Application of mathematical methods in international personality relations. Research methods of international relations: materials of the manual. Text of the scientific work on the topic "Modern Methods of Research in International Relations"

in economics, social psychology, sociology and demography.

Sociological theories of O. Comte and E. Durkheim since XIX. in., nourished the idea of ​​transferring them from sociology to other social sciences. The decisive influence on the formation of new directions in the study of international relations was exerted by the almost coinciding in time and interconnected appearance of the general theory of systems, the principles of which were set forth in the 1930s by L. von Bertalanffy, and cybernetics.

They gave a powerful impetus to behavioristics (from the English word behavior or behavior) 36, i.e.

the study of behavior at the individual, collective and social levels by measuring it. The prerequisites for the rapid development of behaviorism in the 50s, the so-called "behaviorist revolution" in the social sciences, were laid by American psychologists (C. Merriam, G. Lasswell) in the 1920s-30s, when they substantiated the idea

studying political behavior as the main subject of political research

science 37.

Based on general systems theory, information theory and cybernetics, the behaviorist direction

became dominant among the "modernist" in the study of international relations. And in the very

behaviorist direction can be conditionally distinguished groups of researchers: 1) operated

non-mathematical concepts, in particular, based on the theory of structural and functional analysis by T.

Parsons and D. Easton's method of systems analysis of politics; 2) who used quantitative methods and such

mathematical theories like J. von Neumann's game theory or N. Wiener's and W. Ross Ashby's information theory

(K. Deutsch, L. Singer, D. Modelsky, A. Rapoport).

We emphasize once again that one should beware of a rigid classification of `` modernist '' directions: it was a flow of various variations, a fusion of ideas and methods of exact and humanitarian knowledge, a shift of efforts from the development of a universal theory based on historical and philosophical knowledge to the theory of systems and at the same time to empirical research based on the measurement of observable data outside their ideological or philosophical significance.

However, the very rejection of philosophical views as a theoretical basis for the study of international relations, as many Soviet international experts believed, in fact could mean an appeal to the philosophy of "neopositivism." One way or another, "modernism" was sharply different from traditional trends in its striving for accurate, empirical evidence.

One of the most prominent "modernists", who was the president of the American Association for Political Science, K. Deutsch thus motivated the appeal to empirical methods: '"Modern methods of storing and returning information, electronic computers make it possible to handle a large amount of data if we know we want to do with them, and if we have an adequate political theory that can help formulate questions and interpret the findings. Computers cannot be used as a substitute for thinking, just as data cannot be used as a substitute for judgment. But computers can help us to carry out the analysis that offers new thinking to the theory ... The availability of large masses of relevant data and computer methods for processing them open up broad and deeper foundations for political theory, at the same time it differs from theory in broader and more complex problems ”38 ...

Most of the supporters of traditional approaches led by G. Morgenthau rejected or skeptically

referred to the application of methods adopted from economics in the study of international relations,

sociology and psychology. Although earlier in the Soviet scientific literature, the difference in

methodology between American "traditionalists" and "modernists", it was essential and at the first

pores reflected opposite approaches.

In our opinion, M. Merle correctly spoke about the advantages and disadvantages of the new methods. Noting about the rejection of them by “political realists” that “it would be absurd to justify the intellectual tradition of the lack of research tools” that expands these methods, he expressed doubts about the possibility of quantifying data on international relations due to the lack of many statistical indicators or the unreliability of statistics in many countries of immense scale and complexity of the international sphere39.

Let's try to extract from the long dispute between "traditionalists" and "modernists" the most

significant arguments of both: (see Table 1) There is no doubt that the arguments of the supporters of the old and new

approaches on each side contained a grain of truth. But on the rejection of "modernism" by traditionalists

an important objective circumstance affected: the views of the "realists" who became the leading school

traditional directions, were confirmed by the practice of US foreign policy, because in essence their own views

she was inspired. Therefore, their reaction to the seemingly heavy heaps in the methodology

was quite understandable. Another thing is that this reaction contradicted the objective trend towards integration.

sciences, expanding the possibilities of humanitarian research by the achievements of natural sciences, their theories and

Arguments of the "traditionalists" Arguments of the ‘modernists"

1. Quantitative and other methods, taken mainly from economic science, are alien to the science of international relations, in which there is no hierarchy and organization inherent in relations within the state (social

economic or political). 1. Traditional approaches have unreliable scientific instruments, assessment criteria are speculative, concepts and terms are vague.

2. In international relations, in addition to material, and non-material factors (national feelings, the will of political leaders) are manifested, which are difficult to systematize, their combination is unique and lends itself only to qualitative assessments 2. The analysis of modern international relations is based on outdated ideas.

3. The distinction between nations (national spirit, traditions, culture) is also qualitative in nature.

3. Inapplicability of the theories of traditionalists, in particular

"Realists" for quantification.

4. The foreign policy of the state acts as a historically conditioned integrity that cannot be quantified, just like strength (power). 4. Limited predictive power of the concepts of traditionalists, their generalizations are unverifiable.

So, let us trace briefly the most essential stages in the formation of American "modernism". Describing new, "modernist" approaches in the study of international relations, experts

it is often said that their essence is focused in the behavioral methods, which ”have already been mentioned and which meant the application of methods for analyzing empirical data, the construction of various models based on system concepts.

2. "FIELD THEORY" QUINCY Wright

One of the pioneers of “modernist” approaches was the renowned historian and sociologist Quincy Wright, who published the two-volume Study of War in 1942. Specializing in the study of war, K. Wright began with the systematization of all data on the wars that took place in the history of mankind. Then, based on the structural-functional method of analysis, he proposed an interdisciplinary approach to the study of international relations, which would combine the consideration of empirical data, their generalization and the development of a general theory, a model that can be verified by an application to reality. K. Wright was puzzled by the creation of a general theory of international relations. He listed 16 disciplines necessary from his point of view to create a scientific theory, the so-called "field theory" of international relations: 1) international politics, 2) military art, 3) the art of diplomacy, 4) foreign policy of the state, 5) colonial government , 6) international organizations, 7) international law, 8) world economy, 9) international communications, 10) international education, 11) political geography, 12) political demography, 13) technocracy, 14) sociology, 15) psychology, 16) ethics of international relations.

K. Wright considered one of the goals of such an “integrated” science to be the ability to foresee the future. He was a sincere pacifist, opposed the Cold War, criticized US foreign policy, in particular the Vietnam War.

3. SYSTEM APPROACH OF MORTON A. KAPLAN

The next notable milestone in the formation of “modernism” after the publication of K. Wright’s book in 1955 was M. Kaplan’s work “System and Process in International Politics” 40 (1957). It is believed that it was in this work that a systematic approach to the study of international

relations based on the general theory of systems, or rather - its version set out in the book

W. Ross Ashby "The Construction of the Brain" 41 (1952). M. Kaplan's work has been widely known for a long time,

but the evolution that has been taking place in international relations since the late 1980s, all the more revives interest in his hypotheses, allowing them to test their predictive capabilities.

M. Kaplan's book is also remarkable for the fact that it reveals the connection, the continuity between the new approach and traditional “realism”, since the initial for the author is the fundamental concept

"Classical" theory - "balance of power". M. Kaplan suggested that from some historical time (approximately from the 18th century) in international relations, global systems were formed, which,

while changing, they retained their main quality - “ultrastability”. Using a concept from cybernetics (“input

Way out ”), he tried more accurately than the“ classics ”to define the basic rules for the optimal behavior of states (“ actors ”) in the“ balance of power ”system that had existed since the 18th century. before World War II. He described six rules for the normal, from his point of view, functioning of the system, in which there should be at least 5

actors. So, each of them had to be guided by the following rules:

1) build up force, but, if possible, prefer negotiations to the conduct of hostilities;

2) it is better to go to war than to miss the chance to increase strength;

3) it is better to end the war than to exclude from the system the main national actor (against whom force was used),

4) obstruct any coalition or actor that seeks to occupy a dominant position in the international system;

5) deter actors who apply supranational principles of organization and behavior;

6) allow defeated or weakened primary actors to take their place in the system as partners and help secondary actors to raise their status.

The system that emerged as a result of World War II is the second global international system

v history, according to M. Kaplan, was defined by him as “free (or“ weakly connected ”) bipolar system”,

v which bipolarity was limited by the action of the UN and the power of the actors who remained neutral. In addition to two real historical systems, M. Kaplan imagined 4 hypothetical ones that can

to form from a “free bipolar system”:

1) a rigid bipolar system, where all actors are drawn into one or another block, and the neutral position is excluded (the system is less stable than “free bipolarity”);

2) the universal international system of the confederal type;

3) a hierarchical system dominated by one bloc, where nation-states would find themselves in the position of autonomous,

4) a “veto” system or a multipolar system in which the number of powers with nuclear weapons and nuclear deterrence is increasing.

Later M. Kaplan supplemented these models with 4 variations:

1) A very free bipolar system, where the degree of nuclear equilibrium would increase, the blocs weakened, and nuclear weapons partially spread.

2) A system of relaxed tension (or detente), which presupposed evolution in the superpowers ("liberalization" of the USSR and democratization of US foreign policy), which made it possible to limit arms to a minimum level.

3) An “unstable bloc system” where the arms race will continue and tensions will rise.

4) Incomplete proliferation system(15-20 countries). It is similar to the previous system, but in it the nuclear potentials of the superpowers do not reach the level of the ability to deliver the first crushing blow, and in it coalitions between the superpowers and small nuclear countries are possible, which would further increase the likelihood of war.

“Realists” criticized M. Kaplan for the abstractness of his models. The Australian scientist H. Bull, who worked at the London Institute for Strategic Studies, reproached M. Kaplan for the fact that his models “are divorced from reality and are incapable of developing any understanding of the dynamics of international politics or

moral dilemmas generated by these dynamics ”42.

While admitting some degree of fairness to such criticism, for the sake of fairness, we recall that

M. Kaplan himself did not at all pretend to be a biblical prophet and quite realistically considered

the possibilities of scientific foresight using system modeling. Emphasizing the failure of any

theory of international relations to predict the future in its specific manifestations, he limited

the predictive value of their hypothetical models by knowing: 1) the conditions for the invariability of the system, 2) the conditions

changes in the system, 3) the nature of these changes.

M. Kaplan's methodology still possessed a certain cognitive value, helping to imagine the likely evolution of international relations. And if none of his proposed 8 hypotheses (apart from the real free bipolar system) was not fully realized, then some of them are still partially confirmed by the trends of modern development. In the Soviet scientific literature until the second half of the 80s, when the principles of “new thinking” were formulated, M. Kaplan's position on the evolution of the USSR was sharply criticized as “unacceptable”, as “completely contrary to reality” or “directed

between countries ”. The process of "perestroika" and the destruction of the USSR, however, prove that today it is impossible not to recognize the scientific significance of M. Kaplan's scenario forecasts.

4. CHARACTERISTIC FEATURES OF "MODERNIST" RESEARCH IN THE LATE 50s - 60s

Since the late 1950s, a real boom in the study of international relations based on

new methods. Thousands of works have appeared, university schools have been formed, which are distinguished not only by methodological criteria, but also by research subjects. Several attempts at classifications have been made in the United States. The most detailed classification of works in English was proposed by the prominent American international specialist Bruce Russet, who compiled a sociometric table of the citation index of more than 70 authors. Having chosen for this publication 1968-1986, he conditionally divided all scientists into 12 groups according to the criteria of methodology or object of research, and of them 15 authors were simultaneously assigned to two groups, 9 - to three groups. The largest group was made up of scientists from Yale University or collaborators, mainly engaged in “international integration” (16 people) 43.

Another detailed classification was given by the American international expert F. Burgess, who singled out seven

directions ("cognitive rationalism", the study of behavior in terms of its goals, reasons, etc.

etc.), “theory of strength”, the study of the decision-making process, theory of strategy, theory of communications, theory

fields (see above for a summary of the method proposed by K, Wright), systems theory (M. Kaplan and his followers) 44.

extremely time consuming. (This work was largely done in the already mentioned

innovations introduced into the science of international relations by "modernists", and then we will consider the main theoretical directions of "modernism" and present a number of specific examples of the application of these methods, in particular, in determining the power of states.

5. APPLICATION OF THE SYSTEM APPROACH

The use of a systems approach meant a major shift in both theory and methodology of studying international relations - a departure from the "state-centric" views on international relations as the "sum" of foreign policies of states.

Another important merit of the "systemists" was that they expanded their ideas about the participants (actors) of the international system, considering as such, in addition to the main actors - states, international organizations, non-state political forces (for example, parties), religious organizations and economic forces, mainly transnational corporations. David Singer of the University of Michigan suggested in a well-known 1961 article the idea of ​​“levels of analysis” that unite two areas - international systems and the nation state. D. Singer identified the main border in his search for phenomena that affect international politics: 1) internal phenomena occurring within the borders of the state, 2) external phenomena occurring outside the border of the state45.

The application of the principle of general systems theory not only expanded the concept of "actors"

international relations (and, in essence, changed the understanding of their structure), but also led international relations to

the formation of the concept of "environment". Let's reproduce the simplest scheme, which is given in many

foreign textbooks and monographs, graphically depicting a systematic approach to the study of political

a sphere that presupposes the existence of an “external environment” (Fig. l):

Picture 1

Often this approach to the analysis of political systems is called the method of D. Iston, which is described in his work "System Analysis of Political Life" *. When applied to international relations, the concept of "environment" becomes more complex. It seems to be quite simple for a state, rather specific for groups of states or coalitions; finally, one can imagine a more complex “external environment *” for the entire system of interstate relations, which can be considered international relations as a whole. But what is the “external environment” for the global system of international relations, if we accept the assumption of its existence? There is no unambiguous answer to this question in the scientific literature.

In the 60s, a number of works appeared in the United States aimed at studying the foreign policy of the state, considered "surrounded by the environment." Several interesting publications on this topic belong to the spouses G. and M. Spraugs *. They proposed the concept of "ecological triad" (the term "ecology" is used here in a broad sense): 1) personality of a certain character (statesman), 2) conditions that surround it (environment), 3) interaction of personality and conditions. G. and M. Sprout distinguish 3 types of interaction:

The first type is environmental possibilism, i.e. opportunities representing the conditions in which the decision-maker operates. These conditions change historically. For example, they say. Napoleon could not threaten Moscow with nuclear bombing (neither could the Germans in 1914, although they could reach Moscow faster with the help of railways than Napoleon could), the Romans could not move their legions from Italy to Britain within hours or even days, Theodore Roosevelt in 1905 could not raise American prestige by sending a man to the moon (he decided to send the American flag on a trip around the world), the Persian king Darius could not use the phone to clarify differences with Alexander before the Macedonian campaign in Asia; the Spaniards in the Middle Ages could not rely on the resources of the New World to repel the Islamic invasion of the Iberian Peninsula, etc.

The main idea of ​​G. and M. Spraugov is that the decision-makers are limited by the opportunities provided by the world around them.

The second type of interaction is environmental probabilism, i.e. the probability with which this or that event will occur. In other words, assuming that states interact, the authors focus on the likelihood of an individual's actions in a certain way in a “certain environment”. For example, what was the likelihood that the United States and the USSR would become rivals as two superpowers after World War II? Or what is the possibility of interaction between Burma and Bolivia, small states in different regions of the world, separated by thousands of miles?

The third type of interaction is cognitive behavio sm, i.e. behavior of a person making a decision based on knowledge of the environment. Such a person interacts with the surrounding world through the images of this surrounding world. She acts on the basis of how she perceives this world. This perception can be very different from reality.

6. USE OF CYBERNETIC CIRCUITS IN A SYSTEM APPROACH

A powerful impetus to the systems approach is given by the theory of communication and the means of cybernetics. As a result of their application, the concept of states, nations, political regimes has been formed as cybernetic systems with “input” and “output”, controlled by a feedback mechanism (“stimulus” - “reaction”). The pioneer and largest representative of the “cybernetic” approach was the patriarch of American political science K. Deutsch.

