Power has always accrued in the hands of those societies that have managed to imbue themselves of a collective vision of global affairs of such a nature as to mobilize them in the pursuit of their shared goals throughout generations. Such is the kind of power that Mallmann (1994) defines as ethnic-political, since ethnic groups are social groups mobilized by a common culture, to be differentiated from other groups for which power can only be the result of their insertion into a society and of their participation in the hegemonic political coalition that controls it. The latter is defined as primary power while secondary power would be the one based on a society’s ability to access "natural resources", as well as on its capacity to transform them in order to enjoy favorable conditions vis-à-vis other societies or States. Wallerstein (1984) proposes a different four tier classification: State power, ethnic-demographic power, class power (as defined in Marxist terms), and domestic-entities power. In this paper, temporal changes in a series of "primary power" and "secondary power" indicators, as defined by Mallmann (1994), will be analyzed with a view to quantifying "State power" throughout the second half of the century.

On this basis we will try to identify trends for the main world powers in order to thereby establish relative power variations among and between them. Paul Kennedy (1987), for instance, analyses and describes the rise and fall of world powers throughout the last five centuries. Following Kennedy’s approach, a nation projects its military might on the basis of its economic resources but the high cost of maintaining military supremacy ultimately causes its fall. Indeed, major powers in a crisis situation react by increasing defense expenditures thereby debilitating themselves by way of a non productive allocation of their available resources. For Kennedy there has been, throughout history, a significant correlation between productive capabilities and military might. In his work he clearly shows that the relative strengths of major world powers never remain constant, due in particular to the irregular growth pattern followed by each society and to the greater advantages provided to one over the other by developments in technology and organization. Following we will undertake a preliminary approach to a quantitative analysis of world power distribution. In so doing, we will avoid an analysis of Schattschneiders’s (1960) power models. This suggests that the end result of conflict among powers depends not on their relative strengths but on the scenario in which such a conflict takes place. It would ensue that in politics the most important strategy is to predetermine the scope of a conflict. Even more so if, assuming power balances shift once the scope of a conflict is widened, it is understood as inevitable that the weaker party will foster such an expansion. It follows that the ultimate power of a State resides in its capacity to forge strategic alliances in order to consolidate its goals, even if it has "less" power in comparative terms.

Measuring the relative power of states has been a constant problem for geopolitics given that it can not be measured in a direct way (Taylor, 1985). The first mathematical models applied to the dynamics of power were developed by Lewis F. Richardson between 1920 and 1950. Richardson (1953) was most probably one of the founding fathers of mathematical sociology. His models, in general terms, concentrated on the study of the dynamics of the arms races that took place in Europe during the XIX and early XX centuries. His analysis of the power of nations remained circumscribed to "military power".

More often than not, to estimate the power of a State or a Nation, some of the more relevant characteristics of States are chosen and combined in some ingenious way to formulate a predetermined ordinal classification (Mallmann, 1994; Muir, 1981;Neumann,1997). In general, such theoretical approaches can intuitively be held as reasonable although not always satisfactory since the measurement units or dimensions chosen for each indicator are definitively arbitrary.

Taking into account the weaknesses of prior models, and the fact that in such models each power indicator is static in its scope ( for only one year), we will try to develop certain criteria for the establishment of a power index capable of showing changes in the long term (some 50 years), and which includes "non dimensional" units in order to avoid, thereby, inconsistencies derived from adding "apples and pears". The proposed model has the following characteristics:

1. It is suggested that chosen power variables be represented as a fraction (fp) of the total available resources on Earth for each variable. Some of the possible categories could be the following: natural resources (land and sea territory, energy production, monetary reserves in national Central Banks, Gross Domestic Product, total exports,…); human resources (population,…); military resources (military expenditures, military personnel, nuclear power,…); research and innovation resources ( number of scientists, technology experts, artists, scientific publications, innovations and patents, etc.). Such values as assumed by each variable would factor in time ( i.e. would fluctuate from year to year).

2. Each fraction of the factors identified in (1) must necessarily be "modulated" by a quality parameter (i.e. the Humid Pampa’s land quality is not the same as that of the Sahara desert). This Cp factor will assume values between 0 and 1. Due to a factoring-in of technology and organizational change, as well as of each society’s own dynamics, such quality indicators will be time-dependent.

3. Each "Nation-State" society will have a different synergic integration level (Is), (or antagonic disaggregation), which will have an effect on the dynamics of the use of each power factor. Thus, some will see their power index increase while others will see it decrease sensibly. Mallmann (1994) concentrates on a detailed study of possible synergic and antagonic indicators of a societal origin. He considers different degrees of ethnic, religious and linguistic integration, as well as a so-called political synergy coefficient along which to classify societies within certain rythmic dynamics (Mallmann and Lemarchand, 1998 and Mallmann, 1999).

