# Electoral quota

In proportional representation systems, an electoral quota is the number of votes a candidate needs to be guaranteed election.

## Admissible quotas

An admissible quota is a quota that is guaranteed to apportion only as many seats as are available in the legislature. Such a quota can be any number between:
${\frac {\text{votes}}{{\text{seats}}+1}}\leq {\text{quota}}\leq {\frac {\text{votes}}{{\text{seats}}-1}}$

## Common quotas

There are two commonly-used quotas: the Hare and Droop quotas. The Hare quota is unbiased in the number of seats it hands out, and so is more proportional than the Droop quota (which tends to be biased towards larger parties); however, the Droop quota guarantees that a party that wins a majority of votes in a district will win a majority of the seats in the district.

### Hare quota

The Hare quota (also known as the simple quota or Hamilton's quota) is the most commonly-used quota for apportionments using the largest remainder method of party-list representation. It was used by Thomas Hare in his first proposals for STV. It is given by the expression:
${\frac {\text{total votes}}{\text{total seats}}}$
On average, the Hare quota gives no advantage to larger or smaller parties. Specifically, the Hare quota is unique in being unbiased in the number of seats it hands out. This makes it more proportional than the Droop quota (which is biased towards larger parties).
However, it is sometimes possible for larger parties to manipulate the Hare quota in their favor by running each candidate on their own party list. Because a single Droop quota's worth of votes is enough to guarantee a candidate will win one of the remainder seats, this strategy allows the large party to win the seats more cheaply (at the cost of only a single Droop quota), restoring the imbalance in favor of larger parties. The difficulty of this strategy increases with the number of seats and the electoral threshold.

### Droop quota

The Droop quota is used in most single transferable vote (STV) elections today and is occasionally used in elections held under the largest remainder method of party-list proportional representation (list PR). It is given by the expression:
    ${\frac {\text{total votes}}{{\text{total seats}}+1}}$
It was first proposed in 1868 by the English lawyer and mathematician Henry Richmond Droop (1831–1884), who identified it as the minimum amount of support needed to secure a seat in semiproportional voting systems such as SNTV, leading him to propose it as an alternative to the Hare quota.
However, the Droop quota has a substantial seat bias in favor of larger parties; in fact, the Droop quota is the most-biased possible quota that can still be considered to be proportional.
Today the Droop quota is used in almost all STV elections, including those in India, the Republic of Ireland, Northern Ireland, Malta, and Australia.

### Uniform quota

In some implementations of STV, a "uniform quota" has been set by law as a fixed number of votes (rather than being specified as a percentage of all votes). Candidates reaching the quota are elected, with their surplus transferred away. This system was used in New York City from 1937 to 1947. Under such a system, the number of representatives varies from election to election depending on voter turnout, as a higher turnout allows more candidates to reach the quota. Seats were allocated to each borough in proportion to voter turnout (rather than population). Across its history, New York City's total seats on council varied from 17 to 26 depending on turnout.