Index Comparisons

NationalPowerMain

There are several simple quantitative indices of national power or capacity. In this page, we compare the new index (NPI) with a few others:

    • the GNI index, in which power is measured by the relative size of gross-national income;
    • the CINC, a Composite Index of National Capability, which contains six components:
      • The population size
      • Total Urban Population
      • Total Steel and Iron Production
      • Total Primary Energy Consumption
      • Total Military Personnel
      • Total Military Budget
    • the log-GNI

If you have installed the CDF Player from Mathematica, you will see an interactive graph in which you can choose or manipulate several different parameters. (If you would rather see actual index values in a tabular form, go to the Tables page.)

      • Choice of Indices: NPI(default), GNI, CINC or logGNI.
      • Two countries (A and B) to compare out of 187 countries;
      • the saliency ratio–the importance of true component (0.2 to 4.0, with the default of 2.0);

The winning probability of A is the losing probability of B, and vice versa. Therefore, the winning probability of Germany over the United States is .297 (= 1.0 – 0.703). The winning probability of a stronger nation will increase as the saliency of the true component increases, and it will decrease as the saliency of the true component decreases. You may find some of these probabilities surprising, but there is no external evidence that may contradict these results.

On the other hand, you will find that the winning probabilities implied by other indices (especially by GNI and CINC) clearly contradict the known facts and, therefore, the index values are not acceptable. To make these claims concrete, please examine the winning probabilities implied by GNI or CINC for countries at the upper end of the power scale, for instance, the United States and Germany. Click the GNI button, above, then you will note that the winning probability of the US over Germany is too high to be credible. You will find similar result when you click CINC button above. For convenience, we have reproduced the three graphs side by side below. (These are static graphs.)

US vs Germany by NPI (left), GNI (middle) and CINC

Note that for GNI and CINC, the two density curves do not overlap at all. This means that the power advantage of the stronger country is such that even the worst possible performance of the stronger country will be always better than the best possible performance of the weaker country. In short, the stronger country (the U.S.) in this case will win all the time against Germany, on a variety of contests that involve varying saliency ratios. This is contrary to the known facts. Consequently, the power differences measured by these indices are not credible: these indices exaggerate the differences at the upper end of the scale.

On the other hand, if you compare countries not at the top echelon, for instance, Sweden and Togo, you will notice that the winning probability of the higher nation implied by GNI and CINC is too small to be credible: Sweden’s winning probability over Togo implied by the GNI and CINC are .597 and .555, respectively, while the winning probability implied by NPI is .976. We believe the NPI provide much more credible probability than the other two.

Sweden vs Togo by NPI (left), GNI (middle) and CINC

In summary, these two indices–GNI and CINC–distort the true power differences in such a way that they squeeze the differences at the lower end and stretch them at the higher end. One of the main reasons for such a distortion is due to the use of raw data scales without proper transformations. For instance, population size, GNI or GDP, GDP per capita, military budget, and so on, are highly skewed and cannot be used as components of power index. Many other existing measures of national capacity suffers from similar problems. These highly skewed raw values cannot be assumed to be proportional to the latent capacity that they are supposed to reflect. There are other more sophisticated measures, but they usually rely on at least one untransformed component such as population size, GDP, users of internet, etc. The “raw scales” of these components need to be transformed properly before they can be integrated into a composite scale of national power.

The results from log-GNI is similar to the results from NPI and the relationship between NPI and log-GNI is fairly linear. we suggest that log-GNI can be used as a quick and handy substitute for NPI.

To end this section, we introduce an interactive bubble chart, in which the relationships among four indices are shown. As a default, we show the relationship between NPI and log-GNI, which is fairly linear. By moving the mouse pointer over a circle, you can see identifying information for each circle. Of course, you can see an interactive graph for every two pair of indices. See the Glossary for a fuller description of variables used in the graph.

