Decomposition

NPI_Decomposition_3_dims_1

The index of national power (NPI) has two components — one component is based on population size and another is based on the human development quotient. (The resulting index and subcomponent values for each nation is available in a tabular form. )

where RPI is raw population index and HDQ is normed human development index. RPI has the following form:

Note the log-transformation, where N is the population size in 2012 and Nmin is taken to be 3000, which represents the minimal population assumed essential for sustainable reproduction.
The HDQ sub-index is based on the 2012 human development index (HDI), and normed against the highest value in 2012, which happens to be the value of Norway:

Since we are not as familiar with the geometric mean and the multiplicative form as with the additive mean (average), it is informative to see the mathematical results in a graphic form.

This interactive graph shows the relationship among three variables in a two dimensional space. The top slanting line with a 45 degree angle and round hollow dots represents the maximum possible (hypothetical) power of a nation, to be reached if a nation obtained the highest possible human development (hdi = 1). So on this diagram, there is only one red-dot on that line–that of Norway. Each red dot represents the relative power position of each nation. By moving the mouse over a dot, you can identify a nation and the relevant statistics for that nation.

The height (y-value) of each dot is the relative power of a nation, given by the multiplication of two terms (squareroots of RPI and HDQ), i.e., the geometric means of RPI and HDQ. Meanwhile, the x-values represent the square roots of RPI. The highest red-dot represents the United States. The position of these red-dots are given by the intersection of the vertical lines from a given x-value and the slanting lines representing the square root of the HDQ. In this graph, we have just added six slanting lines, representing the relative degree of human development: squareroots of {1, .9, .8, .7, .5, .3}.

(If you have the CDF Player from Mathematica (free program) installed, you will see an interactive graph, in which you can view tooltips for each point on the graph by moving your mouse pointer over a dot. Tooltips contain the following information for each country:

  • Name of the country (associated with the dot);
  • Power index value and ranking;
  • Population index value and ranking;
  • Human development quotient and ranking;
  • Magnitude of growth potential and ranking.

If you do not see the interactive graph, you have to install the free CDF Player from Wolfram Research.)

The following table contains component information:

