13. Multivariate Power Formulas
13.14 Alcock / Newcombe 1970 CA
Norman Zinkan Alcock (1918−2007) was a Canadian nuclear physicist. He studied engineering at Queen's University in Kingston, Ontario, and he did a master's degree in electrical engineering at the California Institute of Technology. In 1949 he got his PhD in physics from McGill University. In 1961 he founded the Canadian Peace Research Institute (CPRI) dedicated to peace research. It ceased operation in 1981. Alan G. Newcombe (1923−1991) was a Canadian chemist. He did his PhD in chemistry at McMaster University. In 1962 he joined together with his wife the CPRI. In 1976 they founded then the Peace Research Institute − Dundas (PRID). In 1970 Alcock and Newcombe published the article "The perception of national power" (ALCOCK & NEWCOMBE 1970) that presents their formula for approximating national power.
After emphasizing the ubiquitous importance of the concept of power in political science, they proceed to declare that "if international relations is to become a science it will have to establish a definitive quantitative measure for its most basic variable—national power" (ALCOCK & NEWCOMBE
1970: 335). They admit that differences may exist between real power and the subjective perception of it, though they insist that objective and subjective power must be based on measurable facts. As for
the application of power formulas for promoting peace, they suggest that quantified power should be used as the basis for weighted voting in the UN General Assembly, instead of the floundering "one nation, one vote" principle (compare sections 13.7, 13.37).195
They liken their approach to the previous efforts of Simon Schwartzman and Manuel Mora y Araujo (section 13.11). Similarly they asked 38 Canadian citizens to rank 122 nations,196 and they calculated the average rank order of countries. They decided on three factors of national power: (1) population, (2) GNP per capita, and (3) area divided by population, which is the reciprocal of population density (compare section 13.9). They ranked those three factors, and then they used multiple regression analysis to arrive at this formula:
relative_power = −16.1 + 0.69 POPrank
+ 0.49 (GNP / POP)rank + 0.08 (area / POP)rank POP = population
Given the low importance of the third factor, they drop it, and arrive at this formula:
relative_power = −8.85 + 0.67 POPrank + 0.47 (GNP / POP)rank
POP = population
Another multiple regression analysis using GNP instead of GNP per capita produces this formula:
relative_power = 9.4 − 0.09 POPrank + 0.93 GNPrank POP = population
This last formula is almost the same as GNP with a Spearman correlation coefficient of 0.995. The ranking based on the last formula and GNP rankings correlate the same with the ranked perceptions, the Spearman correlation coefficients being in both cases 0.85. Ranked military expenditures correlate much better with the ranked perceptions, the Spearman correlation coefficient being 0.92.197 They acknowledge that military expenditures reflect especially well the power of nations at war. The following table presents the complete list of results of the last formula. There appears to be a mistake in ranking, the questionable rankings (68−70) are in italics:
195 In 1971 Newcombe developed the theme further by looking at 20 proposals for weighted voting in the UN General Assembly (NEWCOMBE et alia 1971: 455; compare STRAND et alia 2005). One proposal came from Alcock, who suggested multiplying the square root of the population by the square root of GNP. More often than not proposals for weighted voting of countries are similar to power formulas. A major difference is that these proposals usually contain a bonus of sorts for smaller countries so as to keep the "one nation, one vote" principle but with more limited impact.
196 "The ten most powerful nations were to be rated separately, the remainder into four groups of decreasing power; each such group comprised 28 nations. The nations were then scored from 1 to 10 if they were in the first group, 24.5 if in Group B, 52.5 if in Group C, 80.5 if in Group D, and 108.5 if in Group E" (ALCOCK &NEWCOMBE 1970: 337−338).
197 This raises the question: Why do they choose not to include military expenditures in their multiple regression analysis? The realist answer may well be that the resulting power formula would then not be conducive to peace. If voting in the UN General Assembly were based on such a power formula, the more militarized states would have more voting power – and the less militarized an incentive to become more militarized.
