Droop quota
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In the study of electoral systems, the Droop quota (sometimes called the Hagenbach-Bischoff, Britton, or Newland-Britton quota) is the minimum number of votes a party or candidate needs to receive in a district to guarantee they will win at least one seat. It is commonly used in single transferable voting election contests.
The Droop quota is used to extend the concept of a majority to multiwinner elections, taking the place of the 50% plus 1 majority in single-winner elections. Just as any candidate with more than half of all votes is guaranteed to be declared the winner in single-seat election, any candidate with a Droop quota's worth of votes is guaranteed to win a seat in a multiwinner election.
Besides establishing winners, the Droop quota is used to define the number of excess votes, i.e. votes not needed by a candidate who has been declared elected. In proportional quota-based systems such as STV or expanding approvals, these excess votes can be transferred to other candidates to prevent them from being wasted.
The Droop quota was first suggested by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as an alternative to the Hare quota, and later by Swiss physicist Eduard Hagenbach-Bischof (in the context of STV and not for the largest remainder method).
Today, the Droop quota is used in almost all STV elections, including those in Australia, the Republic of Ireland, Northern Ireland, and Malta. It is also used in South Africa to allocate seats by the largest remainder method. Switzerland uses the Droop quota, calling it the Hagenbach-Bischof quota.
Although almost universally applied in STV government elections today, some say the Droop quota has a bias in favor of large parties (popular parties in a district).
Like other forms of STV, STV systems that use Droop have the ability to create no-show paradoxes, situations where a candidate or party loses a seat as a result of receiving more votes. This is done when either that increase leaves fewer votes to another candidate or increases the total number of votes cast and thus shifts the quota. Such changes alter the rank order of candidates, thus the order in which elections and eliminations take place, and often produce changes in who wins. Such paradoxes are said to occur regardless of whether the quota is used with largest remainders or STV. But such charges of no-show paradox is based on having knowledge of how a vote would be transferred if a candidate is eliminated, who may not have been in real life. It is clear that any system that uses ranked votes produces different results if candidates are in different order, which is partly set by how votes are split and therefore that charge can apply to any ranked voting system no matter what quota is used. Some analysis states that no-show paradoxes are extremely rare in real-world elections. For one thing, transfers have little effect in general on whom is elected, the winners usually being among the front runners in the first round of counting anyway.