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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.
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 ...
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]
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.
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.
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. [3]