Subsequently, American colleagues, French international experts, recognizing the positive use of cybernetic tools for analyzing such a complex system as the state, criticized K. Deutsch, believing that his methodology overestimates the rational nature of decision-making by the center of the political system and that it is closer to physics than social sciences.

K. Deutsch, explaining the “cybernetic approach” to foreign policy, compared the decision-making process with playing electric billiards. The player sets the initial speed to the ball, it moves, colliding with obstacles that change the trajectory of its movement. The point of falling or stopping depends simultaneously on the initial impulse, subsequent maneuvers of the player and the impact of obstacles.

Criticizing K. Loich, the French internationalists P.-F. Gonidek and R. Sharven draw attention to the fact that

v Unlike physics, obstacles in the international sphere represent not only explicit, but also hidden influences, intersections of interests * (ie, “obstacles” themselves in motion). Therefore, K. Deutsch's "cybernetic" method is more suitable for the analysis of military strategies than politics, since in the military field the behavior of states is more rigid and mutually determined.

Nevertheless, there is no doubt that computers have dramatically expanded the use of mathematical tools in the study of international relations, making it possible to go, in addition to the already used methods of mathematical statistics, algebraic and differential equations, to new methods: computer modeling, solving information-logical problems. But above all, the capabilities of computers stimulated research on proven methods in mathematical statistics aimed at formalizing qualitative characteristics, attempts to measure “strength *”, “power,” “solidarity,” “integration,” “aggressiveness,” etc. Let us clarify that, although a number of methods were specially developed by him for the study of international relations, their development for political science as a whole was of more significant importance.

V Monographs by S. V. Melikhov contain significant reference data on the use of quantitative methods in American political science, mainly factor analysis (as well as multivariate correlation, regression, analysis of variance and time series analysis) * ”.

Famous international scholars who applied mathematical methods in the 50s - 60s * in the USA were A. Rapoport, K. Deutsch, D. Singer, G. Getzkov, O. Holsti, B. Russet, R. Rammel, D. Tsinnes and others. But the extreme popularity of mathematics at that time involved in the so-called * quantitative ”research

v social sciences of many amateurs who did not have a professional mathematics, flaunting some separately "snatched" methods and concepts from the mathematical arsenal.

from about the 70s, when the great, or better to say, inflated hopes were not justified. Soviet international experts from the NMEMO expressed the following opinion on this score: “On the whole, the scarcity of results from the use of mathematics in the“ interdisciplinary ”study of international relations is associated with the underdevelopment of the mathematics itself, which may be suitable for this specificity. Apparently, that branch of mathematics, which would correspond to the considered subject of research, has not yet been developed. Attempts to borrow mathematical tools from other branches of science, which were created specifically for the needs of these branches, turned out to be unsuccessful. ”

7. DIFFICULTIES OF APPLICATION OF MATHEMATICAL KINDS IN POLITICAL SCIENCE

In our opinion, some of the difficulties in the reliable application of mathematical methods in the study of politics and history at a theoretical level are as follows:

1. It is difficult to quantify the spiritual sphere, consciousness, the movement of ideas and mentality, the individual qualities of those who make decisions. With logical thinking, a person is subject to

and the sphere of subconscious drives, emotions, passions affecting rational thinking, which in the behavior of state and political leaders often makes decisions difficult to predict.

Although theoretically the system or “environment” should impose restrictions on their deviation from the most rational choice, history shows that the role of the state leader often turns out to be decisive, while he himself, making a decision, becomes immune to objective information, and acts on the basis of the subjective , to a large extent intuitively, understanding the political process and the intentions of opponents and other actors. As an example, let us recall the behavior of J. Stalin on the eve of Hitler's aggression against the USSR.

2. The second difficulty is related to the first one, but it covers the social sphere as a whole, where many influences, interests, factors intersect, and it seems impossible to establish and measure them relative to each other. Again, history shows that an insignificant, according to visible signs, or large, but formerly unchanged parameter can dramatically change its value and have a decisive impact.

An example from the relatively recent past is the four to fivefold rise in the price of oil in 1973, which in the short term caused the global energy crisis, and in the long term caused the restructuring of the world economy. The same factor in the short term had a beneficial effect on the foreign trade of the USSR, and in the long term contributed to * the maturing crisis of the Soviet economy and the decline of the Soviet system as a whole. Meanwhile, the most significant change in the international economic system of the 70s. was not predicted in the models. So, in the well-known forecast of world development "Goal 2000", published on the eve of the 1973-1974 energy crisis. by the famous American futurologist G. Kahn, the oil factor did not figure among the variables at all ”*. those. many large, but suddenly developed processes in the economic, social and political spheres turn out to be unpredictable, which, of course, is not an indisputable proof of their unpredictability.

3. Finally, some processes seem to be random, stochastic, because the causes that cause them are invisible (at a given time). If you figuratively compare the social sphere with a biolopotan organism, then the reasons for this are similar to a virus that does not show activity for a long time. due to the lack of favorable environmental conditions or their unknown internal "clockwork". With regard to international relations, it is important not to lose sight of the historical aspect, since the origins of some processes not observed by contemporaries are fixed in national traditions and national consciousness. Unlike the evolution of nature (excluding anthropogenic impact and cataclysms), in which the length of time on the scale of human history is minimal, in the world social sphere, the complexity of systems in space is interconnected with strong, historically accelerating mutations.

As if summing up the results of behavioral studies of international relations in the 50s and 60s, the English internationalist L. Reynalls spoke about the revealed methodological difficulties: “We are talking about the problems of inadequacy of intellectual tools. The human mind is completely incapable of creating a system that includes the entire ensemble of constituent elements and interactions on a worldwide scale. Such a system should be simplified.

But as soon as simplification is allowed, reality is immediately falsified, and simplification is nothing more than an abstraction of reality '' **.

One of the leading American behaviorists D. Singer argued the opposite point of view: “We cannot build a global system as a complex of very flexible, mobile co-optations, territorial

and others, including smaller formations, which can now be linked not only through governments, but be internal or extra-national as well as national as in the sphere

In this dispute, the skepticism of traditionalists is understandable, but he can hardly convince a serious researcher that the methods of the exact sciences are a priori unsuitable for the study of international relations. Naturally, these methods first began to be used in demography, economics, which on the subject of research

are, as it were, intermediate between the exact and “purely” humanities, where with the expansion of such a subject of research as the sphere of consciousness, the most adequate forms of cognition (figurative-metaphorical thinking, intuitive-experiential assessments, etc.) also expand. It is no coincidence that the qualitative and other methods of mathematics, biology, physics, transferred through the `` intermediate '' sciences to political science, international relations, by the way, gave the most noticeable results in those studies, the subject of which also turned out to be closer to physics or cybernetics than to purely humanitarian sciences ...

8. EXAMPLES OF APPLICATION OF MATHEMATICAL MEANS IN MODELING MILITARY CONFLICTS AND ARMS RACE (L. RICHARDSON'S MODEL)

These examples primarily relate to the military-strategic area, where the criteria for the behavior of states, as well as the behavior itself, are tightened, and the significance of various influences and interests is assessed in a single dimension of the balance of forces and potentials, i.e. one way or another, the number of factors that are subject to quantification decreases.

Back in the 1930s, the Scottish mathematician L. Richardson began to create a mathematical model of war and international conflict. According to A. Rapoport, L. Richardson viewed international relations as a “physical system”. In the 50s, his method attracted the attention of American authors, but L. Richardson, improving it, retained the priority and achieved widespread acceptance in the West of his model as a classic in the field of military-strategic research using mathematics, which can be seen from the index of its citation in foreign countries. literature. L. Richardson proposed a system of differential equations:

dx / dt = ky - α х + g
				βy

where x and y are the levels of armaments of the two countries, k and l are the “defense coefficients” (the government's idea of ​​the enemy's strategy); α and β - coefficients of the "cost" of military efforts; g and h - coefficients of "aggressiveness" 262 (the degree of militarism or peacefulness of foreign policy).

Another quantitative analysis technique that has found widespread use in

foreign studies, contained in the project "Correlation of War", developed

under the leadership of D. Singer *. It is based on the paired correction technique. D. Singer set the task of establishing, on the one hand, the correlation between the number of wars and the military potential of European states from the Congress of Vienna in 1815 to 1965, on the other hand, between several parameters of wars (occurrence, intensity, duration)

and parameters characterizing the international system (the number and strength of alliances, the number

international organizations).

In the project, using factor analysis, six indicators of military strength were identified: 1) the total population, 2) the population in cities over 20,000 thousand inhabitants; 3) the amount of energy consumed; 4) production of steel and iron;

5) the level of military spending; 6) the size of the armed forces. One project output

states that long-term equilibrium in the European system of the XIX century. hindered the intensity of wars and, conversely, wars of the XX century. caused by changes in the balance of power in favor of one power or coalition. Another less obvious conclusion is

the fact that the intensification of the process of the formation of unions in the XIX century. increased the likelihood

the emergence of wars, while in the international system of 1900-1945. strengthening alliances

game models (G. Gettskov, R. Brody). Game theory originated in the 40s. Since the late 1950s, games in the field of international relations have been simulated without and with the help of computers (O-Benson. J. Crand). Soviet international experts who analyzed them believe that the use of logical and mathematical methods and computer modeling opened up a promising direction, but were restrained by "the insufficiency of the existing mathematical means, and, above all, game theory".

By analogy with war games, “hard” imitations are distinguished, where certain conditions of behavior are set, and “free” ones. The former, as a rule, were used in attempts to model at the global level, the latter - for specific problems (most often for modeling conflicts). It seems that the experience of these models deserves more careful analysis by mathematicians for the possible use of valuable elements. Note that game, simulation models, as well as correlation, static ones, also dealt mainly with the military-strategic area.

MAIN THEORETICAL DIRECTIONS OF "MODERNIST" RESEARCH

The conventionality of dividing the directions of "modernist" (behavioristic) studies of international relations according to two criteria - methodology and theory - is quite obvious. The existing theory itself is the methodological basis of cognition. For example, studies of the process of making foreign policy decisions can be viewed as a methodological principle in the analysis of foreign policy and, at the same time, as a theoretical direction. Nevertheless, theoretical constructions differ from methodology in that they have a specific subject of research. The "classical" approach to the study of international relations in American and Western European science was focused on a universal general theory. And since many "modernist" approaches proceeded from opposite, empirical attitudes, their result was a refusal to search for a global theory and the formation of a number of private theories of international relations.

Abroad, there are many private theories and methods in the study of international relations. According to some estimates, only by the beginning of the 60s there were up to three dozen of them. However, several main ones stand out among them: the theory of international conflicts, the theory of integration, the theory of making foreign policy decisions, and in a broader sense - the theory of foreign policy. Finally, there is such a separate direction as the study of peace problems (Peace research), which stood out from the study of international conflicts.

So, let's look at a number of examples of the characteristic features of particular theories of international relations.

1. GENERAL THEORY OF CONFLICT

The largest of these in terms of the number of studies and publications was the theory of international conflicts. Actually, conflict management is a broader branch of international research that considers conflict as a social phenomenon and behavior in all social spheres. In the United States and other Western countries, there is the so-called “general theory of conflict”, the dominant methodology of which is the systemic, structural-functional approaches in combination with behavioral-cybernetic techniques. The behavioral direction was reflected in the publications of the American magazine "The Journal of Conflict Resolution" founded in 1957. International conflicts turned out to be the central topic on the pages of the journal, which in fact has become a priority scientific publication not only in the field of the study of conflicts, but to a large extent in the study of international relations in the United States as a whole. One of its most famous representatives is the conflict expert Kenneth Boulding.

The behavior of participants in an international conflict is considered by behaviorists approximately according to the scheme, which is given in the famous work on quantitative methods, published under the editorship of D. Singer (see Fig. 2).

Picture 2

S - incentives caused by the behavior of states R - behavior of each state

r - stimulus score

s - intentions expressed depending on perception.

International conflicts is a topic that in the 70s and 80s, perhaps, became a priority for Soviet international scholars as well. In any case, by the number of monographs in comparison with other subjects of the theory of international relations. The authors of foreign and domestic works emphasized that the main tendencies of development and contradictions of the international sphere are focused in international conflicts, and if we take into account that the global problem of war was interpreted by many Western scholars as an integral part of conflict management, then the theory of international conflicts is logical to consider in approaching it to the level of general theory international relations. It is the vastness and significance of the subject that explains why the main direction in research on the general theory of conflict has taken the study of international conflicts.

The study of international conflicts in most cases pursues applied goals. Therefore, in

foreign conflictology from an applied point of view most often at the beginning two levels of analysis were distinguished: 1) analysis of the causes, structure and dynamics of conflicts, 2) "therapy", i.e. development of methods for their settlement (UN, international court in The Hague, negotiations, application of international legal norms, force). Then the third level emerged - the prevention of international conflicts. In particular, the idea of ​​the possibility of conflict prevention and the need to develop appropriate means for this was formulated by the director of the Center for the Study of Conflicts at London University Cottage J. Burton.

2. THEORY OF INTEGRATION

Among the studies on the theory of international integration in Anglo-American literature, the works of K. Deutsch “Political community at the international level. Definition and Measurement Problems ”,“ Political Community and the North Atlantic Space. International Organization in the Light of a Historical Experiment ”, as well as“ Nationalism and Social Communication ”and a number of other works.

Considering that there can be no universal law according to which cooperation and integration processes develop, K. Deutsch named several conditions necessary for this. Among them, he first of all highlighted the commonality of political values ​​and such psychological factors as knowledge of partners, the development of trade, the intensity of cultural exchange and exchange of ideas. K. Deutsch put forward a hypothesis about the predominance of communication factors in the formation of political communities and in maintaining their internal unity, cohesion, considering linguistic communication primarily from the point of view of information exchange. Each nation, people has special communicative means, which are expressed in the consolidated collective memory, symbols, habits, traditions.

Two American authors, R. Cobb and C. Elder, conducted a study on the basis of correlation analysis in order to determine the factors that determine rapprochement and cooperation in international relations, comparing the relationship between the selected fifty states of the world and the relationship within the North Atlantic community. As a result, two factors turned out to be predominant: 1) previous cooperation, 2) economic power, as can be seen from the following diagram (the significance of a number of factors was not revealed) (see Table 2 in the Appendix).

If we take into account that “previous cooperation” is itself the result of the action of other factors, then there remain two leading factors in terms of the level of correlation (economic and military power).

Other authors emphasize the predominance of the factor of the leading political force, the "hotbed" of integration. From these positions, the history of the USA, Canada, Australia and South Africa was considered by the Belgian internationalist J. Barrea, who believes that integration tends to develop around the “core area”, representing one (possibly more) more powerful state, attracting into its orbit the surrounding area.

3. THEORY OF FOREIGN POLITICAL DECISION MAKING

Publications on this topic can be divided into "purely scientific", in which real processes are analyzed, and scientific and applied, in which methods are developed to optimize decision-making. In Anglo-American studies, there are several approaches to assessing the process of foreign policy decisions.

One of the most popular in the 40-50s was the socio-psychological approach, in particular, the so-called "method of operational cipher" or "code". It was used by the sociologist N. Leits, who, on the basis of an analysis of Russian literature and the works of the Bolsheviks, tried to reconstruct the system of values ​​(beliefs) of Soviet leaders and open their perception of the outside world. His goal was to create a collective image of the “Bolshevik perception” of reality, in order to try to understand the behavior of leaders based on this. Modified, this approach was then transformed into a psychological test of 10 questions, asked in order to find out a politician's view of the world. Philosophical questions were also clarified, for example, "Is the political universe in essence some kind of harmony or clash?", "Is the future in politics predictable?" In addition, the list includes "instrumental" questions that clarify someone's behavior in the world of politics: "What is the best way to choose, goals or objects of political action?"

