Introduction

The indicator of national power is currently the most informative and popular indicator in the world that integrally characterizes the aggregate potential of a particular country and at the same time makes it possible to compare the level of its power and socio-economic development with other states. So, RAND corporation¹ in its report “Measuring National Power” notes the extreme importance of regular assessment and analysis of the national power indicator for the adjustment of strategic documents related to the country's long-term development, as well as its foreign policy [15].

A lot of publications proposed one variable (for example, land area, GDP, military spending, government spending, production of electricity, steel, etc.) to assess national power, and the main argument in favor of this approach is that when a set of dissimilar components is reduced to a single indicator, their original meaning is lost, and the integral value is difficult to interpret due to the subjectivity of the set of influencing factors and their weights. On the other hand, according to the adherents of this approach, such large aggregates as GDP or steel output implicitly include many secondary indicators, so the use of multivariate data sets and mathematical methods of statistical analysis is redundant [8]. Nevertheless, most researchers adhere to the opposite point of view, since the modern world is complex, and its complexity is constantly increasing, as well as relations between countries, therefore the use of one variable to measure national power is a deliberate simplification and greatly limits its objective assessment, since it should be multilateral and cover various aspects of the country's development (social, economic, military, territorial, etc.).

Coefficients of correlation between national power integral values given in the most cited works were calculated in the paper [7]. The average value of the correlation coefficients turned out to be 0.796: for countries with high indices of national power the average value of the correlation coefficient was 0.821, and for countries with low indices it was 0.459. The authors of the study put forward a version that analysts have more information about the situation in powerful states than in weak ones.  Also, the following hypothesis was proposed as an explanation: for countries with different levels of development it is incorrect to use the same set of indicators with the same weights.

Andrew Marshall, a mathematician, foreign policy strategist and director (from 1975 to 2013) of the United States Department of Defense's Office of Net Assessment, the Pentagon's think tank, foresaw several key moments in world history (for example: 1) the demise of the USSR, which, in his opinion, should have happened with high probability after the preliminary weakening of the Soviet economy in the process of an arms race; 2) the emergence of China as a world power, etc.). Although most of Marshall's works are put into the secret archive for obvious reasons, in publicly available works he wrote many times about the need to carry out a comprehensive assessment of national power and its components of potential opponents, predominantly the USSR. In particular, he noted that due to the difference in methodologies and understanding of priorities in the country's development, Soviet assessments differ significantly from American ones, and in order to plan an effective US military strategy, it is necessary to take into account differences in the corresponding assessments [5].

American geopolitician and one of the founders of the school of political realism Nicholas John Spykman in his work “America's Strategy in World Politics: the United States and the Balance of Power” proposed eleven factors belonging to the following five categories: (1) geographical (area, type of borders, natural resources); (2) demographic (population size, ethnic homogeneity); (3) military (size of the armed forces); (4) economic (integral indicator of economic and technological development, integral indicator of financial stability); (5) psychological (indicators of social integration, political stability and the level of patriotism). As you can see, he paid great attention to psychological factors and considered them key in intercountry confrontation noting that an effective means of weakening the state is to undermine national cohesion, but at the same time he emphasized that these components of national power are extremely difficult to formalize [14].

Founder of political realism and one of the leading experts in the USA for foreign policy issues Hans Morgenthau in the first edition of his bestseller in the theory of international politics “Politics Among Nations. The Struggle for Power and Peace” proposed the following elements of national power [10]: (1) geography, (2) natural resources, (3) industrial potential, (4) military potential, (5) population, (6) national character, (7) national morale, (8) the quality of diplomacy, and in the second edition he added one more element - (9) the quality of government [11]. Noting the importance of each of the listed components of national power, Morgenthau emphasized that the first five of them can be directly determined based on statistics, and the remaining four - only through surveys.

