Penrose method
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The Penrose method is a method, devised in 1946 by Professor Lionel Penrose, for allocating seats or votes in legislatures based on the square root of the population of the representative's district or state. It has been proposed as a method for apportioning representation in a United Nations Parliamentary Assembly.
In the "square root of the millions" version of the Penrose method, the United States would get 16 representatives; India would get 26; and China would get 32[1]. According to INFUSA, "The square-root method is more than a pragmatic compromise between the extreme methods of world representation unrelated to population size and allocation of national quotas in direct proportion to population size; Penrose showed that in terms of statistical theory the square-root method gives to each voter in the world an equal influence on decision-making in a world assembly"[2].
Under the Penrose method, the 14 most populous nations get fewer seats than they would under one man, one vote; the other nations get more seats.
Rank | Country | Population | Percent of world population |
Seats | Percent of total seats |
--- | World | 6,434,577,575 | 100.00% | 721.32 | 100.00% |
1 | People's Republic of China | 1,306,313,812 | 20.30% | 36.14 | 5.01% |
2 | India | 1,080,264,388 | 16.79% | 32.87 | 4.56% |
3 | United States | 297,200,000 | 4.62% | 17.24 | 2.39% |
4 | Indonesia | 241,973,879 | 3.76% | 15.56 | 2.16% |
5 | Brazil | 186,112,794 | 2.89% | 13.64 | 1.89% |
6 | Pakistan | 162,419,946 | 2.52% | 12.74 | 1.77% |
7 | Bangladesh | 144,319,628 | 2.24% | 12.01 | 1.67% |
8 | Russia | 143,420,309 | 2.23% | 11.98 | 1.66% |
9 | Nigeria | 128,771,988 | 2.00% | 11.35 | 1.57% |
10 | Japan | 127,417,244 | 1.98% | 11.29 | 1.56% |
11 | Mexico | 106,202,903 | 1.65% | 10.31 | 1.43% |
12 | Philippines | 87,857,473 | 1.37% | 9.37 | 1.30% |
13 | Vietnam | 83,535,576 | 1.30% | 9.14 | 1.27% |
14 | Germany | 82,468,000 | 1.28% | 9.08 | 1.26% |
15 | Egypt | 77,505,756 | 1.20% | 8.80 | 1.22% |
16 | Ethiopia | 73,053,286 | 1.14% | 8.55 | 1.18% |
17 | Turkey | 69,660,559 | 1.08% | 8.35 | 1.16% |
18 | Iran | 68,017,860 | 1.06% | 8.25 | 1.14% |
19 | Thailand | 65,444,371 | 1.02% | 8.09 | 1.12% |
20 | France | 60,656,178 | 0.94% | 7.79 | 1.08% |
21 | United Kingdom | 60,441,457 | 0.94% | 7.77 | 1.08% |
22 | Democratic Republic of the Congo | 60,085,804 | 0.93% | 7.75 | 1.07% |
23 | Italy | 58,103,033 | 0.90% | 7.62 | 1.06% |
24 | South Korea | 48,422,644 | 0.75% | 6.96 | 0.96% |
25 | Ukraine | 47,425,336 | 0.74% | 6.89 | 0.95% |
26 | South Africa | 44,344,136 | 0.69% | 6.66 | 0.92% |
27 | Spain | 43,209,511 | 0.67% | 6.57 | 0.91% |
28 | Colombia | 42,954,279 | 0.67% | 6.55 | 0.91% |
29 | Myanmar | 42,909,464 | 0.67% | 6.55 | 0.91% |
30 | Sudan | 40,187,486 | 0.62% | 6.34 | 0.88% |