4. Taking into account the previous considerations, a country power index (Pp), as a function of time, can be established as wherein (p) represents the country or group of countries under analysis (for example, the European Union or Nafta); (s) the synergy coefficient under use; and (i) the fraction of world resources. N would represent the product of all i fractions taken into account. This formula has the following mathematical property:

   That is to say that the sum of the product of all fractions for all countries will always equal 1. Such a property will be of interest once regional alliance policies are analysed. Even more, as by definition the quantities Ci(t) and fi(t) are non dimensional, i.e. are not quantifiable in units, all we need to do is choose the kind of social synergy indicators in order to equally represent them by non dimensional numbers.

5. The above could be made more realistic if it could equally take into account the dependence or weakness of one State vis-a-vis the other. For example, in such cases where external commitments weaken a State’s autonomy in the exercise of power. External indebtedness, border conflicts, massif immigration phenomena, etc. would exemplify such situations. A Pd index, similar to the Pp index, could thus be defined. A matrix of dependency indicators would be required since a certain country P11 might be indebted to another P22, be engaged in an armed conflict with P3, receive migration flows from P3,…Each of these different countries, Pj (with j = 1, 2, 3…), will have its own synergy coefficient and societal characteristics. In this line of thought, a first approach would be to try to measure power balances among pairs of countries. The total power PTT of one country vis-a vis another would be the difference between its own power Pp1p1 and that which is the result of the measurement of its P11 dependence to a certain other P2. Thus considered, the Power Indicator would be defined as:

    

Below, we will apply the proposed formula in a very simplified manner, selecting the most representative power variables whose values it was possible to establish on the basis of published international statistics. To simplify, we shall analyse only power variations for each country between 1950 and 1996. Coefficients for the loss of power due to dependency factors, Pd, will not be taken into consideration for the purposes of this paper. Moreover, in order to simplify calculations it will be assumed that Ci (t) = 1 for all coefficients.

Fractions of power under consideration. Annual values for the period 1950 – 1996 for the following fractions of world totals will be considered: territory, population, gross domestic product, international reserves in central banks, export values and total military expenditures.

Societal synergy indicators. Although Mallmann (1994) defined a very complete set of indicators to measure the degree of synergy within a certain society, the lack of an homogeneous and complete set of data for such indicators for the 1950 to 1996 period, along with the fact that it is not always feasible to establish a non dimensional indicator, implies that this factor can not be represented as originally considered. In replacement, the Human Development Index, as calculated following the United Nations Development Program’s (UNDP) methodology, has been adopted. The advantage of this indicator is that it fairly well represents the degree of societal synergies in measuring three important components: life expectancy at birth, an education coefficient which takes into account the degree of alphabetization within a society and the average number of school years in its educational system, and the per capita gross domestic product calculated taking into account each society’s purchasing power. Thus, the UNDP developed a non dimensional indicator which fluctuates between 0 and 1, and which allows us to classify each society along the lines of such coefficient’s values. UNDP started publishing the HDI yearly since 1990 and it has calculated its values for each country for 1960, 1970 and 1980. Following the same methodology as the UNDP and with data published in the United Nations Statistical Yearbooks, calculations were also made for the 1950 HDI. Next, using the HDI values for 1950, 1960, 1970, 1980, 1990, 1991,1992, 1993, 1994, 1995 and 1996 and on the basis of a calculation program, an interpolation of the different annual values between 1950 and 1996 was made, using for such purpose a soft adjustment function known as "smoothlowess".

Summing up, the function applied to estimate the evolution in time of the power index is as follows:

Wherein Pp is country p’s power index, HDIp represents its Human Development Index, fsupsup its territorial share in relation to world total, fpoppop its share of the world’s population, fgdpgdp its contribution to world gross domestic product, f res the share of world reserves held by its central bank, fexpexp its share in world exports and fmil.expmil.exp its part in total world military expenditures. All these indicators are shown in annual terms for the period 1950 – 1996.

This is, obviously, a very preliminary approach to a much more complex problem and only some of the many possible variables have been taken into account, with no other purpose but to illustrate the kind of results that can be obtained by applying the proposed formulation.

By way of example, let us take one of the variables of world power, territorial extension. Table 1 shows the fraction of total world territorial extension occupied by the largest countries. Only one year coefficient values are shown since it is obvious that in general, unless we have a situation such as the dismemberment of the former Soviet Union into a number of different countries and the creation of the Russian Federation, which implied a loss of territorial extension, this is the only coefficient among those considered that remains practically constant along the last decades.

It is important to note how a coefficient such as a country’s share of total world exports changes from year to year. This indicator, by showing the fraction of the world markets a country controls, illustrates in a general way its long term capacity to become more or less competitive at the international level. Table 2 shows this indicator’s evolution in time for some Asian countries. It is to be remembered that only a share of the total, a value between 0 and 1, is represented. To obtain its percentage value in relation to world totals, such share is to be multiplied by one hundred.