Nation2 NPIRnk NPIz RPIRnk RPIs HDIRnk HDIs NPIm RPIsqrt HDQsqrt
Afghanistan 145 -0.870 42 0.707 175 0.392 0.526 0.841 0.626
Albania 86 0.141 132 0.535 70 0.784 0.648 0.731 0.886
Algeria 43 0.883 34 0.727 93 0.747 0.737 0.852 0.864
Andorra 167 -1.329 183 0.251 33 0.886 0.471 0.501 0.941
Angola 113 -0.245 55 0.679 148 0.532 0.601 0.824 0.729
Antigua_Barbuda 174 -1.461 181 0.260 67 0.796 0.455 0.510 0.892
Argentina 17 1.314 32 0.732 45 0.849 0.788 0.855 0.922
Armenia 95 0.045 134 0.530 87 0.763 0.636 0.728 0.874
Australia 12 1.586 50 0.686 2 0.982 0.821 0.828 0.991
Austria 28 1.047 90 0.610 18 0.937 0.756 0.781 0.968
Azerbaijan 62 0.486 88 0.618 82 0.769 0.689 0.786 0.877
Bahamas 132 -0.632 167 0.370 49 0.831 0.555 0.609 0.912
Bahrain 103 -0.054 149 0.467 48 0.834 0.624 0.684 0.913
Bangladesh 72 0.332 8 0.834 146 0.539 0.670 0.913 0.734
Barbados 135 -0.677 171 0.349 38 0.864 0.549 0.591 0.929
Belarus 53 0.719 87 0.619 50 0.830 0.717 0.787 0.911
Belgium 20 1.163 76 0.631 17 0.939 0.770 0.795 0.969
Belize 148 -0.970 169 0.360 96 0.735 0.514 0.600 0.857
Benin 142 -0.809 83 0.624 166 0.457 0.534 0.790 0.676
Bhutan 155 -1.186 157 0.423 140 0.563 0.488 0.651 0.751
Bolivia 76 0.292 80 0.627 108 0.707 0.666 0.792 0.841
Bosnia_Herzegovina 85 0.164 125 0.549 81 0.770 0.650 0.741 0.877
Botswana 125 -0.456 143 0.500 119 0.664 0.576 0.707 0.815
Brazil 14 1.473 5 0.853 85 0.764 0.807 0.923 0.874
Brunei_Darussalam 122 -0.406 166 0.378 30 0.895 0.582 0.615 0.946
Bulgaria 59 0.581 95 0.599 57 0.819 0.700 0.774 0.905
Burkina_Faso 157 -1.194 62 0.661 183 0.359 0.487 0.813 0.599
Burundi 161 -1.248 85 0.622 178 0.372 0.481 0.789 0.610
Cambodia 108 -0.175 66 0.654 138 0.569 0.610 0.808 0.754
Cameroon 115 -0.298 53 0.683 150 0.518 0.595 0.826 0.720
Canada 10 1.647 37 0.719 11 0.954 0.828 0.848 0.977
Cape_Verde 153 -1.168 164 0.392 132 0.614 0.491 0.626 0.783
Central_ African_Rep 175 -1.462 117 0.562 180 0.369 0.455 0.750 0.607
Chad 162 -1.278 71 0.640 184 0.356 0.477 0.800 0.597
Chile 29 1.043 58 0.666 40 0.858 0.756 0.816 0.926
China 4 1.874 1 1.000 101 0.732 0.856 1.000 0.856
Colombia 36 0.978 28 0.743 91 0.753 0.748 0.862 0.868
Comoros 179 -1.632 159 0.421 169 0.449 0.435 0.649 0.670
Congo 83 0.205 20 0.768 142 0.559 0.655 0.876 0.748
Congo_DR 182 -1.740 121 0.559 186 0.318 0.422 0.748 0.564
Costa_Rica 69 0.389 115 0.567 62 0.809 0.677 0.753 0.900
Cote_dIvoire 133 -0.648 57 0.676 168 0.452 0.553 0.822 0.673
Croatia 64 0.459 122 0.558 47 0.843 0.686 0.747 0.918
Cuba 52 0.734 75 0.632 59 0.817 0.719 0.795 0.904
Cyprus 94 0.045 153 0.456 31 0.888 0.636 0.675 0.942
Czech 26 1.054 79 0.627 28 0.914 0.757 0.792 0.956
Denmark 41 0.901 108 0.578 15 0.943 0.739 0.761 0.971
Djibouti 177 -1.505 155 0.435 164 0.466 0.450 0.659 0.683
Dominica 178 -1.621 184 0.244 72 0.780 0.436 0.494 0.883
Dominican_Rep 68 0.394 81 0.625 96 0.735 0.678 0.791 0.857