31 | Argentina | 39,537,943 | 0.61% | 6.29 | 0.87% |
32 | Poland | 38,635,144 | 0.60% | 6.22 | 0.86% |
33 | Tanzania | 36,766,356 | 0.57% | 6.06 | 0.84% |
34 | Kenya | 33,829,590 | 0.53% | 5.82 | 0.81% |
35 | Canada | 32,400,000 | 0.50% | 5.69 | 0.79% |
36 | Morocco | 32,725,847 | 0.51% | 5.72 | 0.79% |
37 | Algeria | 32,531,853 | 0.51% | 5.70 | 0.79% |
38 | Afghanistan | 29,928,987 | 0.47% | 5.47 | 0.76% |
39 | Peru | 27,925,628 | 0.43% | 5.28 | 0.73% |
40 | Nepal | 27,676,547 | 0.43% | 5.26 | 0.73% |
41 | Uganda | 27,269,482 | 0.42% | 5.22 | 0.72% |
42 | Uzbekistan | 26,851,195 | 0.42% | 5.18 | 0.72% |
43 | Saudi Arabia | 26,417,599 | 0.41% | 5.14 | 0.71% |
44 | Malaysia | 26,207,102 | 0.41% | 5.12 | 0.71% |
45 | Iraq | 26,074,906 | 0.41% | 5.11 | 0.71% |
46 | Venezuela | 25,375,281 | 0.39% | 5.04 | 0.70% |
47 | North Korea | 22,912,177 | 0.36% | 4.79 | 0.66% |
48 | Republic of China | 22,894,384 | 0.36% | 4.78 | 0.66% |
49 | Romania | 22,329,977 | 0.35% | 4.73 | 0.66% |
50 | Ghana | 21,029,853 | 0.33% | 4.59 | 0.64% |
51 | Yemen | 20,727,063 | 0.32% | 4.55 | 0.63% |
52 | Australia | 20,229,800 | 0.31% | 4.50 | 0.62% |
53 | Sri Lanka | 20,064,776 | 0.31% | 4.48 | 0.62% |
54 | Mozambique | 19,406,703 | 0.30% | 4.41 | 0.61% |
55 | Syria | 18,448,752 | 0.29% | 4.30 | 0.60% |
56 | Madagascar | 18,040,341 | 0.28% | 4.25 | 0.59% |
57 | Côte d'Ivoire | 17,298,040 | 0.27% | 4.16 | 0.58% |
58 | Netherlands | 16,407,491 | 0.25% | 4.05 | 0.56% |
59 | Cameroon | 16,380,005 | 0.25% | 4.05 | 0.56% |
60 | Chile | 16,267,278 | 0.25% | 4.03 | 0.56% |
61 | Kazakhstan | 15,185,844 | 0.24% | 3.90 | 0.54% |
62 | Guatemala | 14,655,189 | 0.23% | 3.83 | 0.53% |
63 | Burkina Faso | 13,925,313 | 0.22% | 3.73 | 0.52% |
64 | Cambodia | 13,607,069 | 0.21% | 3.69 | 0.51% |
65 | Ecuador | 13,363,593 | 0.21% | 3.66 | 0.51% |
66 | Zimbabwe | 12,746,990 | 0.20% | 3.57 | 0.49% |
67 | Mali | 12,291,529 | 0.19% | 3.51 | 0.49% |
68 | Malawi | 12,158,924 | 0.19% | 3.49 | 0.48% |
69 | Niger | 11,665,937 | 0.18% | 3.42 | 0.47% |
70 | Cuba | 11,346,670 | 0.18% | 3.37 | 0.47% |
71 | Zambia | 11,261,795 | 0.18% | 3.36 | 0.47% |
72 | Angola | 11,190,786 | 0.17% | 3.35 | 0.46% |
73 | Senegal | 11,126,832 | 0.17% | 3.34 | 0.46% |
74 | Serbia and Montenegro | 10,829,175 | 0.17% | 3.29 | 0.46% |
75 | Greece | 10,668,354 | 0.17% | 3.27 | 0.45% |
76 | Portugal | 10,566,212 | 0.16% | 3.25 | 0.45% |
77 | Belgium | 10,364,388 | 0.16% | 3.22 | 0.45% |
78 | Belarus | 10,300,483 | 0.16% | 3.21 | 0.44% |
79 | Czech Republic | 10,241,138 | 0.16% | 3.20 | 0.44% |
80 | Hungary | 10,081,000 | 0.16% | 3.18 | 0.44% |
81 | Tunisia | 10,074,951 | 0.16% | 3.17 | 0.44% |
82 | Chad | 9,826,419 | 0.15% | 3.13 | 0.43% |
83 | Guinea | 9,467,866 | 0.15% | 3.08 | 0.43% |
84 | Sweden | 9,001,774 | 0.14% | 3.00 | 0.42% |
85 | Dominican Republic | 8,950,034 | 0.14% | 2.99 | 0.41% |
