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Cube root law

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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 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 based on the population at the 2020 Census.

This proposal was endorsed by the New York Times editorial board in 2018.[4]

Subsequent analysis

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

In this regard, analysis by Margaritondo gives an optimal formula of: , where A is the size of the assembly, P is the population, and E = 0.45±0.03.

Applying this formula to the U.S. House Of Representatives as of the 2020 Census would give a House of between 379 and 1231 members, while using an exponent of 0.4507 gives 693 (the same result using the cube root rule).

Table comparing OECD nations in 2019

Further information: OECD
Country Lower or unicameral house Population (2019)[6] Lower house size (2019) Cube root of population (nearest person) Difference between lower house and cube root of population Difference between lower house and cube root of population (%) People per representative People per representative (cube root lower house)
Australia House of Representatives 25,364,307 151 294 −143 −49% 167,976 86,327
Austria National Council 8,877,067 183 207 −24 −12% 48,509 42,873
Belgium Chamber of Representatives 11,484,055 150 226 −76 −34% 76,560 50,901
Canada House of Commons 37,589,262 338 335 +3 +1% 111,211 112,213
Chile Chamber of Deputies 18,952,038 155 267 −112 −42% 122,271 71,084
Colombia Chamber of Representatives 50,339,443 172 363 −191 −53% 303,250 136,334
Czech Republic Chamber of Deputies 10,669,709 200 220 −20 −9% 53,349 48,466
Denmark Folketing 5,818,553 179 180 −1 −1% 32,506 32,350
Estonia Riigikogu 1,326,590 101 110 −9 −8% 13,135 12,073
Finland Parliament 5,520,314 200 177 +23 +13% 27,602 31,235
France National Assembly 67,059,887 577 406 +171 +42% 116,222 165,060
Germany Bundestag 83,132,799 709 436 +273 +63% 117,254 190,480
Greece Parliament 10,716,322 300 220 +80 +36% 35,721 48,607
Hungary National Assembly 9,769,949 199 214 −15 −7% 49,095 45,701
Iceland Althing 361,313 63 71 −8 −11% 5,735 5,073
Ireland Dáil 4,941,444 158 170 −12 −7% 31,275 29,011
Israel Knesset 9,053,300 120 208 −88 −42% 75,444 43,438
Italy Chamber of Deputies 60,297,396 630 392 +238 +61% 95,710 153,768
Japan House of Representatives 126,264,931 465 502 −37 −7% 271,537 251,684
Korea, Republic of National Assembly 51,709,098 300 373 −73 −20% 172,384 138,796
Latvia Saeima 1,912,789 100 124 −24 −19% 19,218 15,409
Lithuania Seimas 2,786,844 141 141 0 0% 19,765 19,803
Luxembourg Chamber of Deputies 619,896 60 85 −25 −29% 10,332 7,270
Mexico Chamber of Deputies 127,575,529 500 503 −3 −1% 255,151 253,422
Netherlands House of Representatives 17,332,850 150 259 −109 −42% 115,552 66,975
New Zealand House of Representatives 4,917,000 120 170 −50 −29% 40,975 28,916
Norway Storting 5,347,896 169 175 −6 −3% 31,644 30,581
Poland Sejm 37,970,874 460 336 +124 +37% 82,545 112,971
Portugal Assembly of the Republic 10,269,417 230 217 +13 +6% 44,650 47,246
Slovakia National Council 5,454,073 150 176 −26 −15% 36,360 30,985
Slovenia National Assembly 2,087,946 90 128 −38 −30% 23,199 16,336
Spain Congress of Deputies 47,076,781 350 361 −11 −3% 134,505 130,378
Sweden Riksdag 10,285,453 349 217 +132 +61% 29,471 47,295
Switzerland National Council 8,574,832 200 205 −5 −2% 42,874 41,894
Turkey Grand National Assembly 83,429,615 600 437 +163 +37% 139,049 190,933
United Kingdom House of Commons 66,834,405 650 406 +244 +60% 102,822 164,690
United States House of Representatives 328,239,523 435 690 −255 −37% 754,574 475,840

Historical House sizes

The following table describes how the US House of Representatives would have looked historically under the cube root rule.