Famous American political scientist, founder of the theory of neorealism Kenneth Neal Waltz defined national power as an aggregator of several factors: (1) population size, (2) size of territory, (3) resource endowment, (4) economic capability, (5) military strength, (6) political stability; and (7) political competence [16]. As you can see, the first five elements practically correspond to the factors proposed by Morgenthau, and the remaining two can also be identified with indicators reflecting national character, national morale and the quality of diplomacy. At the same time Waltz noted that to be a world leader it is necessary to lead in all seven areas, and superiority in only some of them cannot compensate for the lag in others. In addition, he emphasized the need to use non-linear formulas for assessing the integral indicator using weights of individual factors that change over time.

Author of the theory of offensive realism, American political scientist John Mearsheimer, unlike Waltz, considered only material factors of national power and in 2001 proposed the following components: (1) GDP, (2) population size, (3) size of the armed forces, (4) the number of nuclear weapons [6].

Based on the analysis of more than 600 publications in some way or another related to the measurement of national power, German researcher Höhn Karl Hermann in his work evaluated the corresponding formulas in terms of the method of calculating them, as well as the country of the authors [1]. Table 1 provides information on the most famous authors of the corresponding formulas, the countries they come from and the number of variables used to assess national power. So, the weighting coefficients of 73% of the formulas were assessed by experts, 10% through surveys, and statistical analysis procedures were used for 17%. As for the countries, 37% of the formulas were offered by specialists from the USA, 16% from China, 7% from Germany, 6% from Japan, 5% from Brazil, 5% from Poland, 4% from Russia (and the USSR), 4% from India, 3% from South Korea, 3% from the UK, 2% from Canada, 1% from Taiwan, 1% from France, 1% from Iran, 1% from Australia, 1% from Argentina, 1% from Kuwait, 1% from Turkey, and 1% from Azerbaijan. As you can see, most researches were and are carried out in the USA and China, which means that the most powerful countries measure this indicator more often than others.

Table 1². Information on the most famous methods of assessing national power

Principles

On the one hand, it would take too much space to mentions here all the formulas used in the methods listed above and, on the other hand, it does not make much sense, since each of the dependencies is subjective and cannot be considered as fundamental for measuring national power. But to get some idea of the way of reducing the components taken into account to the integral index, we will present here information on the method for calculating the Composite Index of National Capability (CINC) proposed by Joel David Singer. It is used to assess national power of different countries of the world and is one of the most cited ones [13]. It is calculated using the following formula:

1. Measuring national power, on the one hand, is of great interest to a wide range of specialists in the field of geopolitics, international relations, economics, mathematics, etc. and, on the other hand, it presents computational complexity, since this integral indicator often combines quantitative and qualitative factors, which are problematic to bring together. On the one hand, it is difficult to quantitatively express such concepts as morale, patriotism, etc. and, on the other hand, a separate problem is the correct weighing of the selected components of national power. But even after this procedure it is unclear whether it is possible to combine many factors that differ greatly in composition into a single integral indicator - for example, the population size, the number of fighters, the coal output, etc. [12].
2. Some works are theoretical and they consider components of national power that do not have a quantitative representation. Nevertheless, almost all studies note the extreme relevance of its comprehensive assessment, since for a successful intercountry confrontation it is necessary to have an objective assessment of all the resources available to assumed opponents.
3. The set of components is significantly influenced by the specialization of researchers. So, economists are primarily guided by economic indicators, representatives of the military professions to a greater extent operate with indicators related to the size of the armed forces, etc.
4. The number of components considered in the studies increases over time due to an increase in the productivity of computers used, as well as an increase in the complexity of the described socio-economic systems and the relations between them.
5. In most cases (more than 80%) factorial weights of the formulas were estimated using estimates of a narrow circle of experts or the average results of surveys carried out among a wider number of respondents. The disadvantage of this approach is subjectivity, ultimately determined by the value of the integral indicator.
6. When analyzing the results of most works, there is a clear feeling that the authors are biased in favor of the states they represent. So, American researchers often overestimate the role of their country in the global balance of power, while others are more realistic about measuring the US national power, nevertheless recognizing the leadership of the USA in certain issues.

Considering the above, let us formulate the principles that we will adhere to when constructing the indicator of national power (as in [2]).

