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The basis for apportionment may be out of date. For example, in the United States, apportionment follows the decennial census. The states conducted the 2010 elections with districts apportioned according to the 2000 Census. The lack of accuracy does not justify the present cost and perceived intrusion of a new census before each biennial election.
For example, the electoral college apportionment and congressional races during the 2020 presidential election year were still based on the 2010 census results; all of the newly redrawn districts based on the 2020 census did not finally come into force until the 2022 midterm election winners were inaugurated in January 2023. [citation needed]
Party-approval voting (also called approval-based apportionment) [7] is a method in which each voter can approve one or more parties, rather than approving individual candidates. It is a combination of multiwinner approval voting with party-list voting.
For illustration, continue with the above example of four parties. The advantage ratios of the four parties are 1.2 for A, 1.1 for B, 1 for C, and 0 for D. The reciprocal of the largest advantage ratio is 1/1.15 = 0.87 = 1 − π *. The residuals as shares of the total vote are 0% for A, 2.2% for B, 2.2% for C, and 8.7% for party D.
In other words, it is impossible to lower the highest vote average by reassigning a seat from one party to another. Every number in this range is a possible divisor. If the inequality is strict, the solution is unique; otherwise, there is an exactly tied vote in the final apportionment stage. [1]: 83
When apportioning seats in proportional representation, it is particularly important to avoid bias between large parties and small parties to avoid strategic voting. André Sainte-Laguë showed theoretically that the Sainte-Laguë method shows the lowest average bias in apportionment, [2] confirmed by different theoretical and empirical ways.
The Knesset (Israel's unicameral legislature), are elected by party-list representation with apportionment by the D'Hondt method. [ a ] Had the Huntington–Hill method, rather than the D'Hondt method, been used to apportion seats following the elections to the 20th Knesset , held in 2015, the 120 seats in the 20th Knesset would have been ...
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.