For easy comparison, we present two static graphs below, comparing the relationship between NPI vs log-GNI and NPI vs raw-GNI.

Here is the comparison table for the four indices of national power, with their ranks and z-scores.

Nation NPIRnk NPIz GNI12Rnk GNI12z logGNIz CINCRnk CINCz
United_States 1 2.52291 1 9.650 2.577 2 7.073
Japan 2 2.11344 3 2.742 2.047 4 1.930
Germany 3 1.99016 5 1.833 1.888 7 0.968
China 4 1.8743 2 7.528 2.470 1 9.991
France 5 1.80563 9 1.169 1.720 10 0.702
Korea_Rep 6 1.77066 12 0.749 1.568 8 0.958
Italy 7 1.73148 10 0.882 1.621 11 0.624
United_Kingdom 8 1.7207 7 1.219 1.735 9 0.817
Spain 9 1.64915 14 0.595 1.495 18 0.312
Canada 10 1.64685 13 0.620 1.508 20 0.275
Russia 11 1.63199 6 1.232 1.739 5 1.754
Australia 12 1.58552 18 0.289 1.303 26 0.091
Mexico 13 1.5202 11 0.861 1.613 16 0.357
Brazil 14 1.4729 8 1.189 1.726 6 0.995
Netherlands 15 1.40758 22 0.177 1.205 32 0.015
Poland 16 1.33188 19 0.221 1.246 27 0.082
Argentina 17 1.31372 21 0.181 1.209 35 -0.033
Iran 18 1.22954 17 0.317 1.325 15 0.418
Sweden 19 1.16766 33 -0.027 0.940 52 -0.123
Belgium 20 1.16256 30 -0.007 0.975 41 -0.076
Turkey 21 1.13136 16 0.460 1.421 12 0.463
Switzerland 22 1.08758 36 -0.042 0.913 83 -0.221
India 23 1.07033 4 2.677 2.038 3 3.521
Saudi_Arabia 24 1.06754 20 0.188 1.216 19 0.286
Ukraine 25 1.05377 38 -0.064 0.868 17 0.335
Czech 26 1.05376 47 -0.109 0.764 56 -0.155
Indonesia 27 1.05095 15 0.468 1.425 14 0.432
Austria 28 1.04721 37 -0.053 0.891 53 -0.144
Chile 29 1.0426 44 -0.087 0.818 48 -0.116
Israel 30 1.03777 50 -0.127 0.714 44 -0.089
Norway 31 1.03735 45 -0.100 0.787 65 -0.192
Greece 32 1.0335 48 -0.109 0.763 43 -0.080
Malaysia 33 1.0261 28 0.013 1.007 39 -0.049
Hong_Kong 34 1.01847 35 -0.040 0.916 187 -999
Romania 35 0.985098 46 -0.107 0.770 47 -0.111
Colombia 36 0.978203 27 0.025 1.024 30 0.042
Thailand 37 0.956478 23 0.098 1.120 23 0.135
Venezuela 38 0.947873 34 -0.027 0.939 36 -0.041
Peru 39 0.919148 41 -0.074 0.847 50 -0.123
Philippines 40 0.903067 31 -0.014 0.963 31 0.019
Denmark 41 0.901097 52 -0.141 0.669 70 -0.200
Egypt 42 0.886463 26 0.040 1.045 21 0.225
Algeria 43 0.882823 39 -0.070 0.857 33 -0.003
Hungary 44 0.879026 57 -0.161 0.599 66 -0.194
Ireland 45 0.870209 59 -0.182 0.512 99 -0.244
New_Zealand 46 0.865773 63 -0.199 0.424 93 -0.237
Singapore 47 0.859741 40 -0.074 0.847 46 -0.110
Finland 48 0.857232 54 -0.149 0.642 59 -0.166
Portugal 49 0.844732 49 -0.125 0.719 62 -0.182
