Concept
The largest remainder method (also known as Hare–Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with various highest averages methods (also known as divisor methods). The largest remainder method requires the numbers of votes for each party to be divided by a quota representing the number of votes required for a seat (i.e. usually the total number of votes cast divided by the number of seats, or some similar formula). The result for each party will usually consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer. This will generally leave some remainder seats unallocated: the parties are then ranked on the basis of the fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all the seats have been allocated. This gives the method its name. There are several possibilities for the quota. The most common are: the Hare quota and the Droop quota. The use of a particular quota with the largest remainders method is often abbreviated as "LR-[quota name]", such as "LR-Droop". The Hare (or simple) quota is defined as follows It is used for legislative elections in Russia (with a 5% exclusion threshold since 2016), Ukraine (5% threshold), Bulgaria (4% threshold), Lithuania (5% threshold for party and 7% threshold for coalition), Tunisia, Taiwan (5% threshold), Namibia and Hong Kong. The Hamilton method of apportionment is actually a largest-remainder method which uses the Hare Quota. It is named after Alexander Hamilton, who invented the largest-remainder method in 1792. It was first adopted to apportion the U.S. House of Representatives every ten years between 1852 and 1900. The Droop quota is the integer part of and is applied in elections in South Africa. The Hagenbach-Bischoff quota is virtually identical, being either used as a fraction or rounded up.
