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The largest remainder methods or quota methods are methods of allocating seats proportionally that are based on calculating a quota, i.e. a certain number of votes needed to be guaranteed a seat in parliament. Then, any leftover seats are handed over to "plurality" winners (the parties with the largest remainders, i.e. the most "leftover" votes).[1] They are typically contrasted with the more popular highest averages methods (also called divisor methods).[2]
Divisor methods are generally preferred by social choice theorists to the largest remainder methods because they are less susceptible to apportionment paradoxes.[2][3] In particular, divisor methods satisfy population monotonicity, i.e. voting for a party can never cause it to lose seats.[3] Such population paradoxes occur by increasing the electoral quota, which can cause different states' remainders to respond erratically.[4] Divisor methods also satisfy resource or house monotonicity, which says that increasing the number of seats in a legislature should not cause a state to lose a seat (a situation known as an Alabama paradox).[3][4]: Cor.4.3.1
When using the Hare quota, the method is known as the Hare–Niemeyer or Hamilton method.
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