United_Arab_Emirates 50 0.801829 29 0.009 0.999 51 -0.123
Kazakhstan 51 0.773916 55 -0.150 0.640 45 -0.110
Cuba 52 0.733554 83 -0.232 0.180 76 -0.207
Belarus 53 0.718818 60 -0.185 0.495 54 -0.145
Vietnam 54 0.701614 43 -0.086 0.821 25 0.117
Sri_Lanka 55 0.68045 65 -0.201 0.412 60 -0.170
Slovakia 56 0.676088 64 -0.200 0.418 73 -0.203
Ecuador 57 0.624997 62 -0.193 0.455 69 -0.198
South_Africa 58 0.596223 24 0.080 1.098 29 0.050
Bulgaria 59 0.581102 74 -0.216 0.312 74 -0.203
Uzbekistan 60 0.54313 69 -0.208 0.369 58 -0.165
Serbia 61 0.528258 77 -0.227 0.224 171 -0.277
Azerbaijan 62 0.48594 76 -0.222 0.267 79 -0.211
Libya 63 0.468455 73 -0.216 0.316 64 -0.186
Croatia 64 0.458532 81 -0.230 0.204 102 -0.247
Tunisia 65 0.450959 72 -0.214 0.330 91 -0.234
Slovenia 66 0.449366 88 -0.241 0.076 127 -0.259
Syria 67 0.426486 66 -0.201 0.410 38 -0.047
Dominican_Rep 68 0.39425 71 -0.214 0.330 87 -0.227
Costa_Rica 69 0.389439 85 -0.239 0.101 136 -0.265
Pakistan 70 0.369517 25 0.057 1.069 13 0.435
Lithuania 71 0.361024 87 -0.241 0.085 116 -0.254
Bangladesh 72 0.331843 42 -0.077 0.842 22 0.140
Panama 73 0.324259 86 -0.240 0.094 141 -0.267
Uruguay 74 0.322288 91 -0.244 0.038 111 -0.252
Kuwait 75 0.297955 56 -0.153 0.630 77 -0.208
Bolivia 76 0.291729 89 -0.243 0.051 84 -0.223
Morocco 77 0.283107 58 -0.174 0.548 37 -0.046
Iraq 78 0.278941 61 -0.193 0.456 34 -0.007
Georgia 79 0.262542 115 -0.261 -0.272 110 -0.251
Qatar 80 0.259206 53 -0.147 0.650 89 -0.231
Lebanon 81 0.255201 84 -0.238 0.122 90 -0.233
Jordan 82 0.214997 97 -0.253 -0.099 71 -0.202
Congo 83 0.204869 51 -0.137 0.682 123 -0.258
Latvia 84 0.187551 103 -0.256 -0.148 129 -0.259
Bosnia_Herzegovina 85 0.164053 104 -0.256 -0.152 118 -0.256
Albania 86 0.141246 111 -0.259 -0.231 132 -0.263
Turkmenistan 87 0.135333 95 -0.248 -0.015 97 -0.243
El_Salvador 88 0.135129 96 -0.250 -0.049 103 -0.247
Estonia 89 0.114488 112 -0.260 -0.258 134 -0.264
Paraguay 90 0.112309 101 -0.256 -0.144 115 -0.254
Nigeria 91 0.109322 32 -0.019 0.953 24 0.126
Oman 92 0.0939456 75 -0.219 0.290 80 -0.214
Ghana 93 0.0538067 93 -0.246 0.012 82 -0.220
Cyprus 94 0.0450048 107 -0.258 -0.194 140 -0.267
Armenia 95 0.0445635 126 -0.265 -0.413 100 -0.245
Honduras 96 0.0193617 106 -0.258 -0.189 114 -0.253
Kenya 97 0.0133515 79 -0.229 0.209 63 -0.185
Jamaica 98 0.0132766 122 -0.264 -0.368 142 -0.267
Guatemala 99 0.00408419 82 -0.231 0.191 92 -0.236
Tajikistan 100 -0.019491 125 -0.265 -0.399 126 -0.259
