13. Multivariate Power Formulas
13.33 Caro 1998 FR
Figure 9: Potential of Developed and Less Developed Countries [Chaczaturov]
Source: CHACZATUROV 1997; author's own calculations.
Even though the (A B C D)0.25 potential of less developed countries is greater in total, it must be realized that, in terms of population, the developed countries represent only the "golden billion" of the world population. The 1:2 population ratio of West to East is less unbalanced in comparison to the 1:4 population ratio of developed countries to less-developed countries.
he adopts. Before presenting his survey and the resulting formulas, he composes a simple power index based on the ranks of ten countries in four variables. Those ranks are added and then ranked again. The following table presents the complete published results of this simple approach:
Table 56: Simple Power Index for 1997 [Caro]
Country Population
rank GNP-PPP
rank
International Trade
rank
Defense Budget PPP
rank
Summed Ranks
rank
United States 3 1 1 1 1
China 1 2 7 2 2
Germany 7 4 2 7 3
Japan 6 3 3 8 3
India 2 5 10 5 5
France 8 6 5 4 6
United Kingdom 9 7 4 6 7
Russia 5 10 8 3 7
Brazil 4 8 9 9 9
Canada 10 9 6 10 10
Source: CARO 1999: 125, 2000a: 22.
The index serves merely as orientation, for he proceeds to introduce a more sophisticated analysis based on a survey he conducted. The survey was conducted in the first semester of 1998 at the Institute of Higher Studies for National Defense [Institut des hautes études de défense nationale − IHEDN]. The IHEDN is a French public institution with the purpose of training military and civilian public servants in defense matters. 214 students agreed to participate in the survey, 36 of whom were in the military, 39 were economists, and 40 were diverse civilian auditors. The average age of the surveyees was 38.5. Caro concedes that the number of surveyees is quite small. He hopes that their superior knowledge on defense matters compensates for this shortcoming (compare section 13.30).
In the survey the surveyees were asked to assign scores ranging 1−15 for the estimated power of 40 selected countries. The scores are then averaged into an interval scale. He subsequently uses multiple regression analysis (or something similar) on these power perception scores to determine the weights for a varying number of selected factors. This way he produces three formulas as the best approximations of power in correlation to the surveyed power perception scores. There are two versions for the three formulas: the version of the three formulas with the higher Pearson correlation coefficients is presented below (CARO 2000a: 28), the other is not (for that see CARO
2000c: 98−99, 101). The formula using only socio-economic factors is:
exponent ( Poweri ) = GNPatPPPi1.15
× ITi0.39
GNPatPPP = GNP at PPP; IT = international trade; i = respective country
The Pearson correlation coefficient for the results of this formula and the power perception scores is 0.94. The formula using only military factors is this:
exponent ( Poweri ) = NCi0.41 × AFPi0.58 × DEPCatPPPi1.20
NC = nuclear capacity; AFP = armed forces personnel; DEPCatPPP = defense expenditures per capita at PPP; i = respective country
The Pearson correlation coefficient for the results of this formula and the power perception scores is 0.89 – not as good as the civilian formula. The factor for nuclear capacity is not entirely clear. He takes account of the nuclear arsenals, the capabilities of countries to develop and produce nuclear weapons rapidly, as well as the aspirations of countries to obtain them. He seems to have initially assigned scores ranging 1−7 to countries based on his evaluation (CARO 1999: 127, 2000c: 97). He then seems to have changed his mind by preferring a simple measure composed of two variables, namely (1) whether a country possesses nuclear weapons (dummy variable) and (2) the number of warheads (CARO 2000a: 26).259 The formula capturing both socio-economic and military factors is:
exponent ( Poweri ) = Ti0.42 × GNPatPPPi0.72 × NCi0.20 × DEatPPPi0.53 T = technology; GNPatPPP = GNP at PPP; NC = nuclear capacity; DEatPPP = defense expenditures at PPP; i = respective country
The Pearson correlation coefficient for the results of this comprehensive formula and the power perception scores is 0.98. The coefficient has to be better than the previous two by logical necessity (the formula being more inclusive). The factor for technology is quantified by adding telephone lines per capita, whether fixed or portable, and the number of computers per capita.
