United States Congressional apportionment
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The membership of the United States House of Representatives changes each decade following the decennial United States Census. Each state receives a number of members of Congress based upon its population. This number also determines the state's number of electors in presidential elections, which equals the size of their congressional delegation (House plus Senate).
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House size
In 1911, Public Law 62-5 set the membership of the U.S. House at 433; with the subsequent admission of Arizona and New Mexico as states, membership increased to 435, where it has remained (except for a brief period from 1959 to 1963 following the admission of Alaska and Hawaii, during which House membership was 437).
Apportionment methods
Apart from the fact that the number of delegates is at least one for each state, as required by the Constitution, this number is in principle proportional to population (equalizing the size of congressional districts nationwide). To arrive at whole numbers, the Method of Equal Proportions is used. The method first assigns one seat to each state, and then assigns each additional seat successively to the state with the highest "priority value", a value for the population per seat. For the latter the question would arise whether the current number of seats or one more should be taken. This is solved by taking an intermediate value, the geometric mean of the two. The resulting priority value is the geometric mean of the current population per seat and the population per seat in the case the state gets the extra seat.
Computing for every state and any number of seats the priority value, and sorting the list in descending order of the resulting values, the first 385 are applicable (seats 51-435) (see Census 2000 Ranking of Priority Values).
The Equal Proportions method has been the fifth distinct method of determining congressional apportionment since the adoption of the United States Constitution. The size of the Congressional delegations from the thirteen original states were assigned by the Constitution for use until the completion of the first U.S. Census. Legislation admitting new states into the union has also designated the number of representatives of states until the time of the next census.
The Equal Proportions Method
Reapportionment of the United States House of Representatives (the lower house of the U.S. Congress) occurs every year ending in "1", the year after the U.S. Census Bureau performs the decennial census mandated by the U.S. Constitution. Once seats have been reapportioned to the various states, each state creates districts of approximately equal population, a process called redistricting.
The United States authorizes there to be 435 members of Congress to be divided up between the 50 states. The seats are "apportioned" out to each state. Apportionment is done each time a new census is taken and they figure out how many people live in a particular state. So the total number of representatives is 435, and they are apportioned out to each state based on the state's population.
Apportionment is done through the "Equal Proportions Method" There is a formula used to do this called "the reciprocal of the geometric mean." How many "seats" could the largest state possibly get? We can take a guess, and that is important in calculating how many seats a state gets. Let's guess the largest state could get a maximum of 60 seats. That's well over the 53 seats that the largest state actually gets, so we are being safe in our estimate.
For starters, each state is automatically guaranteed at least one seat in Congress. So each state already has one seat in the Congress. That means there are a total of 385 seats left to hand out.
If we guess that the largest state could have at most 60 seats in Congress then we need to calculate for every state the "priority values" for each seat. So for each state we would calculate a total of 60 values. That is for each state you calculate their priority in getting a second seat, a third seat, a fourth seat, etc.
The formula for calculating the priority value a state has in getting an additional seat in Congress: P(1/Sqr(n(n-1)))
P is the state's population. n is the seat to assign to them.
California has a population of 33,930,798. So to calculate the priority value of California getting a second seat you do this:
33,930,798 * (1 divided by (the square root of 2(2-1))
The priority value for California getting a second seat is 23,992,697.36.
You would do that calculation for each of the states, and for each seat. We guessed the maximum number of seats a state could get is 60. For a total of 50 states, calculating priority values for a total of 60 seats, that’s a total of 3000 values you would need to calculate.
When you are done, you will have 3000 priority values, 60 for each state. You then sort those numbers. What's the highest priority value? The highest priority value calculated would be 23,992,697.36. That's California's priority value for a second seat. So they get a seat. And now there would be only 384 seats left to assign. The second highest priority value is 14,781,355.91. That's for Texas. So Texas gets a second seat. Now there are 383 seats left to assign. Continue to assign seats until all are gone.
