Electoral quota explained

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:

	votes
	seats+1

\leqquota\leq

	votes
	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);^[1] 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.^[2]

Hare quota

See main article: 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:

	totalvotes
	totalseats

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).

The Hare quota gives no advantage to larger or smaller parties.^[3] However, in small legislatures with no threshold, the Hare quota can be manipulated by running candidates on many small lists, allowing each list to pick up a single remainder seat.^[4]

Droop quota

See main article: 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:^[5]

	totalvotes
	totalseats+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.^[6]

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.

References

Book: Lijphart, Arend . Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990 . Oxford University Press . 1994 . Appendix A: Proportional Representation Formulas . https://janda.org/c24/Readings/Lijphart/Lijphart.html.
Book: Balinski . Michel L. . Fair Representation: Meeting the Ideal of One Man, One Vote . Young . H. Peyton . Yale University Press . 1982 . 0-300-02724-9 . New Haven . registration.
Web site: Notes on the Political Consequences of Electoral Laws by Lijphart, Arend, American Political Science Review Vol. 84, No 2 1990 . dead . https://web.archive.org/web/20060516204603/http://users.ox.ac.uk/~sann2300/041102-ceg-electoral-consequences-lijphart.shtml . 2006-05-16 . 2006-05-16.
See for example the 2012 election in Hong Kong Island where the DAB ran as two lists and gained twice as many seats as the single-list Civic despite receiving fewer votes in total: New York Times report
Woodall . Douglass . Properties of Preferential Election Rules . Voting Matters . 3.
Henry Richmond Droop, "On methods of electing representatives" in the Journal of the Statistical Society of London Vol. 44 No. 2 (June 1881) pp.141-196 [Discussion, 197-202], reprinted in Voting matters Issue 24 (October 2007) pp.7–46.