By the mid-1950s, a socio-psychological interpretation of the motives for decision-making was given by R. Snyder based on the ideas of M. Weber and the structural and functional analysis of T. Parsons. His method assumed the greatest possible consideration of factors, but their consideration through the prism of perception by those who make decisions. (In the early 60s, R. Snyder took up the problem of rationalizing foreign policy decisions).

V further in the USA, as well as in Great Britain, two approaches were most widespread

To evaluating decision making: behavioral, combining socio-psychological aspects with cybernetic concepts; and rational decision theory based on game theory.

The behaviorist approach using cybernetic means in the analysis of foreign policy decisions and actions of the state was one of the first to be applied by the professor of the University of Washington J. Modelski, who operated with the concepts of "force at the entrance" (state means for foreign policy decisions).

Let us reproduce the explanation of the decision-making process, which was developed by the American internationalist O. Holsti, who defended his dissertation on this topic at Stanford University. In his opinion, three phases should be distinguished in an ideal decision-making process. The first is a kind of push from the external environment. Perception of the impact of the external environment - the second phase, the process by which the decision maker selects, sorts, evaluates the information received regarding the surrounding world. Interpreting a deliberate "push" - the third phase. Both perception and interpretation depend on those images that already exist (are embedded) in the consciousness of the person making the decision. O. Holsty gave the following schematic description of perception and its relationship with images from the outside world and the value system of the person making the decision (Fig. 3):

Even if we accept Holst's scheme as adequately describing the behavior of a political leader intending to make a certain decision, it cannot reflect the real process of its adoption. As a rule, many factors operate in it, for example, the structure of power, within which decisions are made. In the 60s and 70s, the concept of a bureaucratic process of making foreign policy decisions (G. Allison, M. Halperin, and others), in which foreign policy actions are presented as a product of interaction between various state structures, a compromise of interests, became widespread in the United States. Emphasizing the special role of bureaucracy, the supporters of this concept chose the main object of the analysis of the decision-making process (and made the meaning of this object absolute) those factors that are underestimated in the socio-psychological interpretation of O. Holsty.

A more complex model of the process of foreign policy decisions was developed by the English internationalist J. Burton, who is also a supporter of structural and functional analysis using the cybernetic stimulus-response scheme. The peculiarity of his approach lies in the development of the concept of “vectors of change”, acting from the outside on the state. J. Burton divides changes into primary and secondary. Primary factors are changes in the environment (geography, geology, biosphere), secondary factors are the result of social interaction of human societies. Let us present a diagram of the decision-making process according to J. Burton, given in his book "System, States, Diplomacy and Rules".

		Table 5
	The factor of changes in the external environment
“Entry of State A		State B ... N
reaction of social groups		government reaction
perception	Perception	perception
		classification and storage of information
	classification and storage of information
	decision process	politics
	execution
domestic law	international action	"Exit" of each state B ... N

internal coercion (police)					external compulsion
affected groups						factors of change
states whose interests are affected				The "entrance" of each state

1

Mathematical statistics and probability theory in modern economic conditions are increasingly integrated with everyday life. All knowledge and experience gained in the study of statistics and probability theory serve as the basis for the training of highly qualified personnel. It can be argued that the methods of mathematical statistics and probability theory are one of the main methods in describing the state of the economy, both at the micro and macro levels. Probability theory is the basis of probabilistic-statistical methods of decision-making in management. In this regard, the application of the theory of probability is relevant in almost all areas of the economy. One of the most striking examples is the banking system, namely the system of lending to individuals and legal entities. The methods used in the theory of probability identify all permissible situations that arise in the lending system. This makes it possible to substantiate all probabilistic directions of development of the banking system using a set of tools characteristic of this system.

methods of probability theory

mathematical model

making decisions

banking system

interest rate

1. Dolgopolova A.F. Modeling of management strategy in socio-economic systems using Markov processes / A.F. Dolgopolova // Bulletin of the agro-industrial complex of Stavropol. - 2011. No. 1. S. 67-69.

2. Dolgopolova A.F., Tsyplakova O.N. The sequence of the regression analysis and its application in economics // Actual problems of theory and practice of accounting, analysis and audit: materials of the Year. 75th scientific-practical. conf. (Stavropol, March 22-24, 2011) / StSAU. Stavropol, 2011 .-- S. 127-129.

3. Zasyadko O. V., Moroz O. V. Interdisciplinary relations in the process of teaching mathematics to students of economic specialties // Polythematic network electronic scientific journal of the Kuban State Agrarian University. 2016. No. 119. S. 349-359.

4. Litvin D.B., Gulai T.A., Dolgopolova A.F. Correction of the dynamic range of statistical data // Statistics yesterday, today, tomorrow: Sat. based on materials from Mezhdunar. scientific-practical conf. 2013.S. 148-152.

5. Shmalko S.P. Formation of professionally oriented thinking among students of economic directions. // Cultural life of the South of Russia. 2010. No. 1. S. 99-101.

In the modern world, when studying mathematical statistics and probability theory, we often wonder about the possibility of applying the existing laws of statistics in everyday life. The knowledge obtained in the study of the methods of mathematics and statistics is the basis, an integral part of the education of highly qualified workers in various spheres of society, including in the economic sphere.

The Probability Theory section studies the laws governing random variables. Methods of mathematical statistics are one of the most important tools of econometric research. This is due to the fact that most micro- and macroeconomic characteristics have the property of random variables, the prediction of the exact values ​​of which is almost impossible. The links between these indicators are usually not strictly functional in nature, but allow the presence of random deviations. As a result, the use of the mechanism of mathematical statistics in economics is natural. Mathematical statistics is the practical side of probability theory. This category is used most often when analyzing data and organizing them into a single whole, for further use and accounting.

For the first time in Russia, the theory of probability became known in the first half of the 19th century. A significant contribution to the development of this science was made by Russian scientists: P.L. Chebyshev, A.A. Markov, A.M. Lyapunov.

Probability theory is the basis of probabilistic and statistical methods of decision-making in management. To be able to use a mathematical mechanism in them, it is necessary to express decision-making methods in terms of probabilistic-statistical models. The application of a specific probabilistic-statistical decision-making method consists of three stages:

The transition from economic, managerial and technological realities to an abstract mathematical and statistical model, i.e. creation of a probabilistic control mechanism, technological process, decision-making procedure, in particular, based on the results of control based on statistical data.

Performing calculations and obtaining conclusions by mathematical methods within the framework of a probabilistic model;

Presentation of the previously obtained conclusions to the existing situation. Making an appropriate decision (for example, on the conformity or non-conformity of the quality of products and services with existing standards).

Mathematical statistics is the practical side of probability theory. Consider the main issues of constructing probabilistic decision-making models in economics. In order to correctly use the normative, technical and methodological documents on probabilistic and statistical methods of decision-making, a certain knowledge base is required. Namely: you should know under what conditions a particular document should be applied, what decisions should be made based on the results of processing the available data, etc.

Only those tools of mathematical statistics that rely on probabilistic models of the corresponding real phenomena and processes can be used to prove theories. We are talking about models of consumer behavior, the possibility of risks, the functioning of technological equipment, obtaining experimental results, etc. A probabilistic model of a real phenomenon should be considered constructed if the quantities under consideration and the relationships between them are expressed in terms of probability theory. The correspondence of the probabilistic model to reality is substantiated using statistical methods for testing hypotheses.

Non-statistical methods of data processing are theoretical, they can only be used for preliminary analysis of data, since they do not make it possible to assess the accuracy and reliability of conclusions obtained on the basis of limited statistical data.

Probabilistic-statistical methods can be applied wherever it is possible to build and substantiate a probabilistic model of the event or process under consideration. Their use is mandatory when conclusions drawn from sample data are carried over to the entire population.

In order to more clearly consider the application of probability theory in economics, let us consider examples when probabilistic-statistical models are a good way to solve economic problems.

Let the bank issue a loan of 5 million rubles. for a period of 5 years. The probability that the loan will not be repaid is assumed to be 5%. What interest rate does the bank need to set in order to make a profit that is not less than the minimum? Let's designate the rate, measured in fractions of one through p. The bank's profit is a random value, since the loan, along with interest, can be returned by the client, or maybe not. The distribution law of this random variable is as follows:

The probability of loan repayment is 0.95. The remaining 0.05 is the risk that the loan will not be returned, and the bank will incur losses in the amount of 5 million rubles. In order to find out what rate k percent needs to be set, we compose the inequality:

That is, the bank must set the interest rate k at least 10.53% in order to minimize risks.

Elements of mathematical statistics can be used not only in lending, but also in insurance.

As you know, the occurrence of an insured event is a random event. Only using mathematical statistics can a relationship be drawn between the amount of the insurance premium and the probability of an insured event. An example is the work of insurance companies. Let the insurance company conclude insurance contracts for one year in the amount of G rubles. It is known that the insured event will occur with probability p and will not happen with probability. Let's compose the distribution law of the indicative random variable X.

Table 1

x = 1 - occurrence of an insured event with probability p;

x = 0 - a situation when the insured event did not occur, with probability q.

Xi is the number of insured events occurring for the i-th policyholder.

Let us denote by n the number of clients with whom the insurance company has entered into a contract.

Thus,

Means, , .

It follows from this that the quantity X is distributed according to the binomial law. Upon the occurrence of insured events, the company will be obliged to pay insurance indemnities in the amount of npG rubles. In order for the balance of the insurance company to turn out to be at least zero, it is necessary to receive an initial contribution from each of pG rubles (i.e. 100p% of L). But the amount of insurance claims can be either more insurance premiums or less. In the first case, the company will remain at a loss, in the second, it will make a profit. In order to protect themselves, companies need to set the amount of the down payment slightly higher than calculated. Then, let is the real interest rate, with the condition that.

Consequently, the company takes from n clients not npG rubles, but rubles. This amount is intended to cover losses from the insured event from the policyholders.

Let γ be the probability that the insurance company will not receive losses.

In this case, the probability of occurrence of no more than insured events will be equal to:.

where Ф is the Laplace function. We can now determine the real insurance rate.

Let γ = 0.99 (ie the insurance company will not go bankrupt with a probability of 99%), p = 0.01;

n = 1000 - number of clients

Using the table of values ​​of the Laplace function, we have that:

It follows that:.

In the same way, you can determine the optimal amount of investment, the result of which cannot be calculated without statistical research.

On the basis of the analyzed examples, one more example can be investigated.

It is known that in order to avoid losses, banks acquire insurance policies when issuing loans. Let the bank issue loans for 3 million rubles. at 15% for a year. The probability that the loan will not be repaid is 0.03. To reduce the risks, the bank buys an insurance policy for each of the loans for L million rubles, issuing an insurance premium of 4% to the insurance company.

Estimate the bank's average profit from one loan if L = 3 (if the insurance policy is issued for 3 million rubles). Let's denote the value:

where 0.04 L - amounts paid by the bank to the insurance company;

X is a random variable - the sum of income and losses of a lending institution, the distribution law of which looks like this:

table 2

It follows that:

That is, when the bank purchases an insurance policy in the amount of 3 million rubles, the bank's profit will be 0.3165 million rubles.

Thus, we can confidently assert that the methods used in the theory of probability and mathematical statistics are an integral part of calculations in the economic sphere and contribute to the efficient operation of the economy as a whole.

Bibliographic reference

Ogay A.A., Sineokov M.S. USE OF METHODS OF MATHEMATICAL STATISTICS AND PROBABILITY THEORY IN ECONOMY // International student scientific bulletin. - 2017. - No. 4-4 .;
URL: http://eduherald.ru/ru/article/view?id=17434 (date accessed: 11/26/2019). We bring to your attention the journals published by the "Academy of Natural Sciences"

MATHEMATICAL METHODS IN INTERNATIONAL RELATIONS. MATHEMATICAL AND APPLIED CALCULATIONS OF REPEATING THE REVOLUTIONARY POSSIBILITIES OF "COLOR SCENARIOS" IN THE COMMONWEALTH OF INDEPENDENT STATES

International relations is an integral part of science, including diplomatic history, international law, world economy, military strategy and many other disciplines that study various aspects of a single object for them. Of particular importance for her is the "theory of international relations", which, in this case, is understood as a set of multiple conceptual generalizations presented by arguing theoretical schools and constituting the subject field of a relatively autonomous discipline. In this sense, the "theory of international relations" is both very old and very young. Already in ancient times, political philosophy and history raised questions about the causes of conflicts and wars, about the means and ways of achieving order and peace between peoples, about the rules of their interaction, etc. - and therefore it is old. But at the same time, it is also young - as a systematic study of the observed phenomena, designed to identify the main determinants, explain behavior, reveal the typical, recurring in the interaction of international factors. Tsygankov P.A. Theory of international relations: textbook / P.A. Tsygankov. - 2nd ed., Rev. and add. - M .: Gardariki, 2007 .-- 557 p.

The sphere of international relations is mobile and constantly changing. Now, during the period of globalization, integration and, at the same time, regionalization, the number and variety of participants in international relations has increased significantly. Transnational actors have emerged: intergovernmental organizations, transnational corporations, international non-governmental organizations, religious organizations and movements, internal political regions, international criminal and terrorist organizations. As a result, international relations have become more complicated, have become even more unpredictable, it has become more difficult to determine the true, real goals and interests of their participants, to develop a state strategy and formulate state interests. Therefore, at present it is important to be able to analyze and evaluate events in the field of international relations, see the goals of their participants, and set priorities. For this it is necessary to study international relations. In the process of studying, methods of study, their advantages and disadvantages, play a significant role. Therefore, the topic “Mathematical Methods in International Relations. Mathematical and applied calculations of the revolutionary possibilities of the "color scenario" in the Commonwealth of Independent States "are relevant and modern.

In this work, a predictive method was applied, which largely helped to build a chain of logically completed conclusions of the study of the likelihood of a repetition of "color revolutions" in the CIS countries. Therefore, it is advisable to begin with the consideration and definition of the concept of this method.

In international relations, there are both relatively simple and more complex predictive methods. The first group may include such methods as, for example, conclusions by analogy, the method of simple extrapolation, the Delphic method, the construction of scenarios, etc. The second - analysis of determinants and variables, systems approach, modeling, analysis of chronological series (ARIMA), spectral analysis, computer simulation, etc. The Delphic method implies a systematic and controlled discussion of the problem by several experts. Experts submit their assessments of this or that international event to the central body, which summarizes and systematizes them, and then returns them to the experts again. Having been carried out several times, such an operation makes it possible to state more or less serious discrepancies in these estimates. Taking into account the generalization, the experts either amend their initial estimates, or strengthen their opinion and continue to insist on it. Studying the reasons for discrepancies in expert assessments allows us to identify previously unnoticed aspects of the problem and fix attention both on the most (in the case of coincidence of expert assessments) and the least (in case of discrepancy) likely consequences of the development of the problem or situation being analyzed. In accordance with this, the final assessment and practical recommendations are developed. Scenario building - this method consists in building ideal (i.e. mental) models of the likely course of events. Based on the analysis of the existing situation, hypotheses are put forward - which are simple assumptions and are not subject to any verification in this case - about its further evolution and consequences. At the first stage, the analysis and selection of the main factors that determine, in the opinion of the researcher, the further development of the situation are carried out. The number of such factors should not be excessive (as a rule, no more than six elements are singled out) in order to provide a holistic vision of the whole multitude of future options arising from them. At the second stage, hypotheses are put forward (based on simple "common sense") about the supposed phases of evolution of the selected factors over the next 10, 15 and 20 years. At the third stage, the selected factors are compared and, on their basis, a number of hypotheses (scenarios) corresponding to each of them are put forward and more or less detailed. This takes into account the consequences of interactions between the selected factors and the imaginary options for their development. Finally, at the fourth stage, an attempt is made to create indicators of the relative probability of the scenarios described above, which for this purpose are classified (quite arbitrarily) according to their degree, their probability. Khrustalev M.A. Systemic modeling of international relations. Abstract for the degree of Doctor of Political Science. - M., 1992, p. 8, 9. The concept of a system (systems approach) is widely used by representatives of various theoretical directions and schools in the science of international relations. Its generally recognized advantage is that it makes it possible to present the object of study in its unity and integrity, and, therefore, helping to find correlations between interacting elements, it helps to identify the "rules" of such interaction, or, in other words, the patterns of functioning of the international system. On the basis of a systematic approach, a number of authors distinguish international relations from international politics: if the constituent parts of international relations are represented by their participants (actors) and "factors" ("independent variables" or "resources") that make up the "potential" of the participants, then the elements of international politics are only actors. Modeling - the method is associated with the construction of artificial, ideal, imaginary objects, situations, which are systems, the elements and relationships of which correspond to the elements and relationships of real international phenomena and processes. Consider this type of this method as - complex modeling Ibid - the construction of a formalized theoretical model, which is a trinary synthesis of methodological (philosophical theory of consciousness), general scientific (general theory of systems) and private scientific (theory of international relations) approaches. The construction is carried out in three stages. At the first stage, "pre-model tasks" are formulated, combined into two blocks: "evaluative" and "operational". In this regard, such concepts as “situations” and “processes” (and their types), as well as the level of information, are analyzed. On their basis, a matrix is ​​built, which is a kind of "map" designed to provide the researcher with the choice of an object, taking into account the level of information security.

