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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 ...
Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, there is a resource to allocate, denoted by h {\displaystyle h} . For example, it can be an integer representing the number of seats in a h ouse of representatives.
By this definition, the Webster method is the least-biased apportionment method, [19] while Huntington-Hill exhibits a mild bias towards smaller parties. [18] However, other researchers have noted that slightly different definitions of bias, generally based on percent errors , find the opposite result (The Huntington-Hill method is unbiased ...
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 ...
They are used in some systems where a formula other than plurality is used to allocate seats. Generally quotas are set at a level that is guaranteed to apportion only as many seats as are available in the legislature. When the electorate is divided into separate districts, the quota is commonly set by reference to valid votes cast in the district.
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 Webster method, also called the Sainte-Laguë method (French pronunciation: [sɛ̃t.la.ɡy]), is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system.
The D'Hondt method, [a] 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.