1. Mandatory use of methods of multivariate statistical analysis. It will eliminate the problem of subjectivity (inherent in expert methods widely used in solving such problems) to some extent when assessing the contribution of factors to the integral indicator.
2. Taking into account the previous point, as well as the mechanism for calculating the components of national power, in which they are dependent on the values of similar indicators in other countries of the world, we assume the formation of a comprehensive database and the mandatory calculation of indicators of national power for all UN member states.
3. To assess national power, it is advisable to use more basic indicators that determine the country's potential (availability of resources, territory, population, etc.), rather than conjuncture variables that often change depending on the current situation. This fundamentally distinguishes them from the indicators used by various rating agencies, which assess countries in terms of living standards, ease of doing business, etc. When selecting components of national power, the best world practices will be taken into account, i.e. we will use scientifically sound parameters most commonly used by reputable think tanks and researchers.
4. A number of researchers note the importance of using the integral indicator of national power as an endogenous variable in complex simulation models aimed at both explaining historical processes (reasons for the weakening of states, their rise, etc.) and analyzing the effectiveness of the state policy, and predicting further development and development of corrective actions (for example, [9]). In this regard, we will link the integral indicator of national power and a simulator of social economic dynamics for more than 100 countries of the world (Social Economic Dynamics, SED model) developed by IT company Guangzhou Milestone Software Co., Ltd with the support of the National Supercomputer Center of China and the Chinese Academy of Social Sciences into a single software and analytical complex [3], [4].
5. Integral indicators of national power for the UN member states are supposed to be calculated for the period from 2010, which will allow both carrying out their monitoring on an ongoing basis, and also forecasting using the developed software and analytical complex.

Data

Table 2. Sources of data used to calculate the index of national power of different countries of the world

• Land area (sq. km)
• Agricultural land (sq. km)
• Forest area (sq. km)

• Gold reserves (in tons)
• Natural gas reserves (tcf)
• Oil reserves (billion barrels)

• Population, total
• Labor force, total
• Life expectancy at birth, total (years)

• GDP converted by PPP (US$)
• Steel production (tonnes)
• Corn production (tonnes)
• Industry (including construction), value added (US$)
• Gross fixed capital formation (US$)
• Broad money (% of GDP)

• Military expenditure (US$))
• Armed forces personnel, total

• Researchers in R&D (people)
• Technicians in R&D (people)
• Research and development expenditure (% of GDP)
• High-technology exports (current US$)
• Scientific and technical journal articles

Calculations

The procedure for processing the original array consists of two stages.

Stage 1. Calculation of integral indices for each of the above groups.

Stage 2. Calculation of indicators of national power by convolution of group integral indices.

Table 3.  Integral indices of the first group of indicators (“geographical characteristics”) for 15 leading countries

Forecast

Main conclusions

1. The use of methods of multivariate statistical analysis when assessing the contribution of factors to the integral indicator of national power made it possible to somewhat remove the problem of subjectivity.
2. The position of some countries in the abovementioned assessment differs from positions in other ratings, since indicators that determine, first of all, the country's potential (availability of resources, territory, population, etc.), and not market variables that often change depending on the current situation were used to measure national power. The most important task is to competently manage the available potential.
3. At the beginning of this article, when reviewing the most cited studies, we mentioned that a number of influential American foreign policy strategists highlighted the extreme importance of taking psychological factors into account when assessing national power. These include such components as the level of patriotism and national cohesion, indicators of social integration, political stability, etc. Countries with high values of these indicators are less vulnerable, and the undermining of these factors entails a serious weakening of the state under consideration. At the same time, it was noted that it was extremely difficult to quantify them and then link them with other indicators.
4. The current geopolitical configuration and the existing system of economic ties in the medium term will continue to strengthen China and weaken the USA. Most countries are slightly sensitive to changes in the trade imbalance between the two main world leaders. India, Russia and Germany still remain potential points of attraction for the formation of new centers of power. In general, we would like to note that there is a high probability that there will be no drastic changes in the global geopolitical situation.