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 will win at least half of all seats in a legislature.

Hare quota
The Hare quota (also known as the simple quota or Hamilton's quota) is the most common the largest remainder method of party-list proportional representation. It was used by Thomas Hare in his first proposals for STV. It is given by the expression:

$$\frac{\text{total votes}}{\text{total seats}}$$

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).

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 cumulative voting. This led him to propose it as an alternative to the Hare quota.

Today the Droop quota is used in almost all STV elections, including those in India, the Republic of Ireland, Northern Ireland, Malta, and Australia.