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Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment.
The Balinski–Young theorem proved in 1980 that if an apportionment method satisfies the quota rule, it must fail to satisfy some apportionment paradox. [3] For instance, although largest remainder method satisfies the quota rule, it violates the Alabama paradox and the population paradox. The theorem itself is broken up into several different ...
Allocation of seats by state, as percentage of overall number of representatives in the House, 1789–2020 census. United States congressional apportionment is the process [1] 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.
Apportionment would become a major topic of debate in Congress, especially after the discovery of pathologies in many superficially-reasonable rounding rules. [ 3 ] : 20 Similar debates would appear in Europe after the adoption of proportional representation , typically as a result of large parties attempting to introduce thresholds and other ...
When using the Hare quota, this rule is called Hamilton's method, and is the third-most common apportionment rule worldwide (after Jefferson's method and Webster's method). [1] Despite their intuitive definition, quota methods are generally disfavored by social choice theorists as a result of apportionment paradoxes.
The Wyoming Rule is a proposal to increase the size of the United States House of Representatives so that the standard representative-to-population ratio would be that of the smallest state, which is currently Wyoming. [1] [2] [3] Under Article One of the United States Constitution, each state is guaranteed at least one representative. If the ...
An apportionment method is denoted by a multivalued function (,); a particular -solution is a single-valued function (,) which selects a single apportionment from (,). A partial apportionment method is an apportionment method for specific fixed values of n {\displaystyle n} and h {\displaystyle h} ; it is a multivalued function M ∗ ( t ...
[The Sixteenth Amendment] was a response to the Income Tax Cases (Pollock v. Farmers' Loan & Trust Co.), and it exempts only "taxes on incomes" from the apportionment rule that otherwise applies to direct taxes. [45] Professor Calvin H. Johnson, a tax professor at the University of Texas School of Law, has written: