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The largest remainder method divides each party's vote total by a quota. Usually, quota is derived by dividing the number of valid votes cast, by the number of seats. The result for each party will consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer.
A joint Politics and Economics series Social choice and electoral systems Social choice Mechanism design Comparative politics Comparison List (By country) Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Condorcet methods Condorcet-IRV Round ...
In fact, they overtook C's fraction, causing C to lose its seat, since the Hamilton method allocates according to which states have the largest fractional remainder. The Alabama paradox gave rise to the axiom known as house monotonicity , which says that, when the house size increases, the allocations of all states should weakly increase.
For algorithms describing how to calculate the remainder, see Division algorithm.) The remainder, as defined above, is called the least positive remainder or simply the remainder . [ 2 ] The integer a is either a multiple of d , or lies in the interval between consecutive multiples of d , namely, q ⋅ d and ( q + 1) d (for positive q ).
In this case, the remaining items are allocated among the agents according to their remainders ⌊ ⌋: the agent with the largest remainder receives one seat, then the agent with the second-largest remainder receives one seat, and so on, until all items are allocated. There are several variants of the LR method, depending on which quota is used:
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Jefferson's method uses a quota (called a divisor), as in the largest remainder method. The divisor is chosen as necessary so that the resulting quotients, disregarding any fractional remainders, sum to the required total; in other words, pick a number so that there is no need to examine the remainders. Any number in one range of quotas will ...
The Hare quota is often used to set electoral thresholds and to calculate apportionments under party-list proportional representation when using the largest remainder method. In such cases, the Hare quota gives unbiased apportionments that do not favor either large or small parties. [1]
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