarity among members of the community are the cornerstone of rational organization of life.

Collaboration between people in combination with solidarity allows them to combine their strength and capabilities to achieve different goals.

Naturally, the main purpose of cooperation between people is to ensure the continuity of life, primarily in the form of ensuring their safety and proper nutrition.

At the same time, the more organized cooperation between people, the higher the likelihood of achieving a specific goal and the less likelihood of risks and losses.

The effectiveness of cooperation is directly related to the physical and psychological features and characteristics of members of society, and their origin goes deep into history.

In this regard, one of the factors directly affecting the effectiveness of cooperation is the attitude of people to the ratio of their personal and social interests.

In other words, this problem is directly related to the attitude of society towards people’s self-interest and their willingness to cooperate with others.

On the other hand, it is also clear that different societies, whose psychological picture was created in favorable or unfavorable conditions, treat this key problem differently.

It is also obvious that in parallel with the development of society and the improvement of the quality of life, a person needs less cooperation with other people to ensure basic vital functions.

This circumstance contributes to the alienation of people from each other and, naturally, strengthens egoistic tendencies in society.

All this indicates that a deep study of the phenomenon of cooperation between people is very important from the point of view of ensuring stability and efficiency of society and other human systems of an arbitrary scale.

These studies can be both traditional or qualitative and quantitative, based on mathematical models of egoism and cooperation of people, the study of which is the subject of the present work.

These problems are typical macrosociological problems, and one of the goals of this work is to show that many high or systemic level characteristics of human systems of arbitrary scale directly depend on the specific characteristics and features of people.

Possible approaches to the problem of quantifying self-interest and cooperation of people

Within the framework of the mathematical theory of human systems, where human life is presented as a stream of actions, it is possible to construct various quantitative models of selfishness or self-interest and cooperation of people.

The flows of human actions, as is done in the quantitative description of flows in various fields of science, can be represented using both deterministic and probabilistic mathematical models.


To read entire paper, click here


How to cite this paper: Barseghyan, P. (2019). Mathematical models of human cooperation and the transformation of human capital into social capital. Part 1. The individual energy field of human interaction with social environment and the formation of social solidarity (asabiya) and social capital; PM World Journal, Vol. VIII, Issue III (April). Available online at



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: and here:  Pavel can be contacted at