Myanmar 101 -0.0404174 68 -0.208 0.372 28 0.054
Macedonia_FYR 102 -0.05033 118 -0.263 -0.332 131 -0.262
Bahrain 103 -0.0535509 110 -0.259 -0.222 120 -0.257
WestBankGaza 104 -0.0616161 132 -0.268 -0.498 185 -999
Kyrgyzstan 105 -0.140683 140 -0.269 -0.583 124 -0.259
Moldova 106 -0.14662 139 -0.269 -0.560 128 -0.259
Trinidad_Tobago 107 -0.166378 105 -0.256 -0.155 125 -0.259
Cambodia 108 -0.175173 100 -0.255 -0.129 67 -0.197
Mongolia 109 -0.177702 138 -0.269 -0.558 135 -0.264
Tanzania 110 -0.183001 80 -0.229 0.206 61 -0.177
Nicaragua 111 -0.212589 130 -0.266 -0.445 121 -0.257
Luxembourg 112 -0.224933 109 -0.259 -0.215 117 -0.255
Angola 113 -0.245272 67 -0.205 0.391 55 -0.149
Mauritius 114 -0.258369 123 -0.265 -0.394 154 -0.274
Cameroon 115 -0.298246 90 -0.244 0.043 88 -0.228
Madagascar 116 -0.351264 121 -0.264 -0.361 95 -0.240
Gabon 117 -0.352847 116 -0.263 -0.316 145 -0.269
Uganda 118 -0.361405 94 -0.247 0.009 78 -0.209
Iceland 119 -0.393627 144 -0.271 -0.664 161 -0.275
Nepal 120 -0.397923 99 -0.255 -0.127 72 -0.203
Montenegro 121 -0.401022 148 -0.273 -0.826 148 -0.270
Brunei_Darussalam 122 -0.406277 120 -0.264 -0.353 147 -0.270
Lao_PDR 123 -0.421482 127 -0.266 -0.420 112 -0.253
Malta 124 -0.421789 145 -0.271 -0.688 162 -0.275
Botswana 125 -0.45576 108 -0.258 -0.205 143 -0.267
Yemen 126 -0.461805 92 -0.246 0.019 68 -0.197
Ethiopia 127 -0.475477 70 -0.210 0.359 42 -0.077
Namibia 128 -0.512049 133 -0.268 -0.501 144 -0.268
Fiji 129 -0.537714 158 -0.275 -1.092 153 -0.273
Senegal 130 -0.551177 114 -0.261 -0.270 96 -0.241
Sudan 131 -0.586509 78 -0.227 0.223 49 -0.118
Bahamas 132 -0.631517 143 -0.270 -0.626 160 -0.275
Cote_dIvoire 133 -0.647849 98 -0.254 -0.122 81 -0.216
Zambia 134 -0.655761 119 -0.264 -0.346 94 -0.238
Barbados 135 -0.677314 154 -0.274 -0.951 167 -0.276
Haiti 136 -0.704839 141 -0.270 -0.596 106 -0.249
Papua_New_Guinea 137 -0.755431 124 -0.265 -0.395 137 -0.265
Malawi 138 -0.780409 136 -0.268 -0.542 107 -0.250
Rwanda 139 -0.783633 134 -0.268 -0.513 101 -0.247
Guyana 140 -0.802755 163 -0.275 -1.218 158 -0.274
Suriname 141 -0.805247 155 -0.275 -1.051 155 -0.274
Benin 142 -0.809086 131 -0.267 -0.470 122 -0.258
Togo 143 -0.811211 150 -0.273 -0.849 130 -0.262
Timor_Leste 144 -0.861502 147 -0.273 -0.820 150 -0.271
Afghanistan 145 -0.870093 102 -0.256 -0.148 75 -0.204
Zimbabwe 146 -0.931953 151 -0.273 -0.875 86 -0.226
Mauritania 147 -0.938548 146 -0.271 -0.720 133 -0.263
