Droop quota

In the study of electoral systems, the Droop quota (sometimes called the Hagenbach-Bischoff quota) is the minimum number of votes needed for a party or candidate to guarantee themselves one extra seat in a legislature. It 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.

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Besides establishing winners, the Droop quota is used to define the number of excess votes (votes not needed for a candidate to be ensured victory). In proportional systems such as STV, CPO-STV, and proportional approval (or score) voting, 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 an improvement to the earliest proposals for the single transferable vote (using the Hare quota). It was later independently used by Swiss physicist Eduard Hagenbach-Bischoff in the calculation of divisors for the D'Hondt method.

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

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