Census, Year Size AL AK AZ AR CA CO CT DE FL GA HI ID IL IN IA KS KY LA ME MD MA MI MN MS MO MT NE NV NH NJ NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY
1st, 1790 158
2nd, 1800 175
3rd, 1810 194
4th, 1820 213
5th, 1830 235
6th, 1840 258
7th, 1850 286
8th, 1860 316 10 4 4 5 1 2 11 17 14 7 12 7 6 7 13 8 2 8 12 3 7 39 10 24 1 29 2 7 11 6 3 16 8
9th, 1870 338 9 4 5 5 1 2 10 22 15 11 3 12 6 6 7 13 10 4 7 15 1 1 3 8 39 10 24 1 31 2 6 11 7 3 11 4 9
10th, 1880 369 9 6 6 2 5 1 2 12 23 15 12 7 12 7 5 7 13 12 6 8 16 3 1 3 8 38 11 24 1 32 2 7 12 12 3 11 5 10
11th, 1890 398 10 7 8 3 5 1 3 12 1 25 14 12 9 12 7 4 7 14 13 8 8 17 1 7 1 2 9 39 10 1 24 2 34 2 7 2 11 14 2 11 2 5 11 1
12th, 1900 424 10 7 8 3 5 1 3 13 1 27 14 13 8 12 8 4 7 16 14 10 9 18 1 6 1 2 11 41 11 2 24 2 36 2 8 2 11 17 2 2 11 3 5 12 1
13th, 1910 452 11 8 12 4 6 1 4 13 2 28 13 11 8 11 8 4 6 17 14 10 9 16 2 6 1 2 12 45 11 3 23 8 3 38 3 7 3 11 19 2 2 10 6 6 12 1
14th, 1920 473 11 2 8 15 4 6 1 4 13 2 29 13 11 8 11 8 3 6 17 16 11 8 15 3 6 1 2 14 2 46 11 3 26 9 4 39 3 8 3 10 21 2 2 10 6 7 12 1
15th, 1930 498 11 2 7 23 4 6 1 6 12 2 31 13 10 8 11 8 3 7 17 20 10 8 15 2 6 1 2 16 2 51 13 3 27 10 4 39 3 7 3 11 23 2 2 10 6 7 12 1
16th, 1940 509 11 2 8 27 4 7 1 7 12 2 31 13 10 7 11 9 3 7 17 20 11 9 15 2 5 1 2 16 2 52 14 3 27 9 4 39 3 7 3 11 25 2 1 10 7 7 12 1
17th, 1950 533 11 3 7 38 5 7 1 10 12 2 31 14 9 7 10 10 3 8 17 23 11 8 14 2 5 1 2 17 2 53 14 2 28 8 5 37 3 8 2 12 27 2 1 12 8 7 12 1
18th, 1960 564 10 1 4 6 49 6 8 1 16 12 2 2 32 15 9 7 10 10 3 10 16 25 11 7 14 2 4 1 2 19 3 53 14 2 31 7 6 36 3 8 2 11 30 3 1 12 9 6 12 1
19th, 1970 588 10 1 5 6 58 6 9 2 20 13 2 2 32 15 8 7 9 11 3 11 17 26 11 6 14 2 4 2 2 21 3 53 15 2 31 7 6 34 3 8 2 11 32 3 1 13 10 5 13 1
20th, 1980 610 11 1 7 6 64 8 8 2 26 15 3 3 31 15 8 6 10 11 3 11 16 25 11 7 13 2 4 2 3 20 4 48 16 2 29 8 7 32 3 8 2 12 38 4 1 14 11 5 13 1
21st, 1990 629 10 1 9 6 75 8 8 2 33 16 3 3 29 14 7 6 9 11 3 12 15 24 11 7 13 2 4 3 3 20 4 46 17 2 27 8 7 30 3 9 2 12 43 4 2 16 12 5 12 1
22nd, 2000 656 10 2 12 6 79 10 8 2 37 19 3 3 29 14 7 6 9 10 3 12 15 23 11 7 13 2 4 5 3 20 4 44 19 2 27 8 8 29 2 9 2 13 49 5 2 17 14 4 13 1
23rd, 2010 676 10 2 14 6 82 11 8 2 41 21 3 3 28 14 7 6 10 10 3 13 14 22 12 7 13 2 4 6 3 19 5 43 21 2 25 8 8 28 2 10 2 14 55 6 1 18 15 4 12 1
24th, 2020 693 11 2 15 6 83 12 8 2 45 22 3 4 27 14 7 6 9 10 3 13 15 21 12 6 13 2 4 7 3 19 4 42 22 2 25 8 9 27 2 11 2 15 61 7 1 18 16 4 12 1
Census, Year Size AL AK AZ AR CA CO CT DE FL GA HI ID IL IN IA KS KY LA ME MD MA MI MN MS MO MT NE NV NH NJ NM NY NC ND OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY

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. Bibcode:2021FrP.....8..606M. 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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