Table 31: Rank Ordering of Nations in 1967 [Alcock/Newcombe]
Country Canadian
Perception
Relative
Power Country Canadian
Perception
Relative
Power Country Canadian
Perception
Relative Power
USA 1 1 New Zealand 32 36 Lebanon 70 71
USSR 2 2 Colombia 64 37 Guatemala 93 72
UK 3 3 Egypt 20 38 Singapore 80 73
West Germany 6 4 South Korea 49 39 Kenya 62 74
France 4 5 Chile 56 40 Sudan 82 75
Canada 7 6 Cuba 16 41 Afghanistan 79 76
China 5 7 Greece 26 42 El Salvador 101 77
Japan 8 8 Bulgaria 41 43 Jamaica 91 78
Italy 11 9 Malaya 68 44 Luxembourg 81 79
India 12 10 Nigeria 58 45 North Korea 38 80
Brazil 28 11 Thailand 61 46 Tanganyika 84 81
Australia 9 12 Portugal 40 47 Cambodia 54 82
Poland 18 13 Iran 44 48 Costa Rica 96 83
Belgium 25 14 Israel 10 49 Madagascar 102 84
Sweden 14 15 Algeria 42 50 Haiti 97 85
Indonesia 43 16 Peru 67 51 Panama 74 86
Netherlands 19 17 Ireland 52 52 Trinidad 99 87
East Germany 13 18 Taiwan 59 53 Honduras 98 88
Argentina 34 19 Morocco 75 54 Nepal 95 89
Czechoslovakia 15 20 Uruguay 69 55 Bolivia 63 90
Switzerland 35 21 Ceylon 78 56 Albania 55 91
Mexico 36 22 Kuwait 73 57 Cyprus 72 92
Spain 22 23 Congo 57 58 Nicaragua 92 93
Rumania 48 24 Ghana 50 59 Jordan 47 94
South Africa 17 25 Iraq 51 60 Paraguay 86 95
Turkey 30 26 Rhodesia 66 61 Guyana 94 96
Philippines 71 27 Saudi Arabia 46 62 Liberia 87 97
Denmark 27 28 Ethiopia 65 63 Somalia 100 98
Pakistan 37 29 Burma 77 64 Laos 60 99
Venezuela 39 30 South Vietnam 45 65 Iceland 85 100
Hungary 23 31 Syria 53 66 Libya 88 101
Austria 29 32 Ecuador 90 68 Togo 103 102
Yugoslavia 21 33 Dominican Republic 89 69 Mongolia 83 103
Norway 24 34 North Vietnam 33 70
Finland 31 35 Tunisia 76 70
Source: ALCOCK &NEWCOMBE 1970: 336−337.
Countries with major discrepancies between the perception ranks and calculated ranks are highlighted. In the three major cases where a country is underestimated (Indonesia, Philippines, Brazil), it can be observed that these are relatively large developing countries in terms of population.
As for the four major cases where countries are overestimated (Israel, Cuba, North Vietnam, North Korea), it can be observed that these countries are small but militarily active. Over- and underestimation are relative categories in relation to the calculated results. The patterns indicate that it is not the perception that is flawed but the formula that needs adjustment.
Replication: Doran / Hill / Mladenka / Wakata 1974
Contemplating the issue of whether power perceptions may differ across cultures and political systems, Charles Doran, Kim Hill, Kenneth Mladenka, and Wakata Kyoji replicated the study by Alcock and Newcombe in 1974 (DORAN et alia 1974, also 1979). For that purpose they surveyed Finnish, Japanese, and American university students. The Spearman correlation coefficients between the three national groups plus the Canadians surveyed by Alcock and Newcombe are all 0.90 or above. This demonstrates that perceptions are fairly reliable and consistent.198 Like Alcock and Newcombe, they also extend their analysis to the Latin American subset of Schwartzman and Mora y Araujo.
As for determining correlates of national power, their approach differs from Alcock and Newcombe in that they use six variables in their analysis rather than three, using factor analysis199 to distill three factors out of the six variables. The following table displays the degree of association of each variable with the three factors:
Table 32: Factor Scores [Doran et alia]
Variable Factor I Factor II Factor III
Population 0.93 −0.20 0.16
Military Expenditures 0.89 0.39 0.11
Armed Forces 0.90 0.19 0.19
GNP 0.84 0.48 0.15
GNP per capita 0.14 0.98 0.05
Population Density200 0.20 0.06 0.98 Source: DORAN et alia 1974: 440.
Based on these factors, they use multiple regression analysis to arrive at this formula:
power = 0.774 factor_I + 0.492 factor_II + 0.076 factor_III No results for this formula were published.