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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. It belongs to the class of highest-averages methods.
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 ...
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 ]
The seats-to-votes ratio, [1] also known as the advantage ratio, [2] is a measure of equal representation of voters.The equation for seats-to-votes ratio for a political party i is:
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 ...
The seat linkage compensatory mixed system often referred to as MMP originates in Germany, and was later adopted with modifications under the name of MMP in New Zealand.In Germany, where it was differentiated from a different compensatory mixed system it was always known as personalized proportional representation (PPR) (German: personalisiertes Verhältniswahlrecht).
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 Hare quota (also known as the simple quota or Hamilton's quota) is the most commonly-used quota for apportionments using the largest remainder method of party-list representation.