Fundamentals of mathematical modeling in political science

Political processes are a complex system of organizational type. In this article, we are considering certain aspects, which stem from the principle of the system approach and are directly related to management of complex organizational systems. At the same time, the main attention is paid to the close connection of the principle of the system approach and the mathematical modeling of the systems of organizational management. Goals and objectives. The main goal of the article is to consider the ideas of the system approach, which imply the focus of attention on the quality and properties inherent to the system in general. The behavior of separate elements of the system is analyzed only in the context in which these are related to the achievement of the goal and to the effectiveness of the system’s functioning on the whole. Mathematical modeling ensures the fulfillment of the system approach for management organization taking into account the feedback principle. Methods. Mathematical model allows to form a logically harmonious formalized description of the managerial tasks. The following elements of decision-making are distinguished in the formal structure: goals, controllable variables, external variables, uncontrolled parameters, limitations, decision, efficiency criterion. The development of a mathematical model includes the determining of the interrelations between all the elements of the formal structure of the task and portraying them as mathematical expressions (equations, inequalities, etc.). Results. The article presents a decomposition of the process of developing a managerial solution comprising the following stages: verbal task setting (problem statement), forming of a mathematical model, task solving, solution analysis, model correction (if necessary) and finding a corrected solution, implementation of the final decision made in the management practice. In the end of the article, we consider an example of solving a managerial task in accordance with all the listed stages. Conclusion. The use of mathematical modeling and methods of solving managerial tasks in professional activity of a political figure allows to improve the effectiveness of the decisions made by this person and provides him/her with communication means, thanks to using the professional language of mathematics.