Optimal Legislature Size

[Boss_Rahm]

The question is simple: can you construct a formula that for any population P (of a country, state, etc.) spits out the number of representatives that would be in an optimally-sized legislature?

The cube root rule is a common proposal for such a formula: P^(1/3). It gives a reasonable result for a US-sized country, but for smaller values of P I think it produces too many representatives. A million people don't need a hundred representatives.

Instead, I would propose using the square root of one five-hundredth of the population: (P/500)^(1/2). This has the benefit of a fairly intuitive explanation: the number of people per representative is 500 times the size of the legislature.

To illustrate, here are the number of representatives given by this formula for each US Census year, rounded up to the nearest odd number:

Year          Population      Seats
1790    3,929,326     89
1800    5,308,483     105
1810    7,239,881     121
1820    9,638,453     139
1830    12,866,020     161
1840    17,069,453     185
1850    23,191,876     217
1860    31,443,321     251
1870    39,818,449     283
1880    50,189,209     317
1890    62,947,714     355
1900    76,212,168     391
1910    92,228,496     431
1920    106,021,537     461
1930    122,775,046     497
1940    132,164,569     515
1950    150,697,361     549
1960    179,323,175     599
1970    203,302,031     639
1980    226,545,805     675
1990    248,709,873     707
2000    281,421,906     751
2010    308,745,538     787

[President Punxsutawney Phil]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

[Former President tack50]

Actually, 100 representatives for 1 million people seems about reasonable to me for a national legislature at least.

If anything I think where the cube root rule fails is with regional and local legislatures, which need to be smaller than the national legislature yet it results in too big legislatures there. I guess the "4th root" would be a better thing for regional legislatures.

[jimrtex]

Actually, 100 representatives for 1 million people seems about reasonable to me for a national legislature at least.

If anything I think where the cube root rule fails is with regional and local legislatures, which need to be smaller than the national legislature yet it results in too big legislatures there. I guess the "4th root" would be a better thing for regional legislatures.

For California, (approximately 40,000,000 population).

Fourth root is 80, which is the current assembly size and arguably too small.
Cube root is 342, which might be too large - though districts would still be 117K.

Somewhere in between the two might be used.

[Boss_Rahm]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

Go for it. For convenience, here are the legislature sizes by state based on 2010 Census figures:

State        Population      Seats
Alabama   4,802,982   99
Alaska   721,523           39
Arizona   6,412,700   115
Arkansas   2,926,229   77
California   37,341,989   275
Colorado   5,044,930   101
Conn.   3,581,628   85
Delaware   900,877           43
Florida   18,900,773   195
Georgia   9,727,566   141
Hawaii   1,366,862   53
Idaho   1,573,499   57
Illinois   12,864,380   161
Indiana   6,501,582   115
Iowa   3,053,787   79
Kansas   2,863,813   77
Kentucky   4,350,606   95
Louisiana   4,553,962   97
Maine   1,333,074   53
Maryland   5,789,929   109
Mass.   6,559,644   115
Michigan   9,911,626   141
Minn.   5,314,879   105
Miss.   2,978,240   79
Missouri   6,011,478   111
Montana   994,416            45
Nebraska   1,831,825   61
Nevada   2,709,432   75
N. Hamp.   1,321,445   53
N. Jersey   8,807,501   133
N. Mex.   2,067,273   65
New York   19,421,055   199
N. Car.   9,565,781   139
N. Dak.   675,905            37
Ohio   11,568,495   153
Okla.   3,764,882   87
Oregon   3,848,606   89
Penn.   12,734,905   161
R. Island   1,055,247   47
S. Car.   4,645,975   97
S. Dak.   819,761           41
Tenn.   6,375,431   113
Texas   25,268,418   225
Utah   2,770,765   75
Vermont   630,337           37
Virginia   8,037,736   127
Wash.   6,753,369   117
W. Virg.   1,859,815   61
Wisc.   5,698,230   107
Wyoming   568,300            35

[Boss_Rahm]

Actually, 100 representatives for 1 million people seems about reasonable to me for a national legislature at least.

If anything I think where the cube root rule fails is with regional and local legislatures, which need to be smaller than the national legislature yet it results in too big legislatures there. I guess the "4th root" would be a better thing for regional legislatures.

In 1793 the U.S. would have had 159 representatives, more than one for every 25,000 people. That's a bit too many for my taste. In reality there were 105 representatives.

