United States Congressional Apportionment
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The allocation of seats in the United States House of Representatives changes each decade following the decennial United States Census. Each state is apportioned a number of seats 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).
House size
| Ratio of representation in the House | |
|---|---|
| 1789–1793 as by the U.S. Constitution | 30,000 |
| 1793–1803 based on the U.S. Census of 1790 | 30,000 |
| 1803–1813 based on the U.S. Census of 1800 | 33,000 |
| 1813–1823 based on the U.S. Census of 1810 | 35,000 |
| 1823–1833 based on the U.S. Census of 1820 | 40,000 |
| 1833–1843 based on the U.S. Census of 1830 | 47,700 |
| 1843–1853 based on the U.S. Census of 1840 | 70,680 |
| 1853–1863 based on the U.S. Census of 1850 | 93,425 |
| 1863–1873 based on the U.S. Census of 1860 | 127,381 |
| 1873–1883 based on the U.S. Census of 1870 | 131,425 |
| 1883–1893 based on the U.S. Census of 1880 | 151,912 |
| 1893–1903 based on the U.S. Census of 1890 | 173,901 |
| 1903–1913 based on the U.S. Census of 1900 | 194,182 |
| 1913–1923 based on the U.S. Census of 1910 | 212,407 |
- The number of Representatives shall not exceed one for every thirty thousand, but each state shall have at least one Representative (Article I, Section 2, Paragraph 3)
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). If the ratio as specified by the Constitution of one representative for every 30,000 people were maintained today, the House of Representatives would have about 10,000 members.
Apportionment methods
Apart from the fact that the number of delegates is at least 1 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.
First, each state is automatically guaranteed at least one seat in Congress. That means there are a total of 385 seats left to hand out.
The remaining seats are handed out one at a time, to the state that "deserves" another seat the most. Thus, the 51st seat always goes to the largest state (currently California).
Now who gets the 52nd? We need to somehow take into acount the fact that California already has a second seat, and so "deserves" a third one less. That is, we need a mathematical formula that expresses the priority formula that a state should have for getting another seat.
The formula used by the method of equal proportions is
- [A=\frac}]
When all states have 1 seat, the largest value of A corresponds to the largest state. But now that California has 2 seats, its priority value decreases, and it has to take a step back in line. The 52nd seat goes to Texas, the 2nd largest state, but the 53rd goes back to California, and so on until all the seats have been handed out. Each time a state gets a seat, its priority drops and another state comes to the top of the list.
The Census 2000 Ranking of Priority Values (see link above) shows the order in which seats 51-435 were apportioned after the 2000 Census, with additional listings for the next five priorities. North Carolina was allocated the final (435th) seat. Utah (priority list 436) missed a fourth seat by only 857 residents. Legal action by Utah to amend the results, citing irregularities in North Carolina and undercounting of Utah's overseas population, was unsuccessful.
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 | |
| Total: | 65 | 106 | 142 | 186 | 213 | 242 | 232 | 237 | 243 | 293 | 332 | 357 | 391 | 435 |
1920-present
| 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 | |
| Total: | 435 | 435 | 435 | 435 | 435 | 435 | 435 | 435 | 435 |
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
- List of states ordered by number of electors in the presidential elections, which is two more for each state.
- United States Congress
- United States House of Representatives
- Alabama paradox
- Apportionment paradox
- Redistricting
- Partisan mix of congressional delegations
- Gerrymandering
- History of 19th Century Congressional Apportionment In Ohio
External links
- [Congressional Apportionment by the U.S. Census Bureau]
- Cut-the-knot.org:
- * [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]
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