State Congressional Delegation Size
1789-1910
| 1789 | 1790 | 1800 | 1810 | 1820 | 1830 | 1840 | 1850 | 1860 | 1870 | 1880 | 1890 | 1900 | 1910 | |
| Alabama | -- | -- | -- | 1 | 3 | 5 | 7 | 7 | 6 | 8 | 8 | 9 | 10 | 10 |
| Arizona | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 |
| Arkansas | -- | -- | -- | -- | -- | 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 7 |
| California | -- | -- | -- | -- | -- | -- | 2 | 2 | 3 | 4 | 6 | 7 | 8 | 11 |
| Colorado | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 2 | 3 | 4 |
| Connecticut | 5 | 7 | 7 | 7 | 6 | 6 | 6 | 4 | 4 | 4 | 4 | 4 | 5 | 5 |
| Delaware | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Florida | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 4 |
| Georgia | 3 | 2 | 4 | 6 | 7 | 9 | 8 | 8 | 7 | 9 | 10 | 11 | 11 | 12 |
| Idaho | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 2 |
| Illinois | -- | -- | -- | 1 | 1 | 3 | 7 | 9 | 14 | 19 | 20 | 22 | 25 | 27 |
| Indiana | -- | -- | -- | 1 | 3 | 7 | 10 | 11 | 11 | 13 | 13 | 13 | 13 | 13 |
| Iowa | -- | -- | -- | -- | -- | -- | 1 | 2 | 6 | 9 | 11 | 11 | 11 | 11 |
| Kansas | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 3 | 7 | 8 | 8 | 8 |
| Kentucky | -- | 2 | 6 | 10 | 12 | 13 | 10 | 10 | 9 | 10 | 11 | 11 | 11 | 11 |
| Louisiana | -- | -- | -- | 1 | 3 | 3 | 4 | 4 | 5 | 6 | 6 | 6 | 7 | 8 |
| Maine | -- | -- | -- | 7* | 7 | 8 | 7 | 6 | 5 | 5 | 4 | 4 | 4 | 4 |
| Maryland | 6 | 8 | 9 | 9 | 9 | 8 | 6 | 6 | 5 | 6 | 6 | 6 | 6 | 6 |
| Massachusetts | 8 | 14 | 17 | 13* | 13 | 12 | 10 | 11 | 10 | 11 | 12 | 13 | 14 | 16 |
| Michigan | -- | -- | -- | -- | -- | 1 | 3 | 4 | 6 | 9 | 11 | 12 | 12 | 13 |
| Minnesota | -- | -- | -- | -- | -- | -- | -- | 1 | 2 | 3 | 5 | 7 | 9 | 10 |
| Mississippi | -- | -- | -- | 1 | 1 | 2 | 4 | 5 | 5 | 6 | 7 | 7 | 8 | 8 |
| Missouri | -- | -- | -- | -- | 1 | 2 | 5 | 7 | 9 | 13 | 14 | 15 | 16 | 16 |
| 1789 | 1790 | 1800 | 1810 | 1820 | 1830 | 1840 | 1850 | 1860 | 1870 | 1880 | 1890 | 1900 | 1910 | |
| Montana | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 2 |
| Nebraska | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 3 | 6 | 6 | 6 |
| Nevada | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 1 | 1 | 1 |
| New Hampshire | 3 | 4 | 5 | 6 | 6 | 5 | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 2 |
| New Jersey | 4 | 5 | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 7 | 7 | 8 | 10 | 12 |
| New Mexico | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 |
| New York | 6 | 10 | 17 | 27 | 34 | 40 | 34 | 33 | 31 | 33 | 34 | 34 | 37 | 43 |
| North Carolina | 5 | 10 | 12 | 13 | 13 | 13 | 9 | 8 | 7 | 8 | 9 | 9 | 10 | 10 |
| North Dakota | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 2 | 3 |
| Ohio | -- | -- | 1 | 6 | 14 | 19 | 21 | 21 | 19 | 20 | 21 | 21 | 21 | 22 |
| Oklahoma | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 5 | 8 |
| Oregon | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 1 | 2 | 2 | 3 |
| Pennsylvania | 8 | 13 | 18 | 23 | 26 | 28 | 24 | 25 | 24 | 27 | 28 | 30 | 32 | 36 |
| Rhode Island | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 |
| South Carolina | 5 | 6 | 8 | 9 | 9 | 9 | 7 | 6 | 4 | 5 | 7 | 7 | 7 | 7 |
| South Dakota | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 2 | 2 | 2 | 3 |
| Tennessee | -- | 1 | 3 | 6 | 9 | 13 | 11 | 10 | 8 | 10 | 10 | 10 | 10 | 10 |
| Texas | -- | -- | -- | -- | -- | -- | 2 | 2 | 4 | 6 | 11 | 13 | 16 | 18 |
| Utah | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 2 |
| Vermont | -- | 2 | 4 | 6 | 5 | 5 | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 2 |
| Virginia | 10 | 19 | 22 | 23 | 22 | 21 | 15 | 13 | 11 | 9** | 10 | 10 | 10 | 10 |
| Washington | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 2 | 3 | 5 |
| West Virginia | -- | -- | -- | - | -- | -- | -- | -- | -- | 3** | 4 | 4 | 5 | 6 |
| Wisconsin | -- | -- | -- | -- | -- | -- | 2 | 3 | 6 | 8 | 9 | 10 | 11 | 11 |
| Wyoming | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | 1 | 1 | 1 | 1 |
| 1789 | 1790 | 1800 | 1810 | 1820 | 1830 | 1840 | 1850 | 1860 | 1870 | 1880 | 1890 | 1900 | 1910 | |
| U.S. House Total: | 65 | 106 | 142 | 186 | 213 | 242 | 232 | 237 | 243 | 293 | 332 | 357 | 391 | 435 |
1920-present
See also the list of states ordered by number of electors in the presidential elections, which is two more for each state.
