Apportionment (politics) in the context of "Highest averages method"

The United States of America is a federal republic consisting of 50 states, a federal district (Washington, D.C., the capital city of the United States), five major territories, and minor islands. Both the states and the United States as a whole are each sovereign jurisdictions. The Tenth Amendment to the United States Constitution allows states to exercise all powers of government not delegated to the federal government. Each state has its own constitution and government. All states and their residents are represented in the federal Congress, a bicameral legislature consisting of the Senate and the House of Representatives. Each state elects two senators, while representatives are distributed among the states in proportion to the most recent constitutionally mandated decennial census.

Each state is entitled to select a number of electors to vote in the Electoral College, the body that elects the president of the United States, equal to the total of representatives and senators in Congress from that state. The federal district does not have representatives in the Senate, but has a non-voting delegate in the House, and it is entitled to electors in the Electoral College. Congress can admit more states, but it cannot create a new state from territory of an existing state or merge two or more states into one without the consent of all states involved. Each new state is admitted on an equal footing with the existing states.

Party-list proportional representation (list-PR) is a system of proportional representation based on preregistered political parties, with each party being allocated a certain number of seats roughly proportional to their share of the vote.

In these systems, parties provide lists of candidates to be elected, or candidates may declare their affiliation with a political party (in some open-list systems). Seats are distributed by election authorities to each party, in proportion to the number of votes the party receives. Voters may cast votes for parties, as in Spain, Turkey, and Israel (closed lists); or for candidates whose vote totals are pooled together to determine the share of representation of their respective parties, as in Finland, Brazil, and the Netherlands (mixed single vote or panachage).

United States congressional apportionment is the process by which seats in the United States House of Representatives are distributed among the 50 states according to the most recent decennial census mandated by the United States Constitution. After each state is guaranteed a minimum of one seat in the House, most states are then apportioned a number of additional seats which roughly corresponds to its share of the aggregate population of the 50 states. Every state is constitutionally guaranteed two seats in the Senate and at least one seat in the House, regardless of population.

The U.S. House of Representatives' maximum number of seats has been limited to 435, capped at that number by the Reapportionment Act of 1929—except for a temporary (1959–1962) increase to 437 when Alaska and Hawaii were admitted into the Union. The Huntington–Hill method of equal proportions has been used to distribute the seats among the states since the 1940 census reapportionment. Federal law requires the clerk of the United States House of Representatives to notify each state government of the number of seats apportioned to the state no later than January 25 of the year immediately following each decennial census.

In mathematics and political science, the quota rule describes a desired property of proportional apportionment methods. It says that the number of seats allocated to a party should be equal to their entitlement plus or minus one. The ideal number of seats for a party, called their seat entitlement, is calculated by multiplying each party's share of the vote by the total number of seats. Equivalently, it is equal to the number of votes divided by the Hare quota. For example, if a party receives 10.56% of the vote, and there are 100 seats in a parliament, the quota rule says that when all seats are allotted, the party may get either 10 or 11 seats. The most common apportionment methods (the highest averages methods) violate the quota rule in situations where upholding it would cause a population paradox, although unbiased apportionment rules like Webster's method do so only rarely.

The Three-fifths Compromise, also known as the Constitutional Compromise of 1787, was an agreement reached during the 1787 United States Constitutional Convention over the inclusion of slaves in counting a state's total population. This count would determine the number of seats in the House of Representatives, the number of electoral votes each state would be allocated, and how much money the states would pay in taxes. Slave states wanted their entire population to be counted to determine the number of Representatives those states could elect and send to Congress. Free states wanted to exclude the counting of slave populations in slave states, since those slaves had no voting rights. A compromise was struck to resolve this impasse. The compromise counted three-fifths of each state's slave population toward that state's total population for the purpose of apportioning the House of Representatives, effectively giving the Southern states more power in the House relative to the Northern states. It also gave slaveholders similarly enlarged powers in Southern legislatures; this was an issue in the secession of West Virginia from Virginia in 1863. Free black people and indentured servants were not subject to the compromise, and each was counted as one full person for representation.

The Three-fifths Compromise is in Article 1, Section 2, Clause 3 of the United States Constitution. It provides:

The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties.

The method was first described in 1792 by American Secretary of State and later President of the United States Thomas Jefferson. It was re-invented independently in 1878 by Belgian mathematician Victor D'Hondt, which is the reason for its two different names.

The Virginia Plan (also known as the Randolph Plan or the Large-State Plan) was a proposed plan of government for the United States presented at the Constitutional Convention of 1787. The plan called for the creation of a supreme national government with three branches and a bicameral legislature. The plan was drafted by James Madison and Edmund Randolph.

The Virginia Plan was notable for its role in setting the overall agenda for debate in the Convention and, in particular, for setting forth the idea of population-weighted representation in the proposed national legislature. The Virginia Plan favored the interests of states with large populations, and the New Jersey Plan was proposed in response to protect small state interests.

The quota or divide-and-rank methods make up a category of apportionment rules, i.e. algorithms for allocating seats in a legislative body among multiple groups (e.g. parties or federal states). The quota methods begin by calculating an entitlement (basic number of seats) for each party, by dividing their vote totals by an electoral quota (a fixed number of votes needed to win a seat, as a unit). Then, leftover seats, if any are allocated by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular highest averages methods (also called divisor methods).

By far the most common quota method are the largest remainders or quota-shift methods, which assign any leftover seats to the "plurality" winners (the parties with the largest remainders, i.e. most leftover votes).