Cube root law


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

Subsequent analysis

argued 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. 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.

Table comparing OECD nations in 2019 with EIU Democracy Index ranking

Out of the countries listed, Lithuania is the only one to exactly match the cube root rule. Moreover, Denmark, Canada, Ireland and Mexico come close to matching the rule.
Some of these countries have overhang seats in a mixed member proportional system, as a result the size of their parliaments can vary significantly between elections.
CountryLower or unicameral housePopulation Lower house size Cube root of population Difference between lower house and cube root of populationDifference between lower house and cube root of population People per representativePeople per representative Democracy Index Ranking
AustraliaHouse of Representatives25,364,307151294−143−49%167,97686,32715
AustriaNational Council8,877,067183207−24−12%48,50942,87320
BelgiumChamber of Representatives11,484,055150226−76−34%76,56050,90136
CanadaHouse of Commons37,589,262338335+3+1%111,211112,21312
ChileChamber of Deputies18,952,038155267−112−42%122,27171,08419
ColombiaChamber of Representatives50,339,443172363−191−53%303,250136,33453
Czech RepublicChamber of Deputies10,669,709200220−20−9%53,34948,46625
DenmarkFolketing5,818,553179180−1−1%32,50632,3506
EstoniaRiigikogu1,326,590101110−9−8%13,13512,07327
FinlandParliament5,520,314200177+23+13%27,60231,2355
FranceNational Assembly67,059,887577406+171+42%116,222165,06022
GermanyBundestag83,132,799734436+298+68%113,260190,48014
GreeceParliament10,716,322300220+80+36%35,72148,60725
HungaryNational Assembly9,769,949199214−15−7%49,09545,70156
IcelandAlthing361,3136371−8−11%5,7355,0733
IrelandDáil5,123,536174172+2+1%29,44629,7888
IsraelKnesset9,053,300120208−88−42%75,44443,43829
ItalyChamber of Deputies60,297,396400392+8+2%150,743153,76834
JapanHouse of Representatives126,264,931465502−37−7%271,537251,68416
Korea, Republic ofNational Assembly51,709,098300373−73−20%172,384138,79624
LatviaSaeima1,912,789100124−24−19%19,21815,40938
LithuaniaSeimas2,786,84414114100%19,76519,80339
LuxembourgChamber of Deputies619,8966085−25−29%10,3327,27013
MexicoChamber of Deputies127,575,529500503−3−1%255,151253,42289
NetherlandsHouse of Representatives17,332,850150259−109−42%115,55266,9759
New ZealandHouse of Representatives4,917,000120170−50−29%40,97528,9162
NorwayStorting5,347,896169175−6−3%31,64430,5811
PolandSejm37,970,874460336+124+37%82,545112,97146
PortugalAssembly of the Republic10,269,417230217+13+6%44,65047,24628
SlovakiaNational Council5,454,073150176−26−15%36,36030,98543
SloveniaNational Assembly2,087,94690128−38−30%23,19916,33631
SpainCongress of Deputies47,076,781350361−11−3%134,505130,37822
SwedenRiksdag10,285,453349217+132+61%29,47147,2954
SwitzerlandNational Council8,574,832200205−5−2%42,87441,8947
TurkeyGrand National Assembly83,429,615600437+163+37%139,049190,933103
United KingdomHouse of Commons66,834,405650406+244+60%102,822164,69018
United StatesHouse of Representatives328,239,523435690−255−37%754,574475,84030

Historical US House sizes

The following table describes how the US House of Representatives would have looked historically under the cube root rule according to the Huntington–Hill method.
Census, YearSizeALAKAZARCACOCTDEDCFLGAHIIDILINIAKSKYLAMEMDMAMIMNMSMOMTNENVNHNJNMNYNCNDOHOKORPARISCSDTNTXUTVTVAWAWVWIWY
1st, 1790158103313206814161831034
2nd, 180017582571219672016202124530
3rd, 18101947271111196727156222127627
4th, 18202133628131337912256311413242119524
5th, 18302356511036134781133563514172521113522
6th, 1840258925111710125871136646371223262913419
7th, 18502861031511111012212677125884638112529281234184
8th, 18603161044512111714712767138281237391024129271163168
9th, 1870338945512102215113126671310471511383910241312611731149
10th, 1880369966251212231512712757131268163138381124132271212311510
11th, 18903981078351312125141291274714138817171293910124234272111421125111
12th, 190042610783512313127141381284716141091816121141112242362821117221135121
13th, 19104531181246124132281311811846171410916261212451132383383731119221066121
14th, 1920475112815461241322913118118361716118153612142461132694393831021221067121
15th, 19305001127234612612231131081183717201081526121625113327104393731123221067121
16th, 1940512112827471371223113107119371720119152512162521432794393731125211077121
17th, 19505361137385713101223114971010381723118142512172531422885373821227211287121
18th, 19605661014649681216122232159710103101625117142412193531423176363821130311296121
19th, 19705901015658692220132232158791131117261161424222135315231763438211323113105131
20th, 198061211176648822261533311586101131116251171324232044816229873238212384114115131
21st, 19906311019675882233163329147691131215241171324332044617227873039212434216125121
22nd, 2000657102126791082137193329147691031215231171324532044419227882929213495217144131
23rd, 201067710214682118214121332814761010313142212713246319543212258828210214556118154121
24th, 20206951121568312822452234271476910313152112613247319442222258927211215617118164121
Census, YearSizeALAKAZARCACOCTDEDCFLGAHIIDILINIAKSKYLAMEMDMAMIMNMSMOMTNENVNHNJNMNYNCNDOHOKORPARISCSDTNTXUTVTVAWAWVWIWY