As for the operational block, the main thing here is to single out the nature (type) of models (conceptual, theoretical and specific) and their forms (verbal or meaningful, formalized and quantified) on the basis of the triad "general-specific-individual". The selected models are also presented in the form of a matrix, which is a theoretical model of modeling, reflecting its main stages (form), stages (character) and their relationship.

At the second stage, we are talking about building a meaningful conceptual model as the starting point for solving the general research problem. On the basis of two groups of concepts - "analytical" (essence-phenomenon, content-form, quantity-quality) and "synthetic" (matter, movement, space, time), presented in the form of a matrix, a "universal cognitive structure - configurator" is built. setting the general framework for the study. Further, on the basis of identifying the above logical levels of research of any system, the noted concepts are reduced, as a result of which the “analytical” (essential, meaningful, structural, behavioral) and “synthetic” (substrate, dynamic, spatial and temporal) characteristics of the object are distinguished. Relying on the "system oriented matrix configurator" structured in this way, the author traces the specific features and some trends in the evolution of the system of international relations.

At the third stage, a more detailed analysis of the composition and internal structure of international relations is carried out, i.e. building its expanded model. Here, the composition and structure (elements, subsystems, connections, processes), as well as the "programs" of the system of international relations (interests, resources, goals, mode of action, balance of interests, balance of forces, relations) are distinguished. Interests, resources, goals, mode of action constitute the elements of the "program" of subsystems or elements. The resources, characterized as a “non-system-forming element”, are subdivided by the author into resources of means (material-energy and informational) and resources of conditions (space and time).

The "program of the system of international relations" is a derivative in relation to the "programs" of elements and subsystems. Its backbone element is the "correlation of interests" of various elements and subsystems with each other. The non-system-forming element is the concept of "balance of forces", which could be more accurately expressed by the term "ratio of means" or "ratio of potentials". The third derivative element of the specified "program" is the "relation" understood by the author as a kind of evaluative representation of the system about itself and about the environment.

At the same time, it would be wrong to exaggerate the importance of the systems approach and modeling for science, to ignore their weaknesses and shortcomings. The main one is, paradoxical as it may seem, the fact that no model - even the most flawless in its logical foundations - gives confidence in the correctness of the conclusions drawn on its basis. This, however, is recognized by the author of the work discussed above when he speaks of the impossibility of building an absolutely objective model of the system of international relations. Let us add that there is always a certain gap between the model constructed by this or that author and the actual sources of those conclusions that he formulates about the object under study. And the more abstract (that is, the more strictly logically substantiated) the model is, and also the more adequate to reality its author strives to make his conclusions, the wider is the indicated gap. In other words, there is a serious suspicion that when formulating conclusions, the author relies not so much on the model structure he built, but on the initial premises, the “building material” of this model, as well as on others not related to it, including “intuitive logical "methods. Hence the question, which is very unpleasant for the "uncompromising" supporters of formal methods: could those (or similar) conclusions that emerged as a result of a model study be formulated without a model? The significant discrepancy between the novelty of such results and the efforts made by researchers on the basis of systems modeling makes it possible to believe that an affirmative answer to this question looks very reasonable.

As for the systems approach as a whole, its shortcomings are a continuation of its merits. Indeed, the advantages of the concept of "international system" are so obvious that it is used, with few exceptions, by representatives of all theoretical directions and schools in the science of international relations. However, as the French political scientist M. Girard justly noted, few people know exactly what it means in reality. It continues to retain a more or less strict meaning for functionalists, structuralists and systemists. For the rest, it is most often nothing more than a beautiful scientific epithet, convenient for decorating an ill-defined political object. As a result, this concept turned out to be oversaturated and devalued, which makes it difficult to use it creatively.

Agreeing with the negative assessment of the arbitrary interpretation of the concept of "system", we emphasize once again that this does not at all mean doubts about the fruitfulness of the application of both the systems approach and its specific incarnations - system theory and system analysis - to the study of international relations.

The role of predictive methods of international relations can hardly be overestimated: after all, in the final analysis, both analysis and explanation of facts are needed not by themselves, but for the sake of making forecasts of the possible development of events in the future. In turn, forecasts are made in order to make an adequate international political decision. Analysis of the partner's (or adversary's) decision-making process is called upon to play an important role in this.

Thus, in my work, an analysis was made of the possibility of repeating the “color scenario” in the CIS countries by constructing a tabular matrix, which, in turn, presents the criteria for situations at a given moment in a given CIS state. It should be noted that the score for assessing the criteria of situations was 5, since in the countries of the former Soviet Union the trend of comparison according to the system above 5 points remains unchanged, and therefore, the author proposed a 5-point scale, about 100 were proposed as evaluators. people, citizens of the CIS countries, who, according to the system of questionnaires and social polls, answered the proposed questions (criteria) on the Internet (social networks: Facebook, Odnoklassniki, etc.).

The table presents 7 criteria that can most affect the likelihood of a repeat of revolutions in a given region: weakness of the state, weakness of law enforcement agencies, split of elites, spread of an anti-government utopia, external pressure, confrontational agitation and propaganda, activity of the masses. Participants of the Commonwealth of Independent States were proposed on an individual basis, as well as on a regional basis, the average score of the highest probability of repetition was calculated.

As can be seen from the table, Ukraine has close to the maximum score of 4, in which the situation with the problem of the weakness of the political system remains acute to this day, as a result of which the ideas of an anti-government utopia are close to 4 points, which confirms the deplorable situation in this state. Speaking of external pressure, the participants in the social survey gave the maximum score - 5, which is a complete lack of self-determination, dependence on external influence and the helplessness of a given state from foreign interventions and injections of financial investments by it. The split of the elites is also an important problem of this zone, since 5 points were marked according to the schedule, i.e. at the moment, Ukraine is divided into several parts, the split elites dictate their ideas for conducting politics, which undoubtedly puts the state in one of the poorest countries in the world today. The average score for the danger of repeating the "color revolutions" was 4.

Further, we consider the problems of our country - Kyrgyzstan, to which the survey participants determined the maximum score - 5 among all the participants of the CIS countries, when compared with neighboring Tajikistan, our state has military-economic, political and economic weaknesses that prevent our country from being one step ahead neighboring republics. Despite the confrontational agitation and propaganda close to the minimum score - 2, the rest of the criteria are mostly close to - 4, it turns out that at the moment the situation after two revolutions did not give any lessons and the consequences were meaningless. The average score for the likelihood of a repeat of revolutions in our republic was 3.6.

However, for all the paradox, the situation in Tajikistan remains not the best, when compared with the same Georgia, which also suffered two "color revolutions", Tajikistan has socio-economic, political weaknesses, an off-scale unemployment rate demoscope.ru/weekly /2015/0629/barom07.php in this country forces citizens to leave to work in Russia (including the problem of drug trafficking, criminal activities of extremist groups, the danger of religious extremism, clannishness). In Tajikistan, the average score was 3, 4.

Turkmenistan is one of the “closed” countries of the former USSR, today it is in last place, with an average repeat score of the “color scenario” of only 1.7. Whether this result indicates that the state is classified in its economic, political and military issues, or in fact, this state is one of the most prosperous at this time, everyone decides for himself. Even comparing the same Uzbekistan (3 points) on foreign aid issues, Turkmenistan has 2 points, confirming that this country exists to the greatest extent "by itself", providing its people and statehood with its own efforts. Thus, ranking last on this list.

international color revolution state

The work will include a graph of the average repetition rate of "color revolutions" in the CIS countries by individual criteria, ie. if the tabular matrix shows how the evaluation work was carried out according to certain criteria, then the graph allows you to see the whole situation of this issue, where there is the highest repetition rate of the "color scenario", and where - the smallest. From which it turns out that the highest probability of a repeat (on an individual basis) in Ukraine is 4 points, and the lowest in Turkmenistan and Uzbekistan is about 2 points.

However, if Ukraine has the greatest danger of repeating revolutions (4 points), then by division into regional characteristics, the countries of the so-called Transcaucasia (Azerbaijan, Georgia, Armenia) have the highest average score - 2.9, compared to Eastern Europe, which has 2.8 points, Central Asia has 2.7 points, which puts our region in the last place in terms of the possibility of repeating the "color scenario", despite the difference of 0.1 points compared to other regions of the CIS.

The totality of economic (unemployment, low wages, low labor productivity, non-competitiveness of the industry), socio-medical (disability, old age, high morbidity), demographic (single-parent families, a large number of dependents in the family), educational qualifications (low level of education, insufficient professional training), political (military conflicts, forced migration), regional-geographical (uneven development of regions), religious-philosophical and psychological (asceticism, as a way of life, foolishness) causes the Transcaucasian countries to rank first in terms of backwardness and poverty regions of the CIS countries, which will certainly lead to the likelihood of a repeat of revolutionary situations in the region. The discontent of civil society, despite the dictatorship of some states of the Central Asian region (Uzbekistan, Turkmenistan), can spill out through careful external sponsorship and investment influences and specially prepared youth opposition, despite excessive democracy, according to the author, in countries such as Kyrgyzstan, Ukraine the likelihood of a repeat of revolutions is really high, since the consequences of the past “color revolutions” are not justified in any way and the results did not lead to any significant changes, except that only the “top” of power changed.

Summing up, this section largely helped to reveal the essence of the topic "General and specific features of the" color revolutions "in the CIS countries", the method of applied and mathematical analysis led to the conclusion about the likelihood of a repeat situations and not fundamentally change the issues of poverty in Eastern Europe, not to resolve conflicts at the interethnic level in Azerbaijan, Armenia and Georgia and not to end the problem of clannishness and nepotism in Central Asia.

Improvement of computer technology, further development of the mathematical apparatus increases the range of

E. G. Baranovsky, N. N, Vladislavleva
changes in exact methods in the humanities, including in international relations. The use of mathematical methods in conducting political research allows us to expand the traditional methods of qualitative analysis, to increase the accuracy of predictive estimates. International relations are a sphere of public activity with a huge number of factors, events and relationships of a very different nature, therefore, on the one hand, this area of ​​knowledge is very difficult to formalize, but on the other hand, for a complete and systematic analysis, it is necessary to introduce common concepts and a certain unified language: “Politics, dealing with problems of fantastic complexity needs a common language ... There is a need for coherent and universal logic and precise methods for assessing the impact of a given policy on the achievement of goals. You need to learn to clearly understand complex structures in order to make the right decisions. ...
The mathematical tools used today in the study of international relations, in the overwhelming majority of cases, were borrowed from related social sciences, which in turn got them from the natural sciences. It is accepted to distinguish the following types of mathematical means: 1) means of mathematical statistics; 2) the apparatus of algebraic and differential equations; 3) game theory, modeling, on a computer, information-logical systems, "non-quantitative sections" of mathematics.
Mathematical approaches in the analysis of international relations are used in two ways - for solving tactical (local) issues and for analyzing strategic (global) problems. Mathematics also acts as a useful tool for building a model of international relations of various levels of complexity. It should be borne in mind that “the application of quantitative methods in the social sciences is based on the creation of such models, which in their essence depend not so much on the absolute values ​​of the numbers as on their order. Such models are not intended for obtaining numerical results.
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results, but rather to answer questions about whether or not there is a certain property, for example, sustainability. "
When constructing formalized models and applying mathematical methods, the following conditions must be taken into account.
1) Conceptual models should allow formalizing the available information array into quantitatively measurable indicators. 2) When constructing forecasts based on the use of formalized methods, it should be taken into account that they are able to calculate a limited number of options in strictly defined areas of the application.
The main steps in building a formal model include:
1. Development of hypotheses and development of a system of categories.
2. The choice of methods for obtaining conclusions and the logic of transforming theoretical knowledge into practical consequences.
3. The choice of a mathematical display that is adequate to the applied theory.
It should be noted that the problems arising in the construction of a system of hypotheses and categories are the most difficult to solve.The hypothesis should be such a theoretical construction, which, on the one hand, would adequately reflect the qualitative aspects of the research object, and measured units or the isolation of a system of indicators that adequately reflect the state of an object and the changes that occur in it.
There are also special requirements for the categories used in the formalization process. They must correspond not only to theoretical approaches and a system of hypotheses, but also to the criteria of mathematical clarity, that is, to be operational. The best option seems to be the construction of a categorical apparatus according to the "pyramid" principle, so that the content of the most generalized categories is gradually revealed by categories that cover specific phenomena, and reduced to categories that go beyond quantitatively measurable indicators.

