Cube root rule

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This article is about a U.S. congressional apportionment proposal. For the scientific law, see Square–cube law.

The cube root rule or cube root law is an observation in political science that the number of members of a unicameral legislature or the Lower house of a bicameral legislature is about the cube root of the population being represented.[1] The rule was devised by Rein Taagepera in his 1972 paper "The size of national assemblies".[2]

The law has led to a proposal to increase the size of the United States House of Representatives so that the number of representatives would be the cube root of the US population as calculated in the most recent census.[3] The House of Representatives has had 435 members since the Reapportionment Act of 1929 was passed. If the US followed the cube root rule, there would be 693 members of the House of Representatives. The proposal was endorsed by the New York Times's editorial board in 2018.[4]

It has been claimed that experimental data, including the dataset originally used by Taagepera in 1972, fits better to a function with a higher exponent (e.g. a square root function) and that there is sufficient deviation from the rule to question its usefulness.[5]

Table comparing OECD nations in 2019[]

Country Population (2019)[6] Lower house size (2019) Cube root of population (nearest person) Difference between lower house and cube root of population People per representative People per representative (cube root lower house)
Australia 25,364,307 151 294 -143 167,976 86,327
Austria 8,877,067 183 207 -24 48,509 42,873
Belgium 11,484,055 150 226 -76 76,560 50,901
Canada 37,589,262 338 335 +3 111,211 112,213
Chile 18,952,038 155 267 -112 122,271 71,084
Colombia 50,339,443 172 363 -191 303,250 136,334
Czech Republic 10,669,709 200 220 -20 53,349 48,466
Denmark 5,818,553 179 180 -1 32,506 32,350
Estonia 1,326,590 101 110 -9 13,135 12,073
Finland 5,520,314 200 177 +23 27,602 31,235
France 67,059,887 577 406 +171 116,222 165,060
Germany 83,132,799 709 436 +273 117,254 190,480
Greece 10,716,322 300 220 +80 35,721 48,607
Hungary 9,769,949 199 214 -15 49,095 45,701
Iceland 361,313 63 71 -8 5,735 5,073
Ireland 4,941,444 158 170 -12 31,275 29,011
Israel 9,053,300 120 208 -88 75,444 43,438
Italy 60,297,396 630 392 +238 95,710 153,768
Japan 126,264,931 465 502 -37 271,537 251,684
Korea, Republic of 51,709,098 300 373 -73 172,384 138,796
Latvia 1,912,789 100 124 -24 19,218 15,409
Lithuania 2,786,844 141 141 0 19,765 19,803
Luxembourg 619,896 60 85 -25 10,332 7,270
Mexico 127,575,529 500 503 -3 255,151 253,422
Netherlands 17,332,850 150 259 -109 115,552 66,975
New Zealand 4,917,000 120 170 -50 40,975 28,916
Norway 5,347,896 169 175 -6 31,644 30,581
Poland 37,970,874 460 336 +124 82,545 112,971
Portugal 10,269,417 230 217 +13 44,650 47,246
Slovak Republic 5,454,073 150 176 -26 36,360 30,985
Slovenia 2,087,946 90 128 -38 23,199 16,336
Spain 47,076,781 350 361 -11 134,505 130,378
Sweden 10,285,453 349 217 +132 29,471 47,295
Switzerland 8,574,832 200 205 -5 42,874 41,894
Turkey 83,429,615 600 437 +163 139,049 190,933
United Kingdom 66,834,405 650 406 +244 102,822 164,690
United States 328,239,523 435 690 -255 754,574 475,840

See also[]

References[]

  1. ^ Lutz, Donald S. (2006). Principles of Constitutional Design. Cambridge University Press. ISBN 9781139460552.
  2. ^ Taagepera, Rein (1972). "The size of national assemblies". Social Science Research. 1 (4): 385–401. doi:10.1016/0049-089X(72)90084-1.
  3. ^ Kane, Caroline; Mascioli, Gianni; McGarry, Michael; Nagel, Meira (January 2020). Why the House of Representatives Must Be Expanded and How Today's Congress Can Make It Happen (PDF) (Report). Fordham University School of Law. Retrieved 17 September 2020.
  4. ^ "America Needs a Bigger House". New York Times. 9 November 2018. Retrieved 17 September 2020.
  5. ^ Margaritondo, Giorgio (2021). "Size of National Assemblies: The Classic Derivation of the Cube-Root Law is Conceptually Flawed". Frontiers in Physics. 8: 606. doi:10.3389/fphy.2020.614596. ISSN 2296-424X.
  6. ^ "Population, total - OECD members | Data". data.worldbank.org. Retrieved 2020-09-19.
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