Formula
Sources differ as to the exact formula for the Droop quota. As used in the Republic of Ireland the formula is usually written:
- Total Valid Poll = Total number of valid (unspoilt) votes cast in an election.
- Seats = Total number of seats to be filled in the election.
(The extra parentheses, while not strictly necessary from a mathematical standpoint, are often included in order to make the formula seem less ambiguous to non-mathematicians—if calculated out of sequence, an incorrect result would be arrived at, producing an incorrect quota.) It is important to use the Total Valid Poll, which is arrived at by subtracting the spoiled and invalid votes from the total poll.
The Droop quota is the smallest number that guarantees that no more candidates can reach the quota than the number of seats available to be filled. Simply put, the Droop quota is the number without its "decimal part". This gives the Droop quota the special property that it is the smallest integral quota which guarantees that the number of candidates able to reach this quota cannot exceed the number of seats. In a single winner election, in which STV becomes the same as Instant Run-off Voting, the Droop quota becomes a simple integral majority quota–that is, it will be equal to an absolute majority of votes.
While in theory every STV election should see the right number of candidates elected through reaching the quota, in practice many voters may only vote for a small proportion of the candidates on the ballot paper, such as only those candidates from one party, or even only one candidate. Those votes are known as 'NTs', or 'non transferable votes', and the effect of their removal from the total valid poll may be to reduce the total number of votes available to such an extent that the last candidate left in a race may not actually have enough votes to reach the quota. Nevertheless, in reality, as no other candidate may mathematically be able to overtake them as the candidate nearest to the quota, they may in such circumstances be deemed elected "without reaching the quota". The quota is in fact constructed to ensure that it is mathematically impossible for candidates to achieve the quota beyond the number of available seats.
Read more about this topic: Droop Quota
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