In the study of electoral systems, the Droop quota (sometimes called the Hagenbach-Bischoff or Newland-Britton quota^{[lower-alpha 1]}) is the minimum number of votes needed for a candidate to be elected under STV systems used today. It is the preferred quota, being known to be less likely than the Hare quota, to give majority of seats to a minority party.^[1] It is the smallest portion of votes that elects the correct number of members to fill the seats, but no more than that number.

This article includes a list of general references, but it lacks sufficient corresponding inline citations. (May 2010)

Droop quota is the number obtained by dividing the total number of valid votes cast in a district by a number that is one more than the number of places to be filled (members to be elected) and increasing the result to the next whole number.

With each successful candidate having a vote tally equal to the quota, each party will receive its due share of seats, as much as the number of seats in the district can allow anyway. (Of course in STV elections, in odd exceptions candidates will be elected with more or less than quota.)

The Droop quota generalizes the concept of a majority to multiple-winner elections: just as a majority (more than half of votes) guarantees a candidate can be declared the winner of a one-on-one election, having more than one Droop quota's worth of votes measures the number of votes a candidate needs to be guaranteed victory in a multiwinner election.

Besides establishing winners, the Droop quota is used to define the number of excess votes, votes not needed by a candidate who has been declared elected. In proportional quota-rule systems such as STV and CPO-STV, these excess votes are transferred to other candidates, preventing them from being wasted.

The Droop quota was first devised by the English lawyer and mathematician Henry Richmond Droop (1831–1884), as a replacement for the Hare quota.

Today the Droop quota is used in almost all STV elections, including those in the Republic of Ireland, Northern Ireland, Malta, and Australia.^{[citation needed]} It is also used in South Africa to allocate seats by the largest remainder method.^{[citation needed]}

The exact form of the Droop quota for a ${\displaystyle k}$-winner election is given by the formula:^{[lower-alpha 2]}

$${\displaystyle {\frac {\text{total votes}}{k+1}}}$$

plus 1 (or rounded up to next whole number).

In the case of a single-winner election, this reduces to the familiar simple majority rule. Under such a rule, a candidate can be declared elected as soon as they have strictly more than 50% of the vote, i.e. ${\textstyle {\frac {\text{total votes}}{2}}}$.

Sometimes, the Droop quota is written as a share (i.e. percentage) of the total votes, in which case it has value 1⁄k+1.

Any candidate who attains quota or exceeds it is declared elected.

The following election has 3 seats to be filled by single transferable vote. There are 4 candidates: George Washington, Alexander Hamilton, Thomas Jefferson, and Aaron Burr. There are 102 voters, but two of the votes are spoiled.

The total number of valid votes is 100, and there are 3 seats. The Droop quota is therefore ${\textstyle {\frac {100}{3+1}}=25}$, plus 1 = 26. These votes are as follows:

First preferences for each candidate are tallied:

• Washington: 45 Y
• Hamilton: 10
• Burr: 20
• Jefferson: 25

Only Washington has strictly more than 25 votes. As a result, he is immediately elected. Washington has 19 excess votes that can be transferred to their second choice, Hamilton. The tallies therefore become:

• Washington: 26 Y
• Hamilton: 29Y
• Burr: 20
• Jefferson: 25

Hamilton is elected, so his excess votes are redistributed. Thanks to Hamilton's support, Jefferson receives 29 votes to Burr's 20 and is elected.

Sometimes there may be a tie between two candidates. The tiebreaking rules are discussed below.

• List of democracy and elections-related topics