Methods for the analysis of international conflicts
The formalization of political science categories and a system of hypotheses, the construction of a model of a conflict situation and process on this basis suggests that within the framework of a formal description, it is necessary to present as many ideas as possible in the most capacious form. At this stage, the important points are the generalization and simplification of international processes and phenomena. The greatest difficulty is the translation of qualitative categories into a quantitative (measurable) form, which essentially boils down to assessing the significance of each category ... For this, the scaling method is used.
The following methods can be attributed to the mathematical tools used in the applied analysis of international relations.
I. Extrapolation. The methodology is an extrapolation of events and phenomena of the past for the future period, for which data collection is carried out in accordance with selected indicators for certain time intervals. As a rule, extrapolation is done only for short time intervals in the future, because with a longer time frame, the probability of error increases significantly. This is called the predictive depth. To determine it, you can use the dimensionless indicator of the depth (range) of forecasting, proposed by V. Belokon:? =? t / tx,? t is the absolute lead time; tХ is the value of the evolutionary nickel of the predicted object. Formalized methods are effective if the value of the depth of lead? " 1.
The basis of extrapolation methods is the study of time series, which are time-ordered sets of measurements of certain characteristics of the object or process under study. The time series can be represented as follows:
уt = Xt +? t where
Xt is a deterministic non-random component of the process; 136

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? t is a stochastic random component of the process.
If the deterministic component (trend) хt characterizes the existing dynamics of the development of the process as a whole, then the stochastic component еt reflects random fluctuations or noises of the process. Both components of the process are determined by some functional mechanism that characterizes their behavior in time. The forecasting task is to determine the type of extrapolating functions хt, еt on the basis of the initial empirical data. To estimate the parameters of the selected extrapolation function, the least squares method, the exponential smoothing method, the probabilistic modeling method and the adaptive smoothing method are used.
2. Correlation and regression analysis. This method allows you to identify the presence or absence of relationships between variables, as well as to determine the nature of such relationships, that is, to find out what is the cause (independent variable) and what is the effect (dependent variable).
For the linear case, the multiple regression model is written as:
Y = X x? +? where
Y is the vector of values ​​of the function (dependent variable); X is a vector of values ​​of independent variables;
? - vector of values ​​of the coefficients;
? is a vector of random errors.
3. Factor analysis. A systematic approach to forecasting complex objects means the maximum possible consideration of the set of variables that characterize the object and the relationships between them. Factor analysis allows making such accounting and at the same time reducing the dimension of system studies. The main idea of ​​the method is that variables (indicators) closely correlated with each other indicate the same reason. Among the available indicators, their groups are searched for, which have a high level (value) of correlation, and on their basis, so-called complex variables are created, which are combined by

N., G. Baranovsky, N. N. Vladislavleva
Methods for analyzing international conflicts
the correlation effect. Based on the indicators,
factors.
1. Spectral analysis. This method allows you to fairly accurately describe the processes, the dynamics of which contains oscillatory or harmonic components. The process under study can be represented as:
x (t) = x1 (t) + x2 (t) + x3 (t) +? (t), where
х1 (t) - secular level;
х2 (t) - seasonal fluctuations with a twelve-month period; x3 (t) - fluctuations with a period longer than seasonal, but less than the corresponding fluctuations of the secular level;
? (t) - random fluctuations with a wide range of periods, but with low intensity.
Spectral analysis allows you to identify fundamental vibrations in complex structures and calculate the frequency and duration of the phase. The method is based on the selection of the structure of the oscillatory process and the construction of a graph of sinusoidal oscillations. For this, chronological data are collected, an oscillation equation is drawn up, cycles are calculated, on the basis of which graphs are built.
5. Game theory. One of the main methods for analyzing conflict situations is game theory, which began with the works of von Neumann in the 20s and 40s. After a period of rapid prosperity and an excessive abundance of research from the 50s to the early 70s, the development of game theory began to decline markedly. Disappointment in game theory is partly due to the fact that, despite the many mathematical results and proven theorems, the researchers failed to make significant progress in solving the problem they set themselves: to create a model of human behavior in society and learn to predict the possible outcomes of conflict situations. However, the effort was not in vain. It turned out that of the concepts developed in game theory, they are very convenient for describing all kinds of problems that arise in the study of conflict situations.

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Techniques for building and modeling models
international conflicts
Game theory allows you to: structure a problem, present it in a visible form, find areas of quantitative estimates, orderings, preferences and uncertainty, identify dominant strategies, if they exist; fully solve the problems that are described by stochastic models: identify the possibility of reaching an agreement and explore the behavior of systems capable of agreement (cooperation), that is, the interaction area near the saddle point, equilibrium point or Pareto agreement. However, many questions remain for the possibilities offered by game theory. Game theory is based on the principle of average risk, which is not always true for the behavior of participants in a real conflict. Game theory does not take into account the presence of random variables describing the behavior of the conflicting parties, does not allow a quantitative description of the structural components of a conflict situation, does not take into account the degree of awareness of the parties, the ability of the parties to quickly change goals, etc. However, this does not detract from the advantages that the application of game theory provides for solving problems at certain stages of the conflict. It should be noted that there are two ways for a systematic study of conflicts: 1. To describe the interaction of systems in a fairly general form, taking into account all significant factors and, on the basis of systemography, to detect and investigate the possible nature of the interaction of the conflicting parties, the causes of the conflict, mechanisms, course, outcomes, etc. . p. Such models are obtained on a large scale, requiring large computational resources, but at the same time they give a multifaceted rather reliable result. 2. Assume that the parties, causes and nature of the conflict are known, highlight the main factors, build simple calculation models to assess the weight of the a priori factor and the results of the conflict. The path is narrow enough, but economical and efficient, giving specific results for the parameters of interest in a short period of time. Both methods are used, depending on the nature of the research tasks. For strategic research aimed at identifying the

E. G. Baranovsky, N. N. Vladislavleva
Methods for the analysis of international conflicts
potential conflicts, influence on the entire system of international relations, the formation of a long-term strategy of the state's behavior in relation to a possible conflict situation, the degree of influence directly on the interests of the state, etc., of course, the first method of organizing the study is preferable. To solve short-term tasks of a tactical nature, the second of the described methods is used.
In addition to this division, it is proposed to consider the application of various mathematical methods depending on the stage of the conflict and the set of specific structural components of the conflict situation or process that need to be assessed. For example, in order to develop and describe the behavior strategy of one or another participant at a stage when the conflict has not yet developed into an armed phase and it is possible to negotiate a mutually acceptable agreement, it is proposed to consider the possibility of applying game theory. Within the framework of the theory of cooperative agreements, the issue of sustainability will be considered; an agreement has already been reached, which is an important point in post-conflict settlement. We will use quantitative analysis to assess “acceptable damage” and “pain threshold”. As mentioned earlier, one of the most important structural components of a conflict situation is potential, in particular an indicator of the tension of the conflict. To construct the stress curve, it is proposed to use factor analysis, methods of mathematical statistics and probability theory. Let's consider the proposed methods in more detail.
The resolution of a conflict means reaching a mutually acceptable agreement between the parties to the conflict. Politicians instinctively choose the best among the worst outcomes as the starting point from which they begin to develop a cooperative stance. The minimax principle, game theory and the procedure for reconciling the interests of the parties in cooperative games formalizes this practice.
Negotiations and coordination of the positions of the parties contribute to the achievement of compromises, which can be the desired solution to the conflict. At the same time, the parties involved in the conflict

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Methods for constructing and analyzing models of international conflicts
can use various basic strategies of behavior. By entering into alliances, blocs of states can improve their bargaining power and secure a greater degree of cooperation from partners. Sophisticated methods of using threats, sanctions and even the use of force are used by states to force other states to cooperate with them. The threat of non-cooperation may result in fewer benefits for both parties. A small state can convince a larger state to cooperate with it in such a way that each of them, acting together, will receive more benefits. On the other hand, the larger state may impose cooperation on the smaller one, because the latter may be in dire need of the gains that may result from such cooperation.
Before proceeding to a formalized presentation of the basic concepts of game theory, it is necessary to dwell on two important conditions for the application of this method: the participants' awareness of the situation and the formation of their goals. In game-theoretic modeling of conflict situations, they usually proceed from the assumption that the entire situation of the conflict is known to all participants, in any case, each participant clearly represents his interests, opportunities and goals. Of course, in real conditions, the refinement of ideas takes place right up to the very end of negotiations on the choice of a joint solution. However, the idealization adopted in game theory seems to be justified, at least as an initial stage of scientific analysis.
The process of forming the goals of the participants is most clearly described in the work of Yu.B. Germeier. ...
Any decision can be presented as a result
striving to achieve some goal in the considered
process.
Any process from the point of view of making a decision or forming goals is adequately described by a finite set of certain values ​​(1
E. G. Baranovsky, N., N. Vladislavleva
Methods for the analysis of international conflicts

3. The purpose of the decision maker can be expressed in
in the form of certain tendencies to the values ​​of Wi and only to them. In the general case, there can be several participants (n) in the process pursuing different goals.
4. Objectives should be formulated as clearly as possible and not change during the process time considered in the decision. The variability of the goal over time entails the impossibility of making clear rational decisions.
5. Goals can be set, instilled and nurtured.
6. The process of setting goals should be distinguished by caution, clarity and stability over time. The goals should be structurally simplified with an increase in the dimension of the process. For the formation of goals; only the most general and crude characteristics of the multitude of changes XV should be used. To facilitate the process of forming goals, an orienting analysis of the ways of forming goals and a language for describing these ways is necessary.
A well-defined goal can be expressed as
the desire to increase some unified scalar efficiency criterion w0, defined as a function of only the vector W: w0 = Ф (W)
Basically, in practice, the following types of elementary methods of forming unified criteria (criteria convolution) are used:


b) lexicographic convolution of criteria, when the maximum of the criterion Wi is first sought, then on the set

a) the choice of one (for example, the first) as a single criterion when imposing restrictions of the form Wi> Аi (i> 1) on the others, or in general only imposing restrictions Wi> Аi on all criteria. In the latter case, a single criterion can be
to represent in the form:

Chapter IV
Methods for constructing and analyzing models of international conflicts

the criterion W2 is maximized, etc. until all the criteria are exhausted or at the next iteration the maximum is reached at a single point;
c) summation with weights or economic convolution:

where? i are some positive numbers, usually normalized by the condition

d) minimum-type convolution (Germeier convolution):

Here, in principle, Wio is any constant, but it is most natural to take the minimum value of the i-th criterion as Wio, and the maximum (desired) value as Wim.
Economic convolution is applied if the deterioration in the value of one of the criteria can in principle be compensated for by an improvement in the value of any other. With the Hermeier convolution, the criteria are not interchangeable. When modeling conflict situations, the second method of convolution is often used, since it is believed that it is impossible to negotiate if it is assumed that any increase in the risk of a conflict escalating into an armed stage can be compensated for by some other advantages.
Sustainable agreements. Let us dwell on a systematic presentation of the main questions of the theory of cooperative agreements. We will adhere to the generally accepted concept of cooperation as a kind of association of entities (individuals, organizations, countries) that satisfies three conditions: 1) all entities participate in cooperation voluntarily; 2) all subjects can voluntarily dispose of their resources; 3) it is beneficial for all subjects to participate in cooperation.

E. G. Baranovsky, N. N. Vladislavleva
Methods for the analysis of international conflicts
Cooperative agreements (institutions of consent) are the basis of the modern theory of conflict as a set of mathematical methods that allow one to study the informal connections that arise between the parties to the conflict and help to find a solution to the conflict by building institutions of agreement.
Let there are n participants in the conflict, they are assigned numbers i = = 1, ..., n and they form the set N = (1, ..., n). All actions that the participant with number 1 can take to achieve their goals are limited to the set Xi. Elements xi of this set are usually called strategies. The complete set х = (х1, ..., хn) of strategies of all participants is called the outcome of the conflict situation.
In order to set the interests, aspirations of each participant, it is necessary to describe which of the possible outcomes of the conflict situation are most preferable for him, which are less. A very general and technically convenient way of such a description is related to the objective functions or the participants' payoff functions. Suppose that for each participant i (i = 1, ..., m) a function fi (x) = fi (x1, ..., xn) is given on the set of all possible outcomes, that is, the value fi depends not only on own strategy xi. Outcome x is more preferable for participant i than outcome y if and only if fi (x)> fi (y). In what follows, we will conventionally call the values ​​fi (x) the “payoffs” of the corresponding participants.
Let the participants in the conflict situation come together to jointly choose their strategies (in practice, these are political negotiations between the parties to the conflict). In principle, they can agree on the implementation of any outcome of the conflict. But since each participant strives for the greatest possible value of his "gain" and cannot but reckon with a similar desire of partners, some outcomes will certainly not be realized, and different versions of agreements have different degrees of "viability."
Let one of the participants (participant 1) completely abandon all relationships with partners and decide to act on their own.

Chapter IV
Methods for constructing and analyzing models of international conflicts
independently, If participant i chooses some of his own strategy xi, then the "gain" he has received will be, in any case, not less than the minimum of the objective function fi (x) = fi (x1, ..., xn), for all possible values ​​of the variables x1 ..., xn, except for xi. Having chosen his strategy xi in such a way as to maximize this minimum, participant i will be able to expect to win

Consequently, the proposal of a variant that barks to participant i a “gain” less than the guaranteed result? I has no chance of getting his consent. Therefore, we will assume that, as possible variants of a joint solution, only outcomes x are discussed that satisfy the inequalities fi (x)>? I; for all iєN. The set of such outcomes will be denoted by IR - the set of individually rational outcomes. Note that it is not necessarily empty: if each participant applies his own guaranteeing strategy, then the outcome from the set IR is realized.
The question of the sustainability of a possible agreement is very important. The discussed option may be beneficial when compared with the guaranteed result? I, but not beneficial compared to unilateral violation of the agreement.
Let the participants agree on a joint choice of some outcome x. For the stability of this agreement, it is necessary that violation of it by any participant is not beneficial to the violator. If there are two participants (N = (1, 2)), then this condition is written as the fulfillment of two systems of inequalities:

for all у1єX1, y2єX2, or as the fulfillment of the system of equations

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Methods for the analysis of international conflicts
For an arbitrary number of participants, we introduce the notation
x ¦¦ yi is the outcome of the conflict in which participant i applies strategy yi, and all other participants apply strategy xj. Then the stability conditions for the agreement on the choice of the outcome х = (х1, ..., хn) consist in the fulfillment of the inequalities fi (х)> fi (х II уi) for all i є N, yiєxi, or in the fulfillment of the equalities:

these conditions were first formulated by J. Nash in 1950. The outcomes satisfying them are called equilibrium according to Nash, as well as equilibrium points, or simply equilibria. The set of outcomes will be denoted by NE.
It does not follow from the definition of equilibrium that equilibrium outcomes should exist at all. Indeed, it is not difficult to construct examples of conflict situations that do not have equilibrium outcomes at all. All that theory can offer to participants in such situations is to expand the set of outcomes (that is, a set of collective strategies), either by finding unaccounted for strategic opportunities, or deliberately introducing additional opportunities. As general methods of such expansion, it can be indicated that, firstly, taking into account the natural dynamics of a violation, beneficial from the point of view of short-term interests, may turn out to be disadvantageous if we take into account more distant consequences; secondly, an increase in mutual awareness of the participants - if the parties to the conflict manage to organize an effective system of mutual control, then the potential violator of the agreement will have to take into account the possibility of an unfavorable reaction of partners to his deviation from the strategy envisaged by the agreement, which will nullify the benefits of violating the agreement.
However, the existence of equilibrium outcomes does not mean that it will be easy for participants to conclude a cooperative agreement. Consider an example called the Prisoner's Dilemma. Two participants have two strategies "peacefulness" and "aggressiveness". Participants' preferences on a set of four outcomes are as follows. In na-

Chapter IV
Methods for constructing and analyzing models of international conflicts
the best position turns out to be a participant who has chosen the strategy of aggressiveness against a peace-loving partner. In second place is the outcome, in which both participants are peaceful. This is followed by an outcome in which both are aggressive, and, finally, the worst thing is to be peaceful, against an aggressive partner. By assigning conditional numerical values ​​of the "payoff" functions to these outcomes, we obtain the following payoff matrix:
(5, 5) (0,10) (10,0) (1, 1).
As is customary in game theory, we assume that the strategies of participant 1 correspond to the rows of the matrix, to the strategies of participant 2, columns (the first row (column) is a peaceful strategy, the second is aggressive), the first number in parentheses is “winning” of participant 1 in the corresponding outcome, the second is “winning” "Participant 2. It is easy to check that it is more profitable for each participant to be aggressive for any partner's strategy, therefore, the only equilibrium outcome is the use of aggressive strategies by both participants, which gives each participant a" payoff "equal to 1. However, this approach is not very attractive for the participants, because by applying strategies of peacefulness, they could both increase their "payoff." Thus, we see that the fulfillment of the Nash conditions is by no means the only requirement that makes sense to present to a potential agreement.
In order to formulate in general terms another natural requirement prompted by the considered example, let us imagine that in the general situation two variants of the agreement are being discussed: to realize the outcome x and to realize the outcome y. Generally speaking, some participants are more profitable with outcome x, others
outcome y. If it happens that the outcome of x is beneficial to someone than y, and the outcome of y is not better for everyone than x, then there seems to be no reason for the participants to agree on the implementation of the outcome y. In this case, the outcome x is said to dominate in the Pareto sense of the outcome y.