Regional groupings: The same analysis could be applied to the study of what would be the accumulated power held by a group of countries united by political, ethnic, religious, trade or military ties, among others. On the basis that

each country in the new grouping’s fi fraction is simply added up. Nevertheless, when considering the "regional" HDI, the annual value of the HDI for each country must be adjusted by each country’s share of the region’s total population and then all such values must be added. Therefore,

Following is a list of those country groupings, basically of a trade related nature, which have been or are in the process of being the object of our analysis:

• EU (European Union): Germany, Austria, Belgium, Denmark, Spain, Finland, France, Greece, Ireland, Italy, Luxembourg, Holland, Portugal, United Kingdom, Sweden.

• OPEC (Organization of Petroleum Exporting Countries): Saudi Arabia, Algeria, Libya, Nigeria, Gabon, Venezuela, Ecuador, Iraq, Kuwait, United Arab Emirates, Qatar, Iran, Indonesia.

• ADE (Asian Dynamic Economies): China, Taiwan, Hong Kong, Korea, Malaysia, Singapore, Thailand.

• NAFTA (North America Free Trade Agreement): Canada, United States, Mexico.

• CIS (Community of Independent States): Armenia, Azerbaidjan, Belarus, Georgia, Kazhakstan, Kirghistan, Moldova, Russian Federation, Tajikhistan, Turkmenistan, Ukraine, Uzbekhistan.

• CEEC (Community of Eastern European Countries): Albania, Bulgaria, Check Republic, Slovaquia, Slovenia, Estonia, Hungary, Letonia, Lithuania, Poland, Rumania.

• MERCOSUR (South American Common Market): Argentina, Brazil, Paraguay, Uruguay.

• OECD (Organisation for Economic Co-Operation and Development): Germany, Austria, Belgium, Denmark, Spain, Finland, France, Greece, Ireland, Iceland, Italy, Luxembourg, Norway, Holland, Portugal, United Kingdom, Sweden, Switzerland, Turkey, Australia, Canada, United States, Japan, Mexico, New Zealand.

What follows is a presentation of the evolution of power indexes, on the basis of the final formula (4) and for the period 1950 – 1996, for a selection of countries and groups of countries taken from among the 56 included in our analysis. Tables 3, 4 and 5 show the results for a selection of Latin American countries, for the so-called intermediate powers, and for the main powers, Nafta and the European Union, respectively.

We believe that quantitative indicators for the study of State power-dynamics are an indispensable tool for the analysis of international relations. The one presented here, of which a simplified version has been applied in a preliminary fashion, already shows their relevance. We have been able to show the indicator’s numerical values and their variations in time for some selected countries and groups of countries. They show the supremacy of Brazil in Latin America; the evolution of some intermediate powers; the supremacy of the United States after 1989; and the equal status shared by NAFTA and the European Union. We shall endeavor to follow this line of research with the goal of making a contribution to the understanding of the dynamics of the indicators of power among States, in particular those of Latin America.

References

• Kennedy, P. (1987), The Rise and Fall of the Great Powers, Random House, New York.

• Mallmann, C.A. (1994), Qué metas para la "segunda" Argentina? 1995 – 2070, A-Z Editora, Buenos Aires; and (1989) Ïnsercion Internacional de Argentina: El poder y las holologias en el mundo actual", en La Encrucijada Argentina, Editorial Tesis, Buenos Aires.
• Mallmann, C.A. (1999), "Towards an interpretation of China’s History from c. 2205 BC. to 2000 AD in terms of a Long Term 'Billow-Like'' Dynamics of Societal Processes", sent for publication in Review (USA).
• Mallmann, C.A. and Lemarchand, G.A. (1998), Generational Explanation of Long-Term "Billow-Like" Dynamics of Societal Processes, Technological Forecasting and Social Change, vol.59 (1), pp.1-30.
• Muir, R. (1981), Modern Political Geography, Macmillan, London
• Neumann, M. (1997), The Rise and Fall of the Wealth of Nations, Edward Elgar, Cheltenham, UK.
• Richardson, L.F. (1953), Arms and Insecurity, Quadrangle Books, Chicago.
• Schattschneider, E.E. (1960), The Semi-Sovereign People, Dryden, Hinsdale, Il.
• Taylor, P.J. (1985), Political Geography: World-Economy, Nation-State and Locality, Longman Group Limited, London.
• Wallerstein, I. (1984), The Politics of World Economy, Cambridge University Press, Cambridge, UK.

Acknowledgment: This paper was prepared and financed within the framework of the UBACYT TC 004 and CONICET PIP 0154/1998 research projects. The authors wish to thank Sergio Labourdette, Ph.D., and Dario Codner, B.A., for their important comments and suggestions throughout the preparation of this paper.

http://www.sela.org
sela@sela.org
   SELA,  Permanent Secretariat
Torre Europa, Fourth floor, Urb. Campo Alegre, Av Francisco de Miranda,
Caracas 1060- Venezuela
Tlf: (58) (212) 955.71.11 Fax: (58) (212) 951.52.92