The following table presents the complete published results as for perceived power and calculated power, using the third formula that includes both socio-economic and military factors:260
Table 57: Index of Calculated Power for 1998 [Caro]
Country Perceived
Power Calculated
Power Country Perceived
Power Calculated Power
United States 14.38 14.8 Mexico 7.10 8.3
China 12.11 11.9 Indonesia 7.12 7.8
France 11.61 11.5 Pakistan 7.38
Japan 12.00 10.9 Argentina 7.18
United Kingdom 11.34 11.4 Iraq 7.09
Russia 11.32 11.3 Singapore 6.93
Germany 11.82 10.5 Ukraine 6.87
India 10.24 9.7 Egypt 6.81
Italy 9.8 Syria 6.75
South Korea 9.5 Chile 6.23
Canada 9.76 9.2 Poland 5.86
Israel 9.92 8.7 Malaysia 5.78
Brazil 8.41 9.0 Morocco 5.76
Australia 8.65 8.7 Nigeria 5.47
Spain 8.44 8.9 Libya 5.37
259 Estimates on nuclear arsenals are notoriously unreliable especially with regard to Israel, India, Pakistan, and North Korea.
Normally estimates are on the number of warheads, disregarding that different warheads may have different explosive yields as measured in megatonnage. One of the treasures of the internet is a website by Robert Johnston who provides estimates on nuclear arsenals, including megatonnage: http://www.johnstonsarchive.net/nuclear/ [16 August 2013].
260 Results also exist for the other versions of the formulas (see CARO 2000c: 104).
Netherlands 8.4 Algeria 5.27
South Africa 8.25 Colombia 4.76
Turkey 7.80 8.5 Uruguay 4.43
Saudi Arabia 8.12 Lebanon 4.30
Thailand 7.9 Sudan 3.32
Iran 7.80 Yemen 3.29
Sweden 7.69 7.8 Zambia 2.50
Source: CARO 2000a: 32, 2000b: 103−104.
In what could be called a postmodernist analysis Francis Rousseaux compared Jean-Yves Caro to other authors on power. He remarks that in comparison to the other authors Caro is concerned with the order of powers. The problematic issue is a random disorder taunting the qualitative. For Rousseaux this approach is a measurement of concordance and has nothing to do with science. The central question remains as how to reconstruct opinion (ROUSSEAUX 2001: 8−10). Guy Teissier is deputy to the French National Assembly and chairman of the National Assembly Committee on National Defense and Armed Forces [Commission de la Defense Nationale et des Forces Armées].
He reflects in a 2006 article on this power analysis of Caro that, among other things, he feels reassured by the fact that it can be demonstrated that nuclear weapons are an advantageous factor for French military power (TEISSIER 2006: 91−92). In this regard, Caro's survey also shows that French defense experts evaluated nuclear weapons as the most important determinant of power among 20 possible determinants (CARO 2000b: 113).261 French Frigate Captain Delorme appreciates the essential importance of military capacity as demonstrated by Caro (DELORME 2006: 4). Caro's approach most likely inspired Polish defense economist Mirosław Sułek to conduct regular surveys as well (section 13.30).
Having Shinn (section 13.13) as well as Alcock and Newcombe (section 13.14) as predecessors in terms of method, Caro used perhaps the best approach available for the quantification of power. He used a perception survey as the basis for multiple regression analysis (or something similar), rather than an arbitrary assignment of weights. Shimbori and colleagues (section 13.8) as well as Saaty and Khouja (section 13.23) used perception surveys to determine the importance of variables. Though Caro surveyed on the relative importance of variables, he did not base the weights on this perceived importance of input variables. He based the weights of variables on the perceived output approximated by power perception. The calculation of the weights via multivariate regression analysis keeps the focus on optimizing output results. This approach can be considered empirical despite limitations (section 16.7). There are minor technical issues providing room for improvement, for example in the way he quantified technology or nuclear capacity. It could further be debated whether it is better to use a linear or nonlinear model. The use of an interval scale rather than a ratio scale is a drawback, because it is not terribly interesting to know that the United States is more powerful than China − no formulaic sophistication is needed to figure that one out − but
261 The determinants were (score in parenthesis, the score range being 1−15): nuclear weapons (12.54), technology (12.19), international trade (11.50), GNP (11.46), armed forces (11.39), economic independence (11.39), diplomacy (10.81), currency (10.59), social cohesion (10.55), military alliance (10.25), wealth per capita (10.25), population (10.09), education system (10.06), natural resources (9.77), institutions (9.50), situation (9.14), language and culture (8.81), territory (8.72), history (8.67), and regional organization (8.16).
it is imperative to know how much more powerful the United States is than China. Nevertheless these problems can be solved. The basic method is sound and workable.