| 1920 | 1930 | 1940 | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 | |
| Alabama | 10 | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 7 |
| Alaska | -- | -- | -- | 1 | 1 | 1 | 1 | 1 | 1 |
| Arizona | 1 | 1 | 2 | 2 | 3 | 4 | 5 | 6 | 8 |
| Arkansas | 7 | 7 | 7 | 6 | 4 | 4 | 4 | 4 | 4 |
| California | 11 | 20 | 23 | 30 | 38 | 43 | 45 | 52 | 53 |
| Colorado | 4 | 4 | 4 | 4 | 4 | 5 | 6 | 6 | 7 |
| Connecticut | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 5 |
| Delaware | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Florida | 4 | 5 | 6 | 8 | 12 | 15 | 19 | 23 | 25 |
| Georgia | 12 | 10 | 10 | 10 | 10 | 10 | 10 | 11 | 13 |
| Hawaii | -- | -- | -- | 1 | 2 | 2 | 2 | 2 | 2 |
| Idaho | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Illinois | 27 | 27 | 26 | 25 | 24 | 24 | 22 | 20 | 19 |
| Indiana | 13 | 12 | 11 | 11 | 11 | 11 | 10 | 10 | 9 |
| Iowa | 11 | 9 | 8 | 8 | 7 | 6 | 6 | 5 | 5 |
| Kansas | 8 | 7 | 6 | 6 | 5 | 5 | 5 | 4 | 4 |
| Kentucky | 11 | 9 | 9 | 8 | 7 | 7 | 7 | 6 | 6 |
| Louisiana | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 7 |
| Maine | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 |
| Maryland | 6 | 6 | 6 | 7 | 8 | 8 | 8 | 8 | 8 |
| Massachusetts | 16 | 15 | 14 | 14 | 12 | 12 | 11 | 10 | 10 |
| Michigan | 13 | 17 | 17 | 18 | 19 | 19 | 18 | 16 | 15 |
| Minnesota | 10 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 8 |
| Mississippi | 8 | 7 | 7 | 6 | 5 | 5 | 5 | 5 | 4 |
| Missouri | 16 | 13 | 13 | 11 | 10 | 10 | 9 | 9 | 9 |
| 1920 | 1930 | 1940 | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 | |
| Montana | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 |
| Nebraska | 6 | 5 | 4 | 4 | 3 | 3 | 3 | 3 | 3 |
| Nevada | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 |
| New Hampshire | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| New Jersey | 12 | 14 | 14 | 14 | 15 | 15 | 14 | 13 | 13 |
| New Mexico | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 |
| New York | 43 | 45 | 45 | 43 | 41 | 39 | 34 | 31 | 29 |
| North Carolina | 10 | 11 | 12 | 12 | 11 | 11 | 11 | 12 | 13 |
| North Dakota | 3 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 |
| Ohio | 22 | 24 | 23 | 23 | 24 | 23 | 21 | 19 | 18 |
| Oklahoma | 8 | 9 | 8 | 6 | 6 | 6 | 6 | 6 | 5 |
| Oregon | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 5 |
| Pennsylvania | 36 | 34 | 33 | 30 | 27 | 25 | 23 | 21 | 19 |
| Rhode Island | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| South Carolina | 7 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
| South Dakota | 3 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |
| Tennessee | 10 | 9 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
| Texas | 18 | 21 | 21 | 22 | 23 | 24 | 27 | 30 | 32 |
| Utah | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 |
| Vermont | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Virginia | 10 | 9 | 9 | 10 | 10 | 10 | 10 | 11 | 11 |
| Washington | 5 | 6 | 6 | 7 | 7 | 7 | 8 | 9 | 9 |
| West Virginia | 6 | 6 | 6 | 6 | 5 | 4 | 4 | 3 | 3 |
| Wisconsin | 11 | 10 | 10 | 10 | 10 | 9 | 9 | 9 | 8 |
| Wyoming | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1920 | 1930 | 1940 | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
Notes
Delegate counts in italics represent temporary counts assigned by Congress until the next decennial census or by the U.S. Constitution in 1789 until the first U.S. Census.
Elections held in the year of a census use the apportionment determined by the previous census.
* The state of Maine was formed out of portions of Massachusetts in 1820.
** The state of West Virginia was formed out of portions of Virginia in 1863.
See also
- United States Congress
- United States House of Representatives
- Alabama paradox
- Apportionment paradox
- Redistricting
External links
Congressional Apportionment by the U.S. Census Bureau
- The Constitution and Paradoxes
- A Java Simulation of Adams' method
- A Java Simulation of Hamilton's method
- A Java Simulation of the Huntington-Hill method
- A Java Simulation of Jefferson's method
- A Java Simulation of Webster's method
- History of Apportionment Legislation
- Forty or Thirty Thousand?