86 | Bolivia | 8,857,870 | 0.14% | 2.98 | 0.41% |
87 | Somalia | 8,591,629 | 0.13% | 2.93 | 0.41% |
88 | Rwanda | 8,440,820 | 0.13% | 2.91 | 0.40% |
89 | Austria | 8,184,691 | 0.13% | 2.86 | 0.40% |
90 | Haiti | 8,121,622 | 0.13% | 2.85 | 0.40% |
91 | Azerbaijan | 7,911,974 | 0.12% | 2.81 | 0.39% |
92 | Switzerland | 7,489,370 | 0.12% | 2.74 | 0.38% |
93 | Benin | 7,460,025 | 0.12% | 2.73 | 0.38% |
94 | Bulgaria | 7,450,349 | 0.12% | 2.73 | 0.38% |
95 | Tajikistan | 7,163,506 | 0.11% | 2.68 | 0.37% |
96 | Honduras | 6,975,204 | 0.11% | 2.64 | 0.37% |
97 | Israel | 6,955,000 | 0.11% | 2.64 | 0.37% |
98 | El Salvador | 6,704,932 | 0.10% | 2.59 | 0.36% |
99 | Burundi | 6,370,609 | 0.10% | 2.52 | 0.35% |
100 | Paraguay | 6,347,884 | 0.10% | 2.52 | 0.35% |
101 | Laos | 6,217,141 | 0.10% | 2.49 | 0.35% |
102 | Sierra Leone | 6,017,643 | 0.09% | 2.45 | 0.34% |
103 | Libya | 5,765,563 | 0.09% | 2.40 | 0.33% |
104 | Jordan | 5,759,732 | 0.09% | 2.40 | 0.33% |
105 | Togo | 5,681,519 | 0.09% | 2.38 | 0.33% |
106 | Papua New Guinea | 5,545,268 | 0.09% | 2.35 | 0.33% |
107 | Nicaragua | 5,465,100 | 0.08% | 2.34 | 0.32% |
108 | Denmark | 5,432,335 | 0.08% | 2.33 | 0.32% |
109 | Slovakia | 5,431,363 | 0.08% | 2.33 | 0.32% |
110 | Finland | 5,223,442 | 0.08% | 2.29 | 0.32% |
111 | Kyrgyzstan | 5,146,281 | 0.08% | 2.27 | 0.31% |
112 | Turkmenistan | 4,952,081 | 0.08% | 2.23 | 0.31% |
113 | Georgia | 4,677,401 | 0.07% | 2.16 | 0.30% |
114 | Norway | 4,593,041 | 0.07% | 2.14 | 0.30% |
115 | Eritrea | 4,561,599 | 0.07% | 2.14 | 0.30% |
116 | Croatia | 4,495,904 | 0.07% | 2.12 | 0.29% |
117 | Moldova | 4,455,421 | 0.07% | 2.11 | 0.29% |
118 | Singapore | 4,425,720 | 0.07% | 2.10 | 0.29% |
119 | Republic of Ireland | 4,130,700 | 0.06% | 2.03 | 0.28% |
120 | New Zealand | 4,098,200 | 0.06% | 2.02 | 0.28% |
121 | Bosnia and Herzegovina | 4,025,476 | 0.06% | 2.01 | 0.28% |
122 | Costa Rica | 4,016,173 | 0.06% | 2.00 | 0.28% |
123 | Lebanon | 3,826,018 | 0.06% | 1.96 | 0.27% |
124 | Central African Republic | 3,799,897 | 0.06% | 1.95 | 0.27% |
125 | Lithuania | 3,596,617 | 0.06% | 1.90 | 0.26% |
126 | Albania | 3,563,112 | 0.06% | 1.89 | 0.26% |
127 | Liberia | 3,482,211 | 0.05% | 1.87 | 0.26% |
128 | Uruguay | 3,415,920 | 0.05% | 1.85 | 0.26% |
129 | Mauritania | 3,086,859 | 0.05% | 1.76 | 0.24% |
130 | Panama | 3,039,150 | 0.05% | 1.74 | 0.24% |
131 | Republic of the Congo | 3,039,126 | 0.05% | 1.74 | 0.24% |
132 | Oman | 3,001,583 | 0.05% | 1.73 | 0.24% |
133 | Armenia | 2,982,904 | 0.05% | 1.73 | 0.24% |
134 | Mongolia | 2,791,272 | 0.04% | 1.67 | 0.23% |
135 | Jamaica | 2,731,832 | 0.04% | 1.65 | 0.23% |
136 | United Arab Emirates | 2,563,212 | 0.04% | 1.60 | 0.22% |
137 | Kuwait | 2,335,648 | 0.04% | 1.53 | 0.21% |
138 | Latvia | 2,290,237 | 0.04% | 1.51 | 0.21% |
139 | Bhutan | 2,232,291 | 0.03% | 1.49 | 0.21% |