E. G. Baranovsky, N. N. Vladislavleva
Methods for the analysis of international conflicts
Outcomes of the conflict that are not dominated by any others, that is, cannot be rejected on the basis of these considerations, are called Pareto optimal or effective. Let us give a precise definition: an outcome x is Pareto optimal if and only if, for any outcome y, the inequality fi (y)> fi (x) for at least one i єN implies the existence of jєN for which fj (y)> fj (x ). Indeed, the above condition means exactly that if there is a participant interested in discussing outcome y instead of outcome x, then there will be a participant interested in the opposite. The set of optimal but Pareto outcomes will be denoted by RO.
In game theory, the set of IR P RO, that is, the set of Pareto optimal individually rational outcomes, is usually called the negotiation set, as if assuming that with reasonable behavior of the participants, negotiations on a joint solution will end from this set.
Along with the advantages that mathematical methods provide, there are a number of difficulties that limit the possibilities of their application for the analysis of international conflicts. The first such difficulty is associated with taking into account the human factor, which plays a significant role in the decision-making process. Possessing logical thinking, a person is also subject to the sphere of subconscious drives, emotions, passions affecting rational thinking, which in the behavior of state and political leaders often makes decisions difficult to predict. Although theoretically a system or environment should impose restrictions on their deviations from the most rational choice, history shows that the role of a state leader often turns out to be decisive, while he himself, making a decision, becomes immune to objective information, and acts on the basis of the subjective largely intuitively, understanding the political process and the intentions of opponents and other actors.
Another difficulty is associated with the fact that some processes seem to be random, stochastic, because at the time of the study, their causes are invisible. If figuratively

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Techniques for building and modeling models
international conflicts
to compare a political song with a biological organism, then the reasons for this are similar to a virus that does not show activity for a long time due to the lack of favorable environmental conditions. With regard to international relations and conflicts, it is important not to lose sight of the historical aspect, since the origins of some of the processes observed by contemporaries are fixed in national traditions and national consciousness.
Of course, mathematical models by themselves cannot answer the question of how to resolve existing contradictions, they cannot become a panacea for all conflicts, but they greatly facilitate the management of conflict processes, reduce the level of resources spent, help to choose the most optimal strategy of behavior, which reduces the amount of losses , including human ones.
To date, applied modeling of international relations is carried out in many institutions of industrialized countries. But, of course, the palm among them belongs to such centers as Stanford, Chicago, California Universities, Massachusetts Institute of Technology, and the International Center for Peacekeeping in Canada.
In the next chapter, we will look at some examples of the prayers of international conflict.

Tsygankov P. Political Sociology of International Relations

Chapter IV. The problem of the method in the sociology of international relations

The main purpose of this chapter is to introduce the most widely used methods, techniques and techniques in the study of international relations and foreign policy. It does not set takai, a rather complex and independent task of how to teach how to use them. However, its solution would be impossible, since this requires, firstly, a detailed description of tech or other methods, illustrated by examples of their specific application in research work in the analysis of a certain object of international relations, and, secondly (and this is the main ), practical participation in one or another scientific-theoretical or scientific-applied project, since, as you know, you cannot learn to swim without entering the water.

It should be borne in mind that each researcher (or research team) usually uses his favorite method (or their group), adjusted, supplemented and enriched taking into account the existing conditions and tools. It is also important to keep in mind that the application of a particular method depends on the object and objectives of the study, as well as (which is very important) on the available material resources.

Unfortunately, it is necessary to note the fact that the special literature devoted to the problem of methods and especially applied methods of analysis of international relations is very few (especially in Russian) and therefore difficult to access.

1. Significance of the problem of the method

The problem of the method is one of the most important problems of science, since ultimately it is about teaching, getting new knowledge, how to apply it in practice. At the same time, this is one of the most difficult problems, which precedes the study of its object by science, and is the result of such a study. It precedes the study of an object because from the very beginning the researcher must possess a certain amount of techniques and means of achieving new knowledge. It is the result of the study, because the knowledge obtained as a result of it concerns not only the object itself, but also the methods of its study, as well as the application of the results obtained in practical activity. Moreover, the researcher is faced with the problem of the method already when analyzing the literature and the need for its classification and evaluation.

Hence the ambiguity in understanding the content of the term "method" itself. It means both the sum of the techniques, means and procedures for research by science of its subject, and the totality of already existing knowledge. This means that the problem of method, while having an independent meaning, is at the same time closely related to the analytical and practical role of theory, which also plays the role of method.

The widespread belief that each science has its own method is only partially true: most social sciences do not have their own specific, only inherent method. Therefore, in one way or another, they refract, in relation to their object, the general scientific methods and methods of other (both social and natural science) disciplines. In this regard, it is generally accepted that the methodological approaches of political science (including the political sociology of international relations) are built around three aspects: the most strict separation of the research position from moral value judgments or personal views; the use of analytical techniques and procedures that are common to all social sciences, which play a decisive role in establishing and subsequent consideration of facts; the desire to systematize, or, in other words, to develop common approaches and build models that facilitate the discovery of "laws" 1.

And although it is emphasized that what has been said does not mean the need to "completely banish" value judgments or personal positions of the researcher from science, nevertheless, he inevitably faces a problem of a broader nature, the problem of the relationship between science and ideology. In principle, one or another ideologue, understood in a broad sense as a conscious or unconscious choice of a preferred point of view, always exists. It is impossible to avoid this, "de-ideologize" in this sense. Interpretation of facts, even the choice of "viewing angle", etc. are inevitably conditioned by the point of view of the researcher. Therefore, the objectivity of research suggests that research must constantly remember about the "ideological presence" and strive to control it, see the relativity of any conclusions, given such a "presence", try to avoid a one-sided vision. The most fruitful results in science can be achieved not with the denial of ideology (this is at best a delusion, but at worst deliberate cunning), but under the condition of ideological tolerance, ideological pluralism and "ideological control" (but not in the sense of the official political ideology in relation to science, and vice versa in the sense of the control of science over any ideology). As for the problem of values, it would not be an exaggeration to say that the difficulties that Russian sociology is experiencing today are connected precisely with the deficit of the value principle. The atmosphere of tough political pressure that prevailed in the country for many years led to the fact that the Soviet sociology of the herd developed within the framework of the American behaviorist tradition, giving preference to operational, instrumental approaches and methods. This allowed her to sort of "get rid" of ideology: Soviet sociologists were among the first among Russian social scientists who stopped believing ideological myths. But, on the other hand, having failed to adopt the traditions of theoretical sociology, for example, the French school with its Durkheim traditions, or the German phenomenological sociology of Max Scheller, etc., Soviet (and the post-Soviet that inherited it) sociology has not yet been able to adapt to the new , the post-non-classical trend in the world social (including sociological, political, and any other) science, where there is a renaissance of values, anthropological approach, attention to socio-cultural specifics, etc.

The foregoing also applies to the so-called methodological dichotomy, which, incidentally, is often observed not only in domestic, but also in Western science of international relations. We are talking about the opposition of the so-called traditional historical-descriptive, or intuitive-logical approach to the operational-applied, or analytic - predictive, associated with the use of methods of exact sciences, formalization, data calculation (quantification), verifiability (or falsifiable) conclusions, etc. In this regard, for example, it is argued that the main drawback of the science of international relations is the protracted process of its transformation into applied science 2. Such statements are too categorical. The process of the development of science is not linear, but rather reciprocal: it is not transformed from a historical-descriptive into an applied one, but the clarification and correction of the theoretical position through applied research (which, indeed, is possible only at a certain, sufficiently high stage of its development) and "return debt ”to“ applied specialists ”in the form of a more solid and operational theoretical and methodological basis.

Indeed, in the world (first of all, American) science of international relations, since the beginning of the 50s of the XX century, the development of many relevant results and methods of sociology, psychology, formal logic, as well as natural and mathematical sciences has been taking place. At the same time, the accelerated development of analytical concepts, models and methods begins, progress towards the comparative study of data, the systematic use of the potential of electronic computing technology. All this contributed to the significant progress of the science of international relations, bringing it closer to the needs of practical regulation and forecasting of world politics and international relations. At the same time, this by no means led to the displacement of the old, "classical" methods and concepts.

Thus, for example, the operational nature of the historical-sociological approach to international relations and its predictive capabilities were demonstrated by R. Aron. One of the most prominent representatives of the "traditional", "historical-descriptive" approach, G. Morgenthau, pointing out the insufficiency of quantitative methods, wrote not without reason that they could far from claim to be universal. A phenomenon so important for understanding international relations as, for example, power, “there is a quality of interpersonal relations that can be checked, evaluated, guessed, but which cannot be quantified ... Of course, it is possible and necessary to determine how many votes can be given over to politics, how many divisions or nuclear warheads the government has; but if I need to understand how much power a politician or government has, then I will have to put aside the computer and the calculating machine and start thinking about historical and certainly qualitative indicators. "

Indeed, the essence of political phenomena cannot be investigated in any way fully using only applied methods. In social relations in general, and in international relations in particular, stochastic processes dominate, which defy deterministic explanations. Therefore, the conclusions of the social sciences, including the science of international relations, can never be finally verified or falsified. In this regard, the methods of "high" theory are quite legitimate here, combining observation and reflection, comparison and intuition, knowledge of facts and imagination. Their benefits and effectiveness are borne out by both contemporary research and fruitful intellectual traditions.

At the same time, as M. Merle correctly noted about the controversy between supporters of "traditional" and "modernist" approaches in the science of international relations, it would be absurd to insist on intellectual traditions where accurate correlations between collected facts are needed. Anything that can be quantified must be quantified 4. We will return to the polemic between "traditionalists" and "modernists" later.

Here it is important to note the illegality of the opposition of "traditional" and "scientific" methods, the falsity of their dichotomy. In fact, they complement each other. Therefore, it is quite legitimate to conclude that both approaches "act on equal grounds, and the analysis of the same problem is carried out independently of each other by different researchers" (see note 4, p. 8). Moreover, within the framework of both approaches, the same discipline can use, albeit in different proportions, different methods: general scientific, analytical and concrete empirical (however, the difference between them, especially between general scientific and analytical, is also rather arbitrary). In this respect, the political sociology of international relations is no exception. Moving on to a more detailed consideration of these methods, it is worth emphasizing once again the conventionality, the relativity of the boundaries between them, their ability to "flow" into each other.

2. General scientific methods

General scientific methods constitute the starting point, the foundation of any discipline, no matter how far from the high theory it is. However, considering the use of general scientific methods in the sociology of international relations, it makes no sense to dwell on the description of such theoretical and philosophical methods as the historical and logical, analysis and synthesis, the principle of priority, the ascent from the abstract to the concrete, etc. All of them take place, but to seek and demonstrate their application in a given discipline, as the experience already available in this regard, 5 shows, is not fruitful. On the other hand, the task of considering the methods that, with all the variety of methodological approaches, are used most often in the science of international relations and which give specific research results, seems to be much more productive. In this sense, the sociology of international relations in its object is characterized by the generalization and systematization of facts based on the study of historical, analytical and other documents, rigorous scientific observations and comparative analysis. This presupposes a refusal to close the boundaries of a particular discipline, an attempt to comprehend the object of study in integrity and, as far as possible, in unity, opening up the prospect of discovering trends and patterns of its functioning and evolution. Hence the importance that is attached in the study of international relations to the systems approach and the method of modeling closely related to it. Let's consider these methods in more detail.

Systems approach

The concept of a system (it will be discussed in more detail below) is widely used by representatives of various theoretical directions and schools in the science of international relations. Its generally recognized advantage is that it makes it possible to present the object of study in its unity and integrity, and, therefore, helping to find correlations between interacting elements, it helps to identify the "rules" of such interaction, or, in other words, the patterns of functioning of the international system. On the basis of a systematic approach, a number of authors distinguish international relations from international politics: if the constituent parts of international relations are represented by their participants (authors) and "factors" ("independent variables" or "resources") that make up the "potential" of the participants, then the elements of international politics only authors 6,7,8 are speaking.

The systems approach should be distinguished from its specific incarnations of systems theory and systems analysis. The systems theory performs the tasks of constructing, describing and explaining systems and their constituent elements, the interaction of the system and the environment, as well as intrasystem processes, under the influence of which there is a change and / or destruction of the system 9. As far as systems analysis is concerned, it solves more specific problems; representing a set of practical techniques, techniques, methods, procedures, thanks to which a certain ordering is introduced into the study of an object (in this case, international relations) (see: note 9, p. 17; note 10, p. 100).

From the point of view of R. Aron, “the international system consists of political units that maintain regular relations with each other and which can be drawn into a general war” 11. Since the main (and, in fact, the only) political units of interaction in the international system for Aron are states, at first glance one might get the impression that he equates international relations with world politics. However, essentially limiting international relations to the system of interstate interactions, R. Aron at the same time not only paid great attention to the assessment of resources, the potential of states, which determines their actions in the international arena, but also considered such an assessment to be the main task and content of the sociology of international relations. At the same time, he represented the potential (or power) of the state as an aggregate consisting of a whole geographic environment, material and human resources, and the ability of collective action (see note 11, p.65). Thus, proceeding from the systematic approach, Aron outlines, in essence, three levels of consideration of international (interstate) relations: the level of the interstate system, the level of the state and the level of its power (potential).

D. Rosenau proposed in 1971 another scheme, which includes six levels of analysis: 1) individuals - "creators" of politics and their characteristics; 2) the posts they hold and the roles they perform; 3) the structure of the government in which they operate; 4) the society in which they live and which they govern; 5) the system of relations between the nation state and other participants in international relations; 6) world system 12. Describing the systems approach presented by various levels of analysis, B. Russett and H. Starr emphasize that the choice of one or another level is determined by the availability of data and the theoretical approach, but not by the whim of the researcher. Therefore, in each case of application of this method, it is necessary to find and define several different levels. At the same time, explanations at different levels do not have to be mutually exclusive, they can be complementary, thereby deepening our understanding.

Serious attention is paid to the systemic approach in the domestic science of international relations. The works published by researchers from IMEMO, MGIMO, ISKAN, IVAN and other academic and university centers testify to the significant advancement of Russian science in the field of both systems theory 13,14 and systems analysis 15,16. So, the authors of the textbook "Fundamentals of the theory of international relations" believe that "the method of the theory of international relations is a systematic analysis of the movement and development of international events, processes, problems, situations, carried out with the help of existing knowledge, foreign policy data and information, special methods and techniques of research "(See note 15, p.68). The starting point for such an analysis is, from their point of view, three levels of research of any system: 1) the level of composition is the set of elements that form it; 2) the level of internal structure is a set of natural relationships between elements; 3) the level of the external structure is the totality of the interconnection of the system as a whole with the environment (note 15, p.70).

Let us consider the method of systems analysis in its static and dynamic dimensions as applied to the study of the foreign policy of the state.

Static measurement includes analysis of "determinants", "factors" and "variables".

One of the followers of Aron, R. Bosk, in his work "Sociology of the World" presents the potential of the state as a set of resources that it has to achieve its goals, consisting of two types of factors: physical and spiritual.

Physical (or directly tangible) factors include the following elements:

1.1 Space (geographic location, its merits and advantages).

1.2 Population (demographic power).

1.3 Economy in such manifestations as: a) economic resources; b) industrial and agricultural potential; c) military power.

In turn, the composition of spiritual (or moral, or social, not directly tangible) factors include:

2.1 Type of political regime and its ideology.

2.2 The level of general and technical education of the population.

2.3 "National morality", the moral tone of society.

2.4 Strategic position in the international system (for example, within a community, union, etc.).

These factors make up a set of independent variables affecting the foreign policy of states, studying which, it is possible to predict its changes 17.

Graphically, this concept can be represented as the following diagram:

The diagram provides a visual representation of both the advantages and disadvantages of this concept. The advantages include its operational efficiency, the possibility of further classification of factors taking into account the database, their measurement and analysis using computer technology. As for the shortcomings, it seems that the most significant of them is the actual absence in this scheme (with the exception of clause 2.4) of environmental factors that have a significant (sometimes decisive) impact on the foreign policy of states.

In this respect, the concept of F. Briar and M.-R. Jalili 18 looks much more complete, which can also be presented in the form of a diagram (see Fig. 2).

