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^[1][a]) is the minimum number of votes needed for a party or candidate to guarantee they will win at least one seat in a legislature.^[3][4]

The Droop quota generalizes the concept of a majority to multiwinner elections. Just as a candidate with a majority (any number exceeding half of all votes) is guaranteed to be declared winner in a one-on-one election, a candidate who holds more than one Droop quota's worth of votes at any point is guaranteed to win a seat in a multiwinner election.^[4]

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-rule systems such as STV or expanding approvals, these excess votes can be transferred to other candidates, preventing them from being wasted.^[4]

The Droop quota was first suggested by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as an alternative to the Hare quota.^[4] Eduard Hagenbach-Bischoff also wrote on the quota in 1888, in his study entitled Die Frage der Einführung einer Proportionalvertretung statt des absoluten Mehres. (Both were clear that their quota was some number just larger than votes/seats plus 1, As Droop put it, "the whole number next greater than the quotient obtained by dividing mV, the number of votes, by n + 1, will be called the quota.")^[5][6]

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.^[4]

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