UNITED STATES CONGRESSIONAL APPORTIONMENT
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(Redirected from United States Congressional apportionment)
The allocation among states of the 435 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).
Reapportionment occurs every year ending in "1", the year after the decennial census. After seats have been reapportioned, each state determines the boundaries of Congressional districts within the state — geographical areas of approximately equal population — a process called redistricting.
The United States Constitution requires that
:''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)
Prior to the twentieth century, the number of representatives increased every decade as more states joined the union, and the population increased.
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. Instead, today one member represents about 650,000 people, which varies by state.
Proposals have been made to add voting representation for the District of Columbia, now represented only by a non-voting delegate, who is not counted as one of the 435 House representatives. A recent bill, the District of Columbia House Voting Rights Act of 2007, if passed, would resolve the issue by permanently increasing House membership to 437. One of the new members would be from the District of Columbia; the other would be from the next state in line to receive another House seat (as described below), presently Utah. The political appeal of this plan lies in its balancing of a new, presumably Democratic seat (D.C.) with a new likely Republican seat (Utah).
Apart from the fact that the number of delegates is at least 1 for each state, as required by the Constitution, a state's number of representatives is in principle proportional to population (thus equalizing the size of congressional districts nationwide). No method of calculating this desired result, however, has been found perfectly satisfactory in practice. Five distinct methods have been used since the adoption of the Constitution, all of them susceptible to mathematical paradoxes.
The Equal Proportions method is the apportionment methodology currently used.
In this method, as a first step, 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).
The apportionment method uses a mathematical formula to express the priority ordering of states for an additional seat. For instance, in the example above, California has already received a second seat and thus "deserves" a third one less.
The formula used by the method of equal proportions is
:
where ''P'' is the population of the state, and ''n'' is the number of seats it currently has. An equivalent, recursive definition is
:
where ''n'' is still the number of seats the state has, and for ''n'' = 1, ''A'' is explicitly defined as
:
A sequential definition may likewise be given where the ''n'' = 1 case is defined as above, but the formula is
:
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[1] 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 the North Carolina count and undercounting of Utah's overseas missionary population (suggested to be as many as 14,000), was unsuccessful. However, Utah may still get a fourth seat if the District of Columbia House Voting Rights Act of 2007 is passed.
★ 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.
1. census.gov
2. The state of Maine was formed out of portions of Massachusetts in 1820.
3. The state of Maine was formed out of portions of Massachusetts in 1820.
4. The state of West Virginia was formed out of portions of Virginia in 1863.
5. The state of West Virginia was formed out of portions of Virginia in 1863.
★ 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
★ Gerrymandering
★ List of U.S. states by population
★ 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
★ 'Thirty-thousand.org:'
:
★ A Brief History of Apportionment
:
★ Forty or Thirty Thousand?
:
★ The Size of the U. S. House of Representatives and its Constituent State Delegations Authorized Number of Seats by Year and by Congress 1789 to 2006
:
★ Outcomes of Presidential Elections and the House Size
Allocation of congressional districts after the 2000 census.
The allocation among states of the 435 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).
Reapportionment occurs every year ending in "1", the year after the decennial census. After seats have been reapportioned, each state determines the boundaries of Congressional districts within the state — geographical areas of approximately equal population — a process called redistricting.
| Contents |
| House size |
| Apportionment methods |
| The Equal Proportions Method |
| State congressional delegation size |
| 1789–1910 |
| 1920-present |
| Notes |
| See also |
| External links |
House size
| Ratio of representation in the House, 1789–1923 | ||
|---|---|---|
| Years | Source | Constituents per Representative |
| 1789–1793 | U.S. Constitution | 30,000 |
| 1793–1803 | U.S. Census of 1790 | 30,000 |
| 1803–1813 | U.S. Census of 1800 | 33,000 |
| 1813–1823 | U.S. Census of 1810 | 35,000 |
| 1823–1833 | U.S. Census of 1820 | 40,000 |
| 1833–1843 | U.S. Census of 1830 | 47,700 |
| 1843–1853 | U.S. Census of 1840 | 70,680 |
| 1853–1863 | U.S. Census of 1850 | 93,425 |
| 1863–1873 | U.S. Census of 1860 | 127,381 |
| 1873–1883 | U.S. Census of 1870 | 131,425 |
| 1883–1893 | U.S. Census of 1880 | 151,912 |
| 1893–1903 | U.S. Census of 1890 | 173,901 |
| 1903–1913 | U.S. Census of 1900 | 194,182 |
| 1913–1923 | U.S. Census of 1910 | 212,407 |
The United States Constitution requires that
:''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)
Prior to the twentieth century, the number of representatives increased every decade as more states joined the union, and the population increased.
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. Instead, today one member represents about 650,000 people, which varies by state.
Proposals have been made to add voting representation for the District of Columbia, now represented only by a non-voting delegate, who is not counted as one of the 435 House representatives. A recent bill, the District of Columbia House Voting Rights Act of 2007, if passed, would resolve the issue by permanently increasing House membership to 437. One of the new members would be from the District of Columbia; the other would be from the next state in line to receive another House seat (as described below), presently Utah. The political appeal of this plan lies in its balancing of a new, presumably Democratic seat (D.C.) with a new likely Republican seat (Utah).
Apportionment methods
Apart from the fact that the number of delegates is at least 1 for each state, as required by the Constitution, a state's number of representatives is in principle proportional to population (thus equalizing the size of congressional districts nationwide). No method of calculating this desired result, however, has been found perfectly satisfactory in practice. Five distinct methods have been used since the adoption of the Constitution, all of them susceptible to mathematical paradoxes.
The Equal Proportions Method
The Equal Proportions method is the apportionment methodology currently used.
In this method, as a first step, 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).
The apportionment method uses a mathematical formula to express the priority ordering of states for an additional seat. For instance, in the example above, California has already received a second seat and thus "deserves" a third one less.
The formula used by the method of equal proportions is
:
where ''P'' is the population of the state, and ''n'' is the number of seats it currently has. An equivalent, recursive definition is
:
where ''n'' is still the number of seats the state has, and for ''n'' = 1, ''A'' is explicitly defined as
:
A sequential definition may likewise be given where the ''n'' = 1 case is defined as above, but the formula is
:
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[1] 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 the North Carolina count and undercounting of Utah's overseas missionary population (suggested to be as many as 14,000), was unsuccessful. However, Utah may still get a fourth seat if the District of Columbia House Voting Rights Act of 2007 is passed.
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''[2] | 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[2] | 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[4] | 10 | 10 | 10 | 10 |
| Washington | — | — | — | — | — | — | — | — | — | — | ''1'' | 2 | 3 | 5 |
| West Virginia | — | — | — | - | — | — | — | — | — | 3[4] | 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 | 437 | 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.
1. census.gov
2. The state of Maine was formed out of portions of Massachusetts in 1820.
3. The state of Maine was formed out of portions of Massachusetts in 1820.
4. The state of West Virginia was formed out of portions of Virginia in 1863.
5. 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
★ Gerrymandering
★ List of U.S. states by population
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
★ 'Thirty-thousand.org:'
:
★ A Brief History of Apportionment
:
★ Forty or Thirty Thousand?
:
★ The Size of the U. S. House of Representatives and its Constituent State Delegations Authorized Number of Seats by Year and by Congress 1789 to 2006
:
★ Outcomes of Presidential Elections and the House Size
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