Symbols

Physical factors

• A.1 - Geographical location
• A.2 - Natural resources
• A.3 - Demographic situation

Structural factors

• B.1 - Political institutions
• B.2 - Economic institutions
• B.3 - Ability to use the physical and social environment; technological, economic and human potential
• B.4 - Political parties
• B.5 - Pressure groups
• B.6 - Ethnic groups
• B.7 - Confessional groups
• B.8 - Language groups
• B.9 - Social mobility
• B.10 - Territorial structure; share of urban and rural population
• B.11 - Level of national accord

Cultural and human factors

• B.1 (Culture):
• B.1.1 Value system
• B.1.2 Language
• B.1.3 Religion
• B.2 (Ideology):
• B.2.1 Authority's self-esteem of their role
• B.2.2 Her self-perception
• B.2.3 Her perception of the world
• B.2.4 Fixed means of pressure
• B.3 (Collective mentality):
• B.3.1 Historical memory
• B.3.2 The image of the "other"
• B.3.3 Line of conduct on international obligations
• B.3.4 Special sensitivity to national security
• B.3.5 Messianic traditions
• B.4 Qualities of the decision maker (decision-makers):
• B.4.1 Perception of one's environment
• B.4.2 Perception of the world
• B.4.3 Physical qualities
• B. 4.4 Morality

As you can see from the diagram, this concept, having all the advantages of the previous one, overcomes its main drawback. Its main idea is the close relationship of internal and external factors, their mutual influence and interdependence in influencing the foreign policy of the state. In addition, within the framework of internal independent variables, these factors are presented here much more fully, which significantly reduces the possibility of missing any important nuance in the analysis. At the same time, the diagram reveals that what has been said is much less relevant to external independent variables, which are only indicated on it, but not structured in any way. This circumstance testifies to the fact that with all the "equality" of internal and external factors, the authors still clearly give preference to the former.

It should be emphasized that in both cases, the authors by no means absolutize the importance of factors in influencing foreign policy. As R. Bosc shows, having entered the war against France in 1954, Algeria did not possess most of the above factors, and nevertheless it managed to achieve its goal.

Indeed, attempts at a naively deterministic description of the course of history in the spirit of the Laplace paradigm as a movement from the past through the present to a predetermined future with particular force reveal their inconsistency precisely in the sphere of international relations, where stochastic processes dominate. The above is especially characteristic of the current transitional stage in the evolution of the world order, which is characterized by increased instability and is a kind of bifurcation point containing many alternative paths of development and, therefore, does not guarantee any predetermination.

Such a statement does not at all mean that any forecasts in the field of international relations are, in principle, impossible. It is about seeing the boundaries, relativity, ambivalence of the predictive capabilities of science. This also applies to such a specific process as the process of making foreign policy decisions.

Decision-making process analysis (PMA) is dynamic dimension systematic analysis of international politics and at the same time one of the central problems of social science in general and the science of international relations in particular. Studying the determinants of foreign policy without taking into account this process may turn out to be either a waste of time, from the point of view of predictive capabilities, or a dangerous delusion, because this process is the “filter” through which the totality of factors affecting foreign policy is “sifted” by the person (s) decision maker (DM).

The classical approach to the analysis of PPR, reflecting the "methodological individualism" characteristic of the Weberian tradition, includes two main stages of research 19. At the first stage, the main decision-makers are identified (for example, the head of state and his advisers, ministers: foreign, defense, security, etc.), and the role of each of them is described. At the same time, it is taken into account that each of them has a staff of advisers who have the authority to request any information they need from a particular government department.

At the next stage, an analysis of the political preferences of decision makers is carried out, taking into account their worldview, wholesale, political views, leadership style, etc. An important role in this respect was played by the works of R. Snyder, H. Brook 20, B. Sapin and R. Jervis.

F. Briar and M.R. Jalili, summarizing the methods of analysis of SPD, distinguish four main approaches.

The first of them can be called the rational choice model, within which the choice of a decision is made by a single and rationally thinking leader on the basis of national interest. It is assumed that: a) the decision maker acts taking into account the integrity and hierarchy of values, about which he has a fairly stable idea; b) he systematically possible consequences of his choice; c) PPR is open to any new information that can influence the decision.

The second approach assumes that the decision is made under the influence of a set of government structures, acting in accordance with established routines. The decision turns out to be broken into separate fragments, but the fragmentation of government structures, the peculiarities of their selection of information, the complexity of mutual relations with each other, differences in the degree of influence and authority, etc. are an obstacle to PMD, based on a systematic assessment of the consequences of one or another choice.

In the third model, the decision is considered as the result of a complex game bargaining between members of the bureaucratic hierarchy, government apparatus, etc. each representative of which has their own interests, their positions, their own ideas about the priorities of the state's foreign policy.

Finally, the fourth approach draws attention to the fact that in many cases decision makers are in a complex environment and have incomplete, limited information. Besides. they are unable to assess the consequences of a given choice. In such an environment, they have to dissect problems by reducing the information they use to a small number of variables.

In the analysis of SPD, the researcher should avoid the temptation to use one or another of these approaches "in their pure form." In real life, the processes described by them vary in a wide variety of combinations, the study of which should show which of them in each particular case should be based on and with which others it should be combined (see note 18, pp. 71-74).

Analysis of the decision-making process is often used to predict the possible evolution of a particular international situation, for example, an interstate conflict. At the same time, not only factors related "directly" to the PPR are taken into account, but also the potential (a set of resources) that a person or a decision-making authority has at his disposal. An interesting technique in this regard, including elements of quantitative formalization and based on various PPR models. is proposed in the article by Sh.Z.

Sultanov "Analysis of decision making and a conceptual forecasting scheme" (see note 10, pp. 71-82).

Modeling

This method is associated with the construction of artificial, ideal, imaginary objects, situations, which are systems, the elements and relationships of which correspond to the elements and relationships of real international phenomena and processes.

One of the common types of modeling that have become widespread in the science of international relations is associated with game theory... Game theory is a theory of decision making in a specific social context, where the concept of "play" applies to all types of human activity. It is based on the theory of probability and is the construction of models for the analysis or forecasting of various types of behavior of actors in special situations. Classical game theory was developed by mathematician D. von Poimann and economist O. Morgenstern in their joint work Game Theory and Economic Behavior, published by Princeton University Press in 1947. In the analysis of the behavior of international actors, it found application in the classic works of A. Rapoport, who explored its epistemological capabilities, 21 and T. Schelling, who extended it to the study of such international phenomena as conflicts, negotiations, arms control, intimidation strategies, etc. NS. 22. The Canadian specialist in the sociology of international relations J.-P. Derriennik considers game theory as a theory of decision-making in a risky situation, or, in other words, as an area of ​​application of the model of subjectively rational action in a situation where all events are unpredictable. If we are talking about a game with several players, then we are dealing with the theory of interdependent decisions, where the risk situation is common, and unpredictability arises for each player from the actions of the other. Risk situations find their solution if its risky nature is eliminated. In a two-player game, when one of the players makes a bad decision, the other gets an extra win. If both play well (that is, act rationally), then neither has a chance to improve their winnings beyond what the rules of the game allow.

In the theory of games, thus, the behavior of decision makers is analyzed in their mutual relations associated with the pursuit of one and the same goal. In this case, the task is not to describe the behavior of the players or their reaction to information about the behavior of the enemy, but to find the best possible solution for each of them in the face of the predicted solution of the enemy. Game theory shows that the number of types of situations players may find themselves in is finite. Moreover, it can be reduced to a small number of game models, differing in the nature of goals, opportunities for mutual communication, and the number of players.

There are games with different numbers of players: one, two or many. For example, the dilemma, whether or not to take an umbrella with you in unstable weather, is a game with one player (because nature does not take human decisions into account), which will cease to be so when meteorology becomes an exact science (see note 23, p. thirty).

In a two-player game, such as the famous Prisoner's Dilemma, players are deprived of the ability to communicate with each other, so each makes a decision based on the idea of ​​the rational behavior of the other. The rules of the game are likened to the rules of a situation in which two people (A and B) who committed a joint crime and fell into the hands of justice receive from their representatives an offer of voluntary confession (that is, of betrayal in relation to their accomplice). In doing so, everyone is warned about the following: I. If A is recognized (P), B is not recognized (H), then A gets freedom (C), B is the maximum punishment (C); 2. If A is not recognized (H), B is recognized (P), then A receives the maximum punishment (C), B freedom (C); 3. If both A and B are confessed, then both receive severe, though not the maximum, punishment (T); 4. If both do not confess, then both receive the minimum punishment (Y).

Graphically, the prisoners' dilemma is presented in the form of the following scheme (Fig. 3):

Ideally, for each of the accomplices, freedom is better than the minimum punishment, the minimum punishment is better than the severe one, and the last one is better than the maximum one: C> Y> T> B. Therefore, for both, the most profitable option would be H, H. In fact, deprived of the opportunity to communicate with another, not trusting him, each expects betrayal by the accomplice (for A it is: N, P) and, trying to avoid B, decides to betray, considering him the least risky, As a result, both choose betrayal ( P, P), and both receive severe punishment.

In terms of symbolic logic, the situation can be represented as follows:

1. (P (A) & P (B)) (S (A) & B (B))

2. (P (A) & P (B)) (B (A) & C (B))

3. (P (A) & P (B)) (T (A) & T (V))

4. (P (A) & P (B)) (U (A) & U (B))

This model was applied to the analysis of many international situations: for example, the foreign policy of Hitlerite Germany, or the arms race of the 50-70s. In the latter case, at the heart of the situation for the two superpowers was the severity of the mutual risk posed by nuclear weapons and the desire of both to avoid mutual destruction. The result was an arms race that was not beneficial to either side.

Game theory allows you to find (or predict) a solution in some situations: that is, to indicate the best possible solution for each participant, to calculate the most rational way of behaving in various types of circumstances. Nevertheless, it would be a mistake to exaggerate its importance as a method for studying international relations, and even more so as a practical method for developing a strategy and tactics of behavior on the world stage. As we have already seen, decisions made in international relations are not always rational in nature. In addition, for example, the Prisoners' Dilemma does not take into account the fact that in the field of international relations there are mutual obligations and agreements, and there is also the possibility of communication between the parties even during the most intense conflicts.

Let us consider another type of complex modeling by the example of the work of M.A. Khrustalev "Systemic modeling of international relations" (see note 2).

The author sets the task of building a formalized theoretical model representing the trinar methodological (philosophical theory of consciousness), general scientific (general systems theory) and special scientific (international relations theory) approaches. The construction is carried out in three stages. At the first stage, "pre-model tasks" are formulated, combined into two blocks: "evaluative" and "operational". In this regard, the author analyzes concepts such as “situations” and “processes” (and their types), as well as the level of information. On their basis, a matrix is ​​built, which is a kind of "map" designed to provide the researcher with the choice of an object, taking into account the level of information security.

As for the operational block, the main thing here is to single out the nature (type) of models (conceptual, theoretical and specific) and their forms (verbal or meaningful, formalized into quantified) on the basis of the “general-specific-individual” triad. The selected models are also presented in the form of a matrix, which is a theoretical model of modeling, reflecting its main stages (form), stages (character) and their relationship.

At the second stage, we are talking about building a meaningful conceptual model as the starting point for solving the general research problem. On the basis of two groups of concepts "analytical" (essence-phenomenon, content-form, quantity-quality) and "synthetic" (matter, movement, space, time), presented in the form of a matrix, a "universal cognitive construction cofigurator" is built, which sets general research framework. Further, based on the allocation of the above logical levels of research of any system, the noted concepts are reduced, as a result of which the "analytical" (essential, meaningful, structural, behavioral) and "synthetic" (substrate, dynamic, spatial and temporal) characteristics of the object are distinguished. Relying on the "system oriented matrix configurator" structured in this way, the author traces the specific features and some trends in the evolution of the system of international relations.

At the third stage, a more detailed analysis of the composition and internal structure of international relations is carried out, that is, the construction of its detailed model. Here, the composition and structure (elements, subsystems, connections, processes), as well as the "programs" of the system of international relations (interests, resources, goals, mode of action, balance of interests, balance of forces, relations) are distinguished. Interests, resources, goals, mode of action constitute the elements of the "program" of subsystems or elements. The resources, characterized as a “non-system-forming element”, are subdivided by the author into resources of means (material-energy and informational) and resources of conditions (space and time).

The "program of the system of international relations" is a derivative in relation to the "programs" of elements and subsystems. Its backbone element is the "correlation of interests" of various elements and subsystems with each other. The non-system-forming element is the concept of "balance of forces", which could be more accurately expressed by the term "ratio of means" or "ratio of potentials". The third derivative element of the specified "program" is the "relation", understood by the author as a kind of evaluative representation of the system about itself and about the environment.

Based on the theoretical model constructed in this way, M.A. Khrustalev analyzes the real processes characteristic of the modern stage of world development. He notes that if the key factor that determined the evolution of the system of international relations throughout its history was interstate conflict interaction within the framework of stable confrontational axes, then by the 90s of the XX century. the prerequisites for the transition of the system to a different qualitative state arise. It is characterized not only by the breakdown of the global confrontational axis, but also by the gradual formation of stable axes of all-round cooperation between the developed states of the world. As a result, an informal subsystem of developed states appears in the form of a world economic complex, the core of which has become the "seven" leading developed countries, which has objectively turned into a governing center that regulates the development of the system of international relations. The fundamental difference between such a "governing center" from the League of the Nation or the UN is that it is the result of self-organization, and not the product of "social engineering" with its characteristic static completeness and weak adequacy to dynamic changes in the environment. As a governing center, the G7 solves two important problems of the functioning of the system of international relations: first, the elimination of the existing and prevention of the emergence in the future of regional confrontational military-political axes; secondly, stimulating the democratization of countries with authoritarian regimes (creating a single world political space). Highlighting, taking into account the model he proposed, also other trends in the development of the system of international relations, M.A. Khrustalev considers the emergence and consolidation of the concept of "world community" and the emphasis on the idea of ​​a "new world order" to be very symptomatic, emphasizing at the same time that the current state of the system of international relations as a whole does not yet correspond to the modern needs of the development of human civilization.

Such a detailed examination of the method of systemic modeling as applied to the analysis of international relations allows one to see both the advantages and disadvantages of both this method itself and the systemic approach as a whole. The advantages noted above include the generalizing, synthesizing nature of the systematic approach. It allows you to discover both the integrity of the object under study and the variety of its constituent elements (subsystems), which can be participants in international interactions, relations between them, space-time factors, political, economic, religious characteristics, etc. The systematic approach makes it possible not only to record certain changes in the functioning of international relations, but also to discover the causal links of such changes with the evolution of the international system, to identify determinants that affect the behavior of states. Systemic modeling gives the science of international relations those opportunities for theoretical experimentation, which it practically lacks in its absence. It also makes it possible for the complex application of applied methods and techniques of analysis in their most diverse combination, thereby expanding the prospects for research and their practical use for explaining and forecasting international relations and world politics.

At the same time, it would be wrong to exaggerate the importance of the systems approach and modeling for science, to ignore their weaknesses and shortcomings. The main one is, paradoxical as it may seem, the fact that no model, even the most flawless in its logical foundations, gives confidence in the correctness of the conclusions drawn on its basis. This, however, is recognized by the author of the work discussed above when he speaks of the impossibility of building an absolutely objective model of the system of international relations (see: note 2, p. 22). Let us add that there is always a certain gap between the model constructed by this or that author and the actual sources of those conclusions that he formulates about the object under study. And the more abstract (that is, the more strictly logically substantiated) the model is, and also the more adequate to reality its author strives to make his conclusions, the wider is the indicated gap. In other words, there is a serious suspicion that when formulating conclusions, the author relies not so much on the model structure he built, but on the initial premises, the “building material” of this model, as well as on others not related to it, including “intuitive logical "methods. Hence the question, which is very unpleasant for the "uncompromising" supporters of formal methods: could those (or similar) conclusions that emerged as a result of a model study be formulated without a model? The significant discrepancy between the novelty of such results and the efforts made by researchers on the basis of systems modeling makes it possible to believe that an affirmative answer to this question looks very reasonable. As B. Russett and H. Starr emphasize in this connection: “to a certain extent, the share of each contribution can be determined using the methods of data collection and analysis, typical for modern social sciences. But in all other respects we remain in the realm of guesswork, intuition and informed wisdom ”(see note 12, p. 37).