Ecuador 57 0.625 64 0.657 89 0.758 0.706 0.810 0.871
Egypt 42 0.886 16 0.784 112 0.693 0.737 0.885 0.833
El_Salvador 88 0.135 103 0.588 107 0.712 0.647 0.767 0.844
Equatorial_Guinea 151 -1.129 158 0.423 136 0.580 0.495 0.650 0.762
Eritrea 171 -1.389 105 0.586 181 0.368 0.464 0.765 0.606
Estonia 89 0.114 147 0.469 33 0.886 0.644 0.685 0.941
Ethiopia 127 -0.475 13 0.793 173 0.415 0.574 0.891 0.644
Fiji 129 -0.538 154 0.436 96 0.735 0.566 0.660 0.857
Finland 48 0.857 110 0.576 21 0.934 0.733 0.759 0.966
France 5 1.806 21 0.768 20 0.935 0.847 0.876 0.967
Gabon 117 -0.353 146 0.484 106 0.715 0.588 0.696 0.846
Gambia 164 -1.296 144 0.491 165 0.460 0.475 0.701 0.678
Georgia 79 0.263 118 0.562 72 0.780 0.662 0.750 0.883
Germany 3 1.990 15 0.785 5 0.963 0.869 0.886 0.982
Ghana 93 0.054 47 0.695 135 0.584 0.637 0.833 0.764
Greece 32 1.034 74 0.632 29 0.901 0.755 0.795 0.949
Grenada 168 -1.342 177 0.273 63 0.806 0.470 0.523 0.898
Guatemala 99 0.004 65 0.655 133 0.608 0.631 0.809 0.780
Guinea 158 -1.211 73 0.634 178 0.372 0.485 0.796 0.610
Guinea_Bissau 180 -1.671 145 0.485 176 0.381 0.430 0.697 0.617
Guyana 140 -0.803 156 0.429 118 0.666 0.534 0.655 0.816
Haiti 136 -0.705 82 0.624 161 0.477 0.546 0.790 0.691
Honduras 96 0.019 93 0.605 120 0.662 0.633 0.778 0.813
Hong_Kong 34 1.018 98 0.597 13 0.949 0.753 0.773 0.974
Hungary 44 0.879 84 0.623 37 0.870 0.736 0.789 0.933
Iceland 119 -0.394 170 0.359 13 0.949 0.583 0.599 0.974
India 23 1.070 2 0.993 136 0.580 0.759 0.997 0.762
Indonesia 27 1.051 4 0.869 121 0.659 0.757 0.932 0.812
Iran 18 1.230 17 0.779 76 0.777 0.778 0.883 0.881
Iraq 78 0.279 38 0.714 131 0.618 0.664 0.845 0.786
Ireland 45 0.870 116 0.563 7 0.959 0.735 0.751 0.979
Israel 30 1.038 94 0.605 16 0.942 0.755 0.778 0.971
Italy 7 1.731 23 0.762 25 0.923 0.838 0.873 0.960
Jamaica 98 0.013 136 0.523 85 0.764 0.632 0.723 0.874
Japan 2 2.113 10 0.819 10 0.955 0.884 0.905 0.977
Jordan 82 0.215 102 0.588 100 0.733 0.656 0.767 0.856
Kazakhstan 51 0.774 60 0.663 69 0.790 0.723 0.814 0.889
Kenya 97 0.013 31 0.736 145 0.543 0.632 0.858 0.737
Kiribati 183 -1.741 180 0.270 121 0.659 0.422 0.520 0.812
Korea_Rep 6 1.771 26 0.747 12 0.952 0.843 0.864 0.976
Kuwait 75 0.298 131 0.537 54 0.827 0.666 0.733 0.910
Kyrgyzstan 105 -0.141 109 0.578 125 0.651 0.614 0.760 0.807
Lao_PDR 123 -0.421 100 0.592 138 0.569 0.580 0.769 0.754
Latvia 84 0.188 142 0.500 44 0.852 0.653 0.707 0.923
Lebanon 81 0.255 120 0.561 72 0.780 0.661 0.749 0.883
Lesotho 152 -1.155 140 0.501 158 0.483 0.492 0.708 0.695
Liberia 163 -1.293 123 0.556 174 0.406 0.475 0.746 0.637
Libya 63 0.468 104 0.586 64 0.805 0.687 0.765 0.897
Liechtenstein 184 -1.742 186 0.192 24 0.925 0.422 0.438 0.962
Lithuania 71 0.361 133 0.530 41 0.857 0.674 0.728 0.925
Luxembourg 112 -0.225 163 0.398 26 0.916 0.604 0.631 0.957
Macedonia_FYR 102 -0.050 138 0.503 78 0.775 0.625 0.710 0.880
Madagascar 116 -0.351 52 0.685 151 0.506 0.588 0.827 0.711