Belize 148 -0.970276 172 -0.276 -1.415 166 -0.276
Maldives 149 -0.993595 165 -0.276 -1.245 163 -0.275
Swaziland 150 -1.01082 149 -0.273 -0.841 156 -0.274
Equatorial_Guinea 151 -1.12854 128 -0.266 -0.425 151 -0.271
Lesotho 152 -1.15529 157 -0.275 -1.058 152 -0.272
Cape_Verde 153 -1.16751 170 -0.276 -1.401 165 -0.276
St._Lucia 154 -1.18084 166 -0.276 -1.297 173 -0.277
Bhutan 155 -1.18581 156 -0.275 -1.054 159 -0.275
Mozambique 156 -1.19257 113 -0.261 -0.267 85 -0.224
Burkina_Faso 157 -1.19364 117 -0.263 -0.331 98 -0.244
Guinea 158 -1.2112 142 -0.270 -0.601 113 -0.253
Mali 159 -1.21205 135 -0.268 -0.529 108 -0.250
Samoa 160 -1.22483 180 -0.277 -1.791 172 -0.277
Burundi 161 -1.24832 152 -0.274 -0.912 105 -0.248
Chad 162 -1.27759 129 -0.266 -0.435 104 -0.248
Liberia 163 -1.29347 168 -0.276 -1.347 138 -0.265
Gambia 164 -1.29613 162 -0.275 -1.155 157 -0.274
Vanuatu 165 -1.3275 177 -0.277 -1.668 170 -0.277
Solomon_Islands 166 -1.32765 175 -0.277 -1.580 168 -0.276
Andorra 167 -1.32861 164 -0.275 -1.224 179 -0.277
Grenada 168 -1.34222 178 -0.277 -1.669 176 -0.277
Sierra_Leone 169 -1.35201 153 -0.274 -0.919 119 -0.257
Seychelles 170 -1.35643 169 -0.276 -1.353 174 -0.277
Eritrea 171 -1.38937 160 -0.275 -1.133 57 -0.160
St._Vincent_Grenadines 172 -1.41803 176 -0.277 -1.648 177 -0.277
Niger 173 -1.42233 137 -0.269 -0.552 109 -0.251
Antigua_Barbuda 174 -1.46119 174 -0.277 -1.564 175 -0.277
Central_ African_Rep 175 -1.46177 159 -0.275 -1.132 139 -0.266
Tonga 176 -1.5005 182 -0.277 -2.028 178 -0.277
Djibouti 177 -1.50506 167 -0.276 -1.346 146 -0.269
Dominica 178 -1.6211 179 -0.277 -1.765 181 -0.277
Comoros 179 -1.63239 181 -0.277 -1.812 164 -0.276
Guinea_Bissau 180 -1.67108 171 -0.276 -1.414 149 -0.270
Micronesia 181 -1.68399 185 -0.277 -2.130 186 -999
Congo_DR 182 -1.74016 173 -0.276 -1.514 40 -0.061
Kiribati 183 -1.74132 186 -0.277 -2.179 180 -0.277
Liechtenstein 184 -1.74166 161 -0.275 -1.153 182 -0.277
Sao_Tome_Principe 185 -1.77158 184 -0.277 -2.125 169 -0.277
St._Kitts_Nevis 186 -1.79174 183 -0.277 -2.037 183 -0.277
Palau 187 -2.33199 187 -0.277 -2.297 184 -0.277

For a fuller exposition of the winning probability model, its associated mathematical properties, and the reasons why existing indices of national power fail the test of external validity, see Jae-On Kim, Sanghag Kim, and Jin Wang, “Index of National Power: How to Assess the Basic National Capacity of a Nation,” Korean Journal of Sociology, 2013, Vol. 47(6):83-140.