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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 ...
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.
For example, the Quota method of Balinsky and Young satisfies house-monotonicity and upper-quota by construction, and it can be proved that it also satisfies lower-quota. [11] It can be generalized: there is a general algorithm that yields all apportionment methods which are both house-monotone and satisfy both quotas.
A quota-capped divisor method is an apportionment method where we begin by assigning every state its lower quota of seats. Then, we add seats one-by-one to the state with the highest votes-per-seat average, so long as adding an additional seat does not result in the state exceeding its upper quota. [30]
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers ...
Notice how the D'Hondt method breaks the quota rule (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37. Adams' method greatly favors smaller parties, giving 2 seats to the smallest party, and would give at least 1 seat to every party receiving at least one vote.
In the study of apportionment, the Hare quota (sometimes called the simple, ideal, or Hamilton quota) is the number of voters represented by each legislator under an idealized system of proportional representation, where every legislator represents an equal number of voters and where every vote is used to elect someone. The Hare quota is the ...
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.