Malawi 138 -0.780 63 0.659 170 0.438 0.537 0.812 0.662
Malaysia 33 1.026 44 0.706 64 0.805 0.754 0.840 0.897
Maldives 149 -0.994 168 0.363 104 0.720 0.511 0.603 0.849
Mali 159 -1.212 67 0.654 182 0.360 0.485 0.808 0.600
Malta 124 -0.422 165 0.379 32 0.887 0.580 0.616 0.942
Mauritania 147 -0.939 127 0.549 155 0.489 0.518 0.741 0.699
Mauritius 114 -0.258 150 0.466 80 0.772 0.600 0.683 0.878
Mexico 13 1.520 11 0.815 61 0.812 0.813 0.903 0.901
Micronesia 181 -1.684 179 0.272 117 0.675 0.429 0.521 0.822
Moldova 106 -0.147 128 0.544 113 0.691 0.613 0.737 0.831
Mongolia 109 -0.178 135 0.525 108 0.707 0.609 0.725 0.841
Montenegro 121 -0.401 160 0.410 52 0.828 0.583 0.640 0.910
Morocco 77 0.283 39 0.714 130 0.619 0.665 0.845 0.787
Mozambique 156 -1.193 48 0.694 185 0.342 0.488 0.833 0.585
Myanmar 101 -0.040 24 0.751 149 0.521 0.626 0.867 0.722
Namibia 128 -0.512 137 0.509 128 0.637 0.569 0.713 0.798
Nepal 120 -0.398 46 0.701 157 0.485 0.583 0.837 0.696
Netherlands 15 1.408 61 0.663 4 0.964 0.800 0.814 0.982
New_Zealand 46 0.866 119 0.561 6 0.962 0.735 0.749 0.981
Nicaragua 111 -0.213 106 0.584 129 0.627 0.605 0.764 0.792
Niger 173 -1.422 59 0.665 186 0.318 0.460 0.815 0.564
Nigeria 91 0.109 7 0.840 153 0.493 0.644 0.917 0.702
Norway 31 1.037 114 0.570 1 1.000 0.755 0.755 1.000
Oman 92 0.094 130 0.538 84 0.765 0.642 0.734 0.875
Pakistan 70 0.370 6 0.845 146 0.539 0.675 0.919 0.734
Palau 187 -2.332 187 0.149 52 0.828 0.351 0.385 0.910
Panama 73 0.324 126 0.549 59 0.817 0.670 0.741 0.904
Papua_New_Guinea 137 -0.755 97 0.598 156 0.488 0.540 0.773 0.699
Paraguay 90 0.112 99 0.592 111 0.701 0.644 0.770 0.837
Peru 39 0.919 40 0.708 77 0.776 0.741 0.841 0.881
Philippines 40 0.903 12 0.797 114 0.685 0.739 0.893 0.828
Poland 16 1.332 33 0.727 39 0.860 0.790 0.853 0.927
Portugal 49 0.845 78 0.627 43 0.854 0.732 0.792 0.924
Qatar 80 0.259 141 0.501 36 0.873 0.662 0.708 0.935
Romania 35 0.985 54 0.681 56 0.823 0.749 0.825 0.907
Russia 11 1.632 9 0.828 55 0.825 0.826 0.910 0.908
Rwanda 139 -0.784 72 0.634 167 0.454 0.537 0.796 0.674
Samoa 160 -1.225 173 0.318 96 0.735 0.484 0.564 0.857
Sao_Tome_Principe 185 -1.772 174 0.318 144 0.550 0.418 0.564 0.741
Saudi_Arabia 24 1.068 45 0.703 57 0.819 0.759 0.838 0.905
Senegal 130 -0.551 69 0.647 154 0.492 0.564 0.805 0.702
Serbia 61 0.528 96 0.598 64 0.805 0.694 0.773 0.897
Seychelles 170 -1.356 182 0.259 46 0.844 0.468 0.509 0.919
Sierra_Leone 169 -1.352 107 0.584 177 0.376 0.468 0.764 0.613
Singapore 47 0.860 112 0.575 18 0.937 0.734 0.758 0.968
Slovakia 56 0.676 111 0.576 35 0.880 0.712 0.759 0.938
Slovenia 66 0.449 139 0.502 21 0.934 0.685 0.708 0.966
Solomon_Islands 166 -1.328 161 0.400 143 0.555 0.471 0.633 0.745
South_Africa 58 0.596 25 0.749 121 0.659 0.702 0.865 0.812
Spain 9 1.649 29 0.741 23 0.927 0.829 0.861 0.963
Sri_Lanka 55 0.680 56 0.678 92 0.749 0.712 0.823 0.865
