Largest remainder method

The largest remainder method (also known as Hare-Niemeyer method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with the highest averages method.

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 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 Hare (or simple) Quota is defined as follows

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. It is used for legislative elections in Russia (with a 7% exclusion threshold since 2007), Ukraine (5% threshold), Tunisia,Namibia and Hong Kong.

...
Wikipedia