Droop quota

The Droop quota is a type of quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR). In an STV election the quota is the minimum number of votes a candidate must receive in order to be elected. Any votes a candidate receives above the quota are transferred to another candidate. The Droop quota was devised in 1868 by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as a replacement for the earlier Hare quota.

Today the Droop quota is used in almost all STV elections, including the forms of STV used in India, the Republic of Ireland, Northern Ireland, Malta and Australia, among other places. The Droop quota is very similar to the simpler Hagenbach-Bischoff quota, which is also sometimes loosely referred to as the 'Droop quota'.

Calculation

Sources differ as to the exact formula for the Droop quota. As used in the Republic of Ireland the formula is usually written:

$\left({\frac {\text{total valid poll}}{{\text{seats}}+1}}\right)+1$

but more precisely

$\operatorname {Integer} \left({\frac {\text{total valid poll}}{{\text{seats}}+1}}\right)+1$

where:

• ${\text{total valid poll}}$ = Total number of valid (unspoiled) votes cast in an election.
• ${\text{seats}}$ = total number of seats to be filled in the election.
• $\operatorname {Integer} ()$ refers to the integer portion of the number, sometimes written as $\operatorname {floor} ()$

One reason Droop quotas are used more often than Hare Quotas for ranked PR methods is because not only do they often help reduce the amount of vote-counting necessary, but they almost entirely eliminate the possibility of a majority of voters receiving a minority of seats compared to Hare Quotas. The Droop Quota is the smallest possible quota that guarantees that there will be as many quotas as there are winners desired.

When there are 5 seats to be filled and 100 votes cast, the Droop quota is 17 votes, which is calculated as: Integer((100/(5+1)) + 1) = Integer((100/6) + 1) = Integer(~16.667 + 1) = Integer(~17.667) = 17 votes.

In the single-winner case, a Droop quota is a majority. In general, Droop quota-based methods tend to leave at least just under a Droop quota unrepresented. See the utility article, as the debate between Hare and Droop quotas somewhat parallels and generalizes the utilitarianism vs. majority rule debate.