St._Kitts_Nevis 186 -1.792 185 0.221 72 0.780 0.416 0.471 0.883
St._Lucia 154 -1.181 175 0.315 88 0.759 0.489 0.561 0.871
St._Vincent_Grenadines 172 -1.418 176 0.276 83 0.768 0.460 0.526 0.876
Sudan 131 -0.587 35 0.724 171 0.434 0.560 0.851 0.658
Suriname 141 -0.805 162 0.398 105 0.716 0.534 0.631 0.846
Swaziland 150 -1.011 151 0.462 141 0.561 0.509 0.680 0.749
Sweden 19 1.168 86 0.619 7 0.959 0.771 0.787 0.979
Switzerland 22 1.088 92 0.606 9 0.956 0.761 0.778 0.978
Syria 67 0.426 51 0.685 116 0.679 0.682 0.828 0.824
Tajikistan 100 -0.019 91 0.606 125 0.651 0.628 0.779 0.807
Tanzania 110 -0.183 27 0.743 152 0.498 0.609 0.862 0.706
Thailand 37 0.956 19 0.769 103 0.723 0.745 0.877 0.850
Timor_Leste 144 -0.862 152 0.461 134 0.603 0.527 0.679 0.777
Togo 143 -0.811 101 0.592 159 0.481 0.533 0.769 0.693
Tonga 176 -1.501 178 0.273 95 0.743 0.451 0.523 0.862
Trinidad_Tobago 107 -0.166 148 0.469 67 0.796 0.611 0.685 0.892
Tunisia 65 0.451 77 0.629 94 0.746 0.685 0.793 0.863
Turkey 21 1.131 18 0.777 90 0.756 0.766 0.881 0.869
Turkmenistan 87 0.135 113 0.573 102 0.731 0.647 0.757 0.855
Uganda 118 -0.361 36 0.722 161 0.477 0.587 0.850 0.691
Ukraine 25 1.054 30 0.740 78 0.775 0.757 0.860 0.880
United_Arab_Emirates 50 0.802 89 0.617 41 0.857 0.727 0.785 0.925
United_Kingdom 8 1.721 22 0.765 26 0.916 0.837 0.875 0.957
United_States 1 2.523 3 0.888 3 0.981 0.933 0.942 0.991
Uruguay 74 0.322 129 0.540 51 0.829 0.669 0.735 0.911
Uzbekistan 60 0.543 43 0.707 114 0.685 0.696 0.841 0.828
Vanuatu 165 -1.328 172 0.339 124 0.655 0.471 0.582 0.810
Venezuela 38 0.948 41 0.707 71 0.783 0.744 0.841 0.885
Vietnam 54 0.702 14 0.791 127 0.646 0.715 0.889 0.804
WestBankGaza 104 -0.062 124 0.554 110 0.702 0.623 0.744 0.838
Yemen 126 -0.462 49 0.690 160 0.480 0.575 0.831 0.693
Zambia 134 -0.656 68 0.649 163 0.469 0.552 0.806 0.685
Zimbabwe 146 -0.932 70 0.647 172 0.416 0.519 0.805 0.645

Legends:

  • NPIRANK: Ranking of National Power in 2012 (by NPI2012 index)
  • NPIZ: NPI transformed into standardized scores (z-scores)
  • NPIS: NPI normed against the strongest nation =1
  • RPIRNK: Rank of population (2012)=rank of RPI
  • RPIS: Population size, transformed (log) and normed
  • HDIRNK: Ranking of Human Development in 2012 = Ranking of HDQ
  • HDIS: HDI normed, is the same as HDQ
  • NPIM: NPISQRT*RPISQRT
  • RPISQRT: Square-root of RPIS, the same as the maximum possible NPI
  • HDQSQRT: Square-root of HDQ

For a full discussion of the decomposition of the index and other justifications of the new index, 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.

To appreciate how the geometric mean and the corresponding multiplicative formula work, please consider two extreme cases–Norway with HDQ =1, and China with RPI=1. The power-hierarchy (the height) of Norway is determined by the value of its square root of RPI, and that of China by its square root of HDQ.