140 | Macedonia | 2,045,262 | 0.03% | 1.43 | 0.20% |
141 | Namibia | 2,030,692 | 0.03% | 1.43 | 0.20% |
142 | Slovenia | 2,011,070 | 0.03% | 1.42 | 0.20% |
143 | Lesotho | 1,867,035 | 0.03% | 1.37 | 0.19% |
144 | Botswana | 1,640,115 | 0.03% | 1.28 | 0.18% |
145 | The Gambia | 1,593,256 | 0.02% | 1.26 | 0.17% |
146 | Guinea-Bissau | 1,416,027 | 0.02% | 1.19 | 0.16% |
147 | Gabon | 1,389,201 | 0.02% | 1.18 | 0.16% |
148 | Estonia | 1,332,893 | 0.02% | 1.15 | 0.16% |
149 | Mauritius | 1,230,602 | 0.02% | 1.11 | 0.15% |
150 | Swaziland | 1,173,900 | 0.02% | 1.08 | 0.15% |
151 | Trinidad and Tobago | 1,088,644 | 0.02% | 1.04 | 0.14% |
152 | East Timor | 1,040,880 | 0.02% | 1.02 | 0.14% |
153 | Fiji | 893,354 | 0.01% | 0.95 | 0.13% |
154 | Qatar | 863,051 | 0.01% | 0.93 | 0.13% |
155 | Cyprus | 780,133 | 0.01% | 0.88 | 0.12% |
156 | Guyana | 765,283 | 0.01% | 0.87 | 0.12% |
157 | Bahrain | 688,345 | 0.01% | 0.83 | 0.12% |
158 | Comoros | 671,247 | 0.01% | 0.82 | 0.11% |
159 | Solomon Islands | 538,032 | 0.01% | 0.73 | 0.10% |
160 | Equatorial Guinea | 535,881 | 0.01% | 0.73 | 0.10% |
161 | Djibouti | 476,703 | 0.01% | 0.69 | 0.10% |
162 | Luxembourg | 468,571 | 0.01% | 0.68 | 0.09% |
163 | Suriname | 438,144 | 0.01% | 0.66 | 0.09% |
164 | Cape Verde | 418,224 | 0.01% | 0.65 | 0.09% |
165 | Malta | 398,534 | 0.01% | 0.63 | 0.09% |
166 | Brunei | 372,361 | 0.01% | 0.61 | 0.08% |
167 | Maldives | 349,106 | 0.01% | 0.59 | 0.08% |
168 | The Bahamas | 301,790 | 0.005% | 0.55 | 0.08% |
169 | Iceland | 296,737 | 0.005% | 0.54 | 0.08% |
170 | Belize | 279,457 | 0.004% | 0.53 | 0.07% |
171 | Barbados | 279,254 | 0.004% | 0.53 | 0.07% |
172 | Vanuatu | 205,754 | 0.003% | 0.45 | 0.06% |
173 | São Tomé and Príncipe | 187,410 | 0.003% | 0.43 | 0.06% |
174 | Samoa | 177,287 | 0.003% | 0.42 | 0.06% |
175 | Saint Lucia | 166,312 | 0.003% | 0.41 | 0.06% |
176 | Saint Vincent and the Grenadines | 117,534 | 0.002% | 0.34 | 0.05% |
177 | Tonga | 112,422 | 0.002% | 0.34 | 0.05% |
178 | Federated States of Micronesia | 108,105 | 0.002% | 0.33 | 0.05% |
179 | Kiribati | 103,092 | 0.002% | 0.32 | 0.04% |
180 | Grenada | 89,502 | 0.001% | 0.30 | 0.04% |
181 | Seychelles | 81,188 | 0.001% | 0.28 | 0.04% |
182 | Andorra | 70,549 | 0.001% | 0.27 | 0.04% |
183 | Dominica | 69,029 | 0.001% | 0.26 | 0.04% |
184 | Antigua and Barbuda | 68,722 | 0.001% | 0.26 | 0.04% |
185 | Marshall Islands | 59,071 | 0.001% | 0.24 | 0.03% |
186 | Saint Kitts and Nevis | 38,958 | 0.001% | 0.20 | 0.03% |
187 | Liechtenstein | 33,717 | 0.001% | 0.18 | 0.03% |
188 | Monaco | 32,409 | 0.001% | 0.18 | 0.02% |
189 | San Marino | 28,880 | 0.0004% | 0.17 | 0.02% |
190 | Palau | 20,303 | 0.0003% | 0.14 | 0.02% |
191 | Nauru | 13,048 | 0.0002% | 0.11 | 0.02% |
192 | Tuvalu | 11,636 | 0.0002% | 0.11 | 0.01% |
193 | Vatican City | 921 | 0.00001% | 0.03 | 0.004% |