Largest Remainder Method - Quotas

Quotas

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 is used for legislative elections in Russia (with a 7% exclusion threshold since 2007), Ukraine (3% threshold), Namibia and Hong Kong. It was historically applied for congressional apportionment in the United States during the 19th century.

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.

The Hare quota tends to be slightly more generous to less popular parties and the Droop quota to more popular parties, and can arguably be considered more proportional than Droop quota although it is more likely to give fewer than half the seats to a list with more than half the vote.

The Imperiali quota

is rarely used since it suffers from the defect that it might result in more seats being allocated than there are available (this can also occur with the Hagenbach-Bischoff quota but it is very unlikely, and it is impossible with the Hare and Droop quotas). This will certainly happen if there are only two parties. In such a case, it is usual to increase the quota until the number of candidates elected is equal to the number of seats available, in effect changing the voting system to the Jefferson apportionment formula (see D'Hondt method).