As for the systems approach as a whole, its shortcomings are a continuation of its merits. Indeed, the advantages of the concept of "international system" are so obvious that it is used, with few exceptions, by representatives of all theoretical directions and schools in the science of international relations. However, as the French political scientist M. Girard rightly swept, few people know exactly what it means in reality. It continues to retain a more or less strict meaning for functionalists, structuralists and systemists. For the rest, it is most often nothing more than a beautiful scientific epithet, convenient for decorating an ill-defined political object. As a result, this concept turned out to be oversaturated and devalued, which makes it difficult to use it creatively 24.

Agreeing with the negative assessment of the arbitrary interpretation of the concept of "system", we emphasize once again that this does not at all mean doubts about the fruitfulness of applying both the systems approach and its specific incarnations of the system theory and systems analysis to the study of international relations.

Systems analysis and modeling are the most general analytical methods, which are a collection of complex research techniques, procedures and interdisciplinary techniques related to the processing, classification, interpretation and description of data. On their basis and with their use, many other analytical methods of a more specific nature appeared and became widespread, which we will consider and pass through.

3. Other analytical methods

The most common of them are content analysis, event analysis, the cognitive mapping method and their many varieties (see: note 2; 10; 16).

Cotpent analysis in political sciences was first applied by the American researcher G. Lasswell and his collaborators in the study of the propaganda orientation of political texts and was described by them in 1949. 25. In its most general form, this method can be presented as a systematic study of the content of a written or oral text with the fixation of the most frequently repeated phrases or plots in it. Further, the frequency of these phrases or plots is compared with their frequency in other written or oral messages, known as neutral, on the basis of which a conclusion is made about the political orientation of the content of the studied text. Describing this method, M.A. Xpy stalev and K.P. Borishpolets distinguish such stages of its application as: text structuring associated with the primary processing of information material; processing the information array using matrix tables; quantification of information material, allowing to continue its analysis using electronic computers (see note 16, pp. 86-94).

The degree of rigor and operability of the method depends on the correctness of the selection of the primary units of analysis (terms, phrases, semantic blocks, topics, etc.) and units of measurement (for example, a word, phrase, section, page, etc.).

Event analysis (or event data analysis) is aimed at processing public information showing "who says or does what, in relation to whom and when." The systematization and processing of the relevant data is carried out according to the following criteria: 1) the subject-initiator (who); 2) plot or "issue - area" (what); 3) the target subject (in relation to whom) and 4) the date of the event (when) (see note 8, pp. 260-261). Events systematized in this way are summarized in matrix tables, ranked and measured using a computer. The effectiveness of this method presupposes the presence of a significant data bank. Scientific and applied projects using event analysis differ in the type of behavior studied, the number of politicians under consideration, the studied time parameters, the number of sources used, the typology of matrix tables, etc.

As for the cognitive mapping method, it is aimed at analyzing how a particular politician perceives a certain political problem.

The American scientists R. Snyder, H. Brook and B. Sapin showed back in 1954 that decisions by political leaders can be based not only and not so much on the reality that surrounds them, but on how they perceive it. In 1976, R. Jervis in his work "Perception and misperception (misperception) in international politics" showed that in addition to emotional factors, the decision taken by a leader is influenced by cognitive factors. From this point of view, the information received by the decision maker is assimilated and ordered by them "corrected" for their own views on the external world. Hence the tendency to underestimate any information that contradicts their value system and the image of the enemy, or, on the contrary, to give an exaggerated role to insignificant events. The analysis of cognitive factors allows us to understand, for example, that the relative constancy of the foreign policy of the state is explained, along with other reasons, and the constancy of the views of the respective leaders.

The method of cognitive mapping solves the problem of identifying the basic concepts that the politician operates with and finding the causal relationships between them. “As a result, the researcher receives a schematic map on which, based on the study of speeches and speeches of a politician, his perception of the political situation or individual problems in it is reflected” (see note 4, p.6).

In the application of the described methods, which have a number of undoubted advantages, the possibility of obtaining new information based on the systematization of already known documents and facts, increasing the level of objectivity, the possibility of measurement, etc., the researcher also faces serious problems.This is the problem of sources of information and its reliability , availability and completeness of databases, etc. But the main problem is the problem of the costs that are required to conduct research using content analysis, event analysis and the method of cognitive mapping. Compilation of a database, their coding, programming, etc. take considerable time, require expensive equipment, necessitate the involvement of appropriate specialists, which ultimately translates into significant sums.

Taking into account these problems, professor at the University of Montreal B. Corany proposed a methodology with a limited number of indicators of the behavior of an international author, which are considered as key (most characteristic) (see: note 8, p. 263265). There are only four such indicators: the method of diplomatic representation, economic transactions, interstate visits and agreements (treaties). These indicators are categorized according to their type (for example, agreements can be diplomatic, military, cultural, or economic) and level of significance. Then a matrix table is compiled, giving a visual representation of the object under study. So, the table reflecting the exchange of visits looks like this:

As for the methods of diplomatic representation, their classification is based on their level (ambassador level or lower level) and taking into account whether it is a direct representation or through the mediation of another country (resident or non-resident). The combination of this data can be represented as follows:

On the basis of such data, conclusions are drawn regarding the way the international author behaves in time and space: with whom he maintains the most intense interactions, in what period and in what sphere they occur, etc.

Using this technique, B. Korani established that almost all the military-political relations that, for example, Algeria had in the 70s, were supported by him with the USSR, while the level of economic relations with the entire socialist camp was rather weak. In fact, most of Algeria's economic relations were aimed at cooperation with the West, and especially with the United States, the "main imperialist power." As B. Korani writes, “such a conclusion, contrary to“ common sense ”and first impressions [recall that Algeria belonged to the countries of“ socialist orientation ”in those years, adhering to the course of“ anti-imperialist struggle and all-round cooperation with the countries of socialism ”P.Ts. ], could not be done, and it was impossible to believe in it without the use of a rigorous methodology supported by data systematization ”(see note 8, p.264). Perhaps this is a somewhat exaggerated estimate. But in any case, this technique is quite effective, sufficiently evidence-based and not too expensive.

However, it should be emphasized and its limitations, which, however, is common to all of the above methods. As the author himself admits, she cannot (or can only partially) answer the question about the causes of certain phenomena. Such techniques and techniques are much more useful at the level of description rather than explanation. They give, as it were, a photograph, a general view of the situation, show what is happening, but without clarifying why. But it is precisely in this that their purpose consists in performing a diagnostic role in the analysis of certain events, situations and problems of international relations. However, for this they need primary material, the availability of data that are subject to further processing and the accumulation of which is carried out on the basis of private methods.

4. Private methods

Private methods are understood as the sum of interdisciplinary procedures used for the accumulation and primary systematization of empirical material ("data"). Therefore, they are sometimes also called "research techniques". To date, more than a thousand of such techniques are known, from the simplest (for example, observation) to quite complex (such as, for example, situational games approaching one of the stages of system modeling). The most famous of them are questionnaires, interviews, an expert survey, an expert meeting. A variation of the latter is, for example, the "Delphic technique" when independent experts submit their assessments of an international event to the central body, which summarizes and systematizes them, and then returns them to the experts. Taking into account the generalization, the experts either amend their initial estimates, or strengthen their opinion and continue to insist on it. In accordance with this, a final assessment is developed and practical recommendations are given.

Let's consider the most common analytical techniques: observation, study of documents, comparison, experiment.

Observation

As you know, the elements of this method are the subject of observation, the object and the means of observation. There are different types of observations. So, for example, direct observation, in contrast to indirect (instrumental), does not imply the use of any technical equipment or tools (television, radio, etc.). It can be external (similar to the one conducted, for example, by parliamentary journalists or special correspondents in foreign countries) and included (when the observer is a direct participant in one or another international event: diplomatic negotiations, a joint project or an armed conflict). In turn, direct observation differs from indirect observation, which is carried out on the basis of information obtained through interviews, questionnaires, etc. In the science of international relations, indirect and instrumental observation is generally possible. The main disadvantage of this method of data collection is the large role of subjective factors associated with the activity of the subject, his (or primary observers) ideological preferences, imperfection or deformation of observation means, etc. (see note 5, pp. 57-58).

Examining documents

With regard to international relations, it has the peculiarity that an “unofficial” researcher often does not have free access to sources of objective information (unlike, for example, staff analysts, experts from international departments or security officials). An important role in this is played by the notions of a particular regime about state secrets and security. In the USSR, for example, the volume of oil production, the level of industrial production, etc., remained the subject of state secrets for a long time; there was a huge array of documents and literature intended only for "official use", the ban on free circulation of foreign publications remained, a huge number of institutions and institutions were closed to "outsiders." There is another problem that complicates the use of this method, which is one of the initial, basic ones for any research in the field of social and political sciences: this is the problem of the financial resources necessary for the acquisition, processing and storage of documents, payment of the associated labor costs, etc. It is therefore clear that the more developed a state is and the more democratic its political regime is, the more favorable opportunities exist for research in the field of social and political sciences. Unfortunately, both of these problems are very relevant for modern Russia. And the exacerbation of the economic crisis, combined with the turn of the value priorities of the mass consciousness towards mercantilism, associated with the loss of many spiritual guidelines, extraordinarily exacerbates the difficulties of research work in general and in the field of international relations, in particular.

The most accessible are official documents: messages from the press services of diplomatic and military departments, information on visits by statesmen, statutory documents and statements of the most influential intergovernmental organizations, declarations and messages from government agencies, political parties and public associations, etc. At the same time, unofficial written, audio and audiovisual sources are also widely used, which in one way or another can contribute to an increase in information about the events of international life: records of the opinions of individuals, family archives, unpublished diaries. Memories of direct participants in certain international events of wars, diplomatic negotiations, official visits can be of great importance. This also applies to the forms of such memories, written or oral, direct or reconstructed, etc. An important role in data collection is played by the so-called iconographic documents: paintings, photographs, films, exhibitions, slogans. Thus, in the conditions of closeness prevailing in the USSR, increased secrecy and, consequently, the practical inaccessibility of unofficial information, American Sovietologists paid great attention to the study of iconographic documents, for example, reports from holiday demonstrations and parades. The features of the design of the columns, the content of slogans and posters, the number and composition of officials present at the podium, and, of course, the types of displayed military equipment and weapons were studied.

Comparison

It is also a method that is common to many disciplines. According to B. Russet and H. Starr, in the science of international relations, it began to be used only in the mid-60s, when the continuous growth in the number of states and other international actors made it both possible and absolutely necessary (see note 12, p. 46). The main advantage of this method lies in the fact that it aims at finding common things that are repeated in the sphere of international relations. The need to compare states and their individual characteristics (territory, population, level of economic development, military potential, length of borders, etc.) among themselves stimulated the development of quantitative methods in the science of international relations and, in particular, measurement. So, if there is a hypothesis that large states are more inclined to unleash war than all others, then there is a need to measure the size of states in order to determine which of them is large and which is small, and by what criteria. In addition to this “spatial” aspect of measurement, it becomes necessary to measure “in time”, that is, to find out in a historical retrospective what size of the state enhances its “inclination” to war (see note 12, p. 4748).

At the same time, comparative analysis makes it possible to obtain scientifically significant conclusions based on the dissimilarity of phenomena and the uniqueness of the situation. So, comparing iconographic documents (in particular, photographs and newsreels), reflecting the dispatch of French soldiers to the active army in 1914 and 1939, M. Ferro discovered an impressive difference in their behavior. The smiles, dances, the atmosphere of general jubilation that prevailed at the Gare de l'Est in Paris in 1914 contrasted sharply with the picture of despondency, hopelessness, and a clear reluctance to go to the front, observed at the same station in 1939. Since these situations could not develop under the influence of the pacifist movement (according to written sources, it was never as strong as on the eve of 1914, and, on the contrary, almost did not manifest itself at all before 1939), a hypothesis was put forward according to which one the explanation for the contrast described above must be that in 1914, unlike in 1939, there was no doubt as to who the enemy was: the enemy was known and identified. The proof of this hypothesis became one of the ideas of a very interesting and original study devoted to understanding the First World War 27.

Experiment

The experimental method as the creation of an artificial situation in order to test theoretical hypotheses, conclusions and position is one of the main in the natural sciences. In the social sciences, the most widespread form of it is imitation games, which are a kind of laboratory experiment (as opposed to a field experiment). There are two types of simulation games: without the use of electronic computers and with its use. In the first case, we are talking about individual or group actions related to the performance of certain roles (for example, states, governments, politicians or international organizations) in accordance with a pre-written scenario. At the same time, the participants must strictly adhere to the formal conditions of the game, controlled by its leaders: for example, in the case of an imitation of an interstate conflict, all parameters of the state, the role of which the participant is playing the economic and military potential, participation in alliances, stability of the ruling regime, etc. should be taken into account. Otherwise, such a game can turn into simple entertainment and a waste of time in terms of cognitive results. Simulation games using computer technology offer much broader research perspectives. Based on the relevant databases, they make it possible, for example, to reproduce a model of diplomatic history. Starting with the simplest and most plausible model for explaining the current events of crises, conflicts, the creation of intergovernmental organizations, etc., then we explore how it fits into previously selected historical examples. Through trial and error, changing the parameters of the original model, adding variables that were previously missed in it, taking into account cultural and historical values, a shift in the dominant mentality, etc., one can gradually move towards achieving its more and more compliance with the reproduced model of diplomatic history and on the basis of comparison these two models put forward reasonable hypotheses regarding the possible development of current events in the future.

Concluding our review of the methods used in the science of international relations, we summarize the main conclusions regarding our discipline.

First, the absence of "own" methods in the sociology of international relations does not deprive it of the right to exist and is not a basis for pessimism: not only social, but also many "natural sciences" are successfully developing, using common "interdisciplinary" methods with other sciences and procedures for examining your object. Moreover, interdisciplinarity is increasingly becoming one of the important conditions for scientific progress in any branch of knowledge. Let us emphasize once again that each science uses general theoretical (characteristic of all sciences) and general scientific (characteristic of a group of sciences) methods of cognition.

Secondly, the most common in the sociology of international relations are such general scientific methods as observation, study of documents, systems approach (systems theory and systems analysis), modeling. Applied interdisciplinary methods (content analysis, event analysis, etc.), as well as private methods for collecting and primary data processing, are widely used in it. At the same time, all of them are modified taking into account the object and goals of the research and acquire new specific features here, consolidating themselves as “their own” methods of this discipline. Let us note in passing that the difference between analytical, applied and private methods is rather relative: the same methods can act both as general scientific approaches and as specific methods (for example, observation).

Thirdly, like any other discipline, the sociology of international relations in its entirety, as a definite set of theoretical knowledge, acts simultaneously as a method of cognizing its object. Hence the attention paid in this work to the basic concepts of this discipline: each of them, reflecting one or another side of international realities, in the epistemological plan bears a methodological load, or, in other words, serves as a guideline for further study of its content, and from the point of view of not only deepening and expanding knowledge, but to their concretization in relation to the needs of practice.

Finally, it should be emphasized once again that the best result is achieved with the complex use of various research methods and techniques. Only in this case, the researcher can hope to find repetitions in the chain of disparate facts, situations and events, that is, some kind of regularities (and deviant, respectively) of international relations.

Notes (edit)

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