Allocation of congressional districts after the 2000 census.

The decennial apportionment also determines the size of each state's representation in the United States Electoral College—any state's number of electors equals the size of its total congressional delegation (i.e., House seat(s) plus Senate seats).

Federal law requires the Clerk of the House to notify each state government of its entitled number of seats no later than January 25 of the year immediately following the census. After seats have been reapportioned, each state determines the boundaries of Congressional districts—geographical areas within the state of approximately equal population—in a process called redistricting.

House size

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 a provision to add one permanent seat each upon the admissions of Arizona and New Mexico as states. As provided, membership increased to 435 in 1912, where it has remained since, with a brief exception from 1959 to 1963 following the admissions of Alaska and Hawaii, during which House membership was 437.

If the ratio floor as specified by the Constitution of one representative for every 30,000 people were maintained, the House of Representatives currently would have about 10,000 members. Instead, the present size of 435 seats means one member represents on average about 650,000 people; but exact representation per member varies by state. Four states ? Wyoming, Vermont, Alaska and North Dakota ? currently have populations smaller than the average for a single district, resulting in over-representation for residents of those states.

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. Recent bills, such as the District of Columbia House Voting Rights Act of 2007, 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.

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 so called "Equal Proportions method" is the apportionment methodology currently used.^[1] The method derives its name from the fact that it guarantees the property that no additional transfer of a seat (from one state to another) will reduce the percentage difference in per capita representation.

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 assign.

The remaining seats are assigned one at a time, to the state that "deserves" another seat the most. Thus, the 51st seat always goes to the most populous 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

A=\frac{P}{\sqrt{n(n+1)}}

where P is the population of the state, and n is the number of seats it currently has. An equivalent, recursive definition is

A_{n}=(A_{n-1})(\frac{n}{n+2})^{-\frac{1}{2}}

where n is still the number of seats the state has, and for n = 1, A is explicitly defined as

A_{1}=\frac{P}{\sqrt{2}}

A sequential definition may likewise be given where the n = 1 case is defined as above, but the formula is

A_{n+1}=(A_{n})(\frac{n-1}{n+1})^{-\frac{1}{2}}

When all states have one seat, the largest value of A corresponds to the largest state. But now that California has two 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^[2] 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 could receive a fourth seat if the District of Columbia House Voting Rights Act of 2007 passes.

Past apportionments

Note: The first apportionment was authorized by the Constitution, not the Census.

Projected changes following the 2010 census

The U.S. Census Bureau will conduct a comprehensive census in April 2010 (2010 census). Based on the populations counted in each state, the United States Congress will be reapportioned based on the Equal Proportions Method defined above. The total number of voting representatives is expected to remain at 435, assuming no legislation passes that would modify the apportionment process. Since the Census Bureau releases population estimates every year, projections have been made that predict the states' populations as of April 2010. One study estimates that fourteen seats would shift between the states as follows:^[3]

The 10-year national growth rate is 12.5%. In this estimate, the population of states losing seats grew at a slower rate and the population of states gaining seats grew at a faster pace. Louisiana is the only state losing a seat that is estimated to have lost population between 2000 and 2010, significantly due to the exodus precipitated by the damage caused by Hurricane Katrina. The losing states are in the industrial northeast and midwest, while gainers are in the southeast, southwest and Pacific northwest.^[3]

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.

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
• Thirty-thousand.org

de:Hill-Huntington-Verfahren