[Boss_Rahm]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

And if you want a Congressional apportionment for 787 seats, here you go:


Alabama   4,802,982   12
Alaska   721,523            2
Arizona   6,412,700   16
Arkansas   2,926,229   7
California   37,341,989   95
Colorado   5,044,930   13
Connecticut   3,581,628   9
Delaware   900,877   2
Florida   18,900,773   48
Georgia   9,727,566   25
Hawaii   1,366,862   4
Idaho   1,573,499   4
Illinois   12,864,380   33
Indiana   6,501,582   17
Iowa   3,053,787   8
Kansas   2,863,813   7
Kentucky   4,350,606   11
Louisiana   4,553,962   12
Maine   1,333,074   3
Maryland   5,789,929   15
Massachusetts   6,559,644   17
Michigan   9,911,626    25
Minnesota   5,314,879   14
Mississippi   2,978,240   8
Missouri   6,011,478   15
Montana   994,416             3
Nebraska   1,831,825   5
Nevada   2,709,432   7
New Hampshire   1,321,445   3
New Jersey   8,807,501   22
New Mexico   2,067,273   5
New York   19,421,055          49
North Carolina   9,565,781   24
North Dakota   675,905           2
Ohio   11,568,495           29
Oklahoma   3,764,882   10
Oregon   3,848,606   10
Pennsylvania   12,734,905   32
Rhode Island   1,055,247   3
South Carolina   4,645,975   12
South Dakota   819,761            2
Tennessee   6,375,431   16
Texas   25,268,418   64
Utah   2,770,765   7
Vermont   630,337           2
Virginia   8,037,736   20
Washington   6,753,369   17
West Virginia   1,859,815   5
Wisconsin   5,698,230   14
Wyoming   568,300                    2

[jimrtex]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

And if you want a Congressional apportionment for 787 seats, here you go:


Alabama 4,802,982 12
Alaska 721,523          2
Arizona 6,412,700 16
Arkansas 2,926,229 7
California 37,341,989 95
Colorado 5,044,930 13
Connecticut 3,581,628 9
Delaware 900,877 2
Florida 18,900,773 48
Georgia 9,727,566 25
Hawaii 1,366,862 4
Idaho 1,573,499 4
Illinois 12,864,380 33
Indiana 6,501,582 17
Iowa 3,053,787 8
Kansas 2,863,813 7
Kentucky 4,350,606 11
Louisiana 4,553,962 12
Maine 1,333,074 3
Maryland 5,789,929 15
Massachusetts 6,559,644 17
Michigan 9,911,626 25
Minnesota 5,314,879 14
Mississippi 2,978,240 8
Missouri 6,011,478 15
Montana 994,416           3
Nebraska 1,831,825 5
Nevada 2,709,432 7
New Hampshire 1,321,445 3
New Jersey 8,807,501 22
New Mexico 2,067,273 5
New York 19,421,055        49
North Carolina 9,565,781 24
North Dakota 675,905         2
Ohio 11,568,495         29
Oklahoma 3,764,882 10
Oregon 3,848,606 10
Pennsylvania 12,734,905 32
Rhode Island 1,055,247 3
South Carolina 4,645,975 12
South Dakota 819,761          2
Tennessee 6,375,431 16
Texas 25,268,418 64
Utah 2,770,765 7
Vermont 630,337         2
Virginia 8,037,736 20
Washington 6,753,369 17
West Virginia 1,859,815 5
Wisconsin 5,698,230 14
Wyoming 568,300                  2

DC would have four electoral votes.

[President Punxsutawney Phil]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

Go for it. For convenience, here are the legislature sizes by state based on 2010 Census figures:

I have one question. Is this better suited for total state house+state senate figures or just the lower house?

[Starry Eyed Jagaloon]

Actually, 100 representatives for 1 million people seems about reasonable to me for a national legislature at least.

If anything I think where the cube root rule fails is with regional and local legislatures, which need to be smaller than the national legislature yet it results in too big legislatures there. I guess the "4th root" would be a better thing for regional legislatures.

I would actually stick with the cube root but push the denominator up to 1,000.

For Context:

Lok Sabha: 1,170
U.S. House: 573
House of Commons: 259
California Assembly: 199
Georgia House: 103
Wyoming House: 24
City Council of New York: 92
Town Council of Rutland, VT: 4

[President Punxsutawney Phil]

https://davesredistricting.org/join/f30c0f12-ba5d-404a-b0bb-5d1c22bebf95
16 seat AZ
Smaller district sizes allows for a district in NE AZ that is almost 39% native in 2018 total population.

[Boss_Rahm]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

Go for it. For convenience, here are the legislature sizes by state based on 2010 Census figures:

I have one question. Is this better suited for total state house+state senate figures or just the lower house?

Lower House only (or a unicameral legislature). I also use these numbers for mixed-member proportional systems.

[President Punxsutawney Phil]

would you be fine if this was turned into a square root state legislature thread using the formula you describe above?

Go for it. For convenience, here are the legislature sizes by state based on 2010 Census figures:

I have one question. Is this better suited for total state house+state senate figures or just the lower house?

Lower House only (or a unicameral legislature). I also use these numbers for mixed-member proportional systems.

Thanks for the clarification.

[President Punxsutawney Phil]

Iowa

https://davesredistricting.org/join/7b8a76cd-0850-46ac-9cf1-2113ddf26ae1


https://davesredistricting.org/join/58e5d05f-b129-4465-9c09-96699b9a0fa2

[President Punxsutawney Phil]

North Carolina

https://davesredistricting.org/join/6aeba72d-169e-4e41-8778-0972ba18bbe1


https://davesredistricting.org/join/826b90b2-9391-4955-b56a-b1218e75e59d