The Droop quota is the minimum number of votes a candidate needs to be elected under STV.

Formula:

• The floor function means you discard any fractional part.

• This ensures that no more candidates can reach the quota than there are seats available.

Why the “+1”?

The “+1” guarantees that only the number of candidates equal to the number of seats can be elected. If you didn’t add 1, it’s theoretically possible for more candidates to exceed the threshold than there are seats.

Example

Say there are 13,456 valid votes and 4 seats:

Apply the floor function:

Then add 1:

Why It Matters

This calculation:

• Prevents over-election

  • This means that only the exact number of candidates needed can reach the quota.

For example, if there are 3 seats to fill, the Droop quota ensures no more than 3 people can meet the quota and get elected outright. Without this feature (e.g. using the Hare quota), it’s possible that more than 3 candidates might mathematically exceed the quota, which would break the system.

• Maximises vote effectiveness

  • Every vote contributes to the election of a candidate. The Droop quota ensures that:

    A vote helps elect someone if its first preference meets the quota.

    Surplus votes (i.e. above the quota) are transferred to help elect another candidate based on the voter’s next preferences.

    So instead of “wasting” votes, the system redistributes them, making as many votes count as possible.

• Ensures proportionality in multi-seat contests

  • In multi-member wards or councils, the idea is that different groups of voters get representation that reflects their actual size.

    For instance:

    If 30% of voters back one group of candidates, they should ideally win about 30% of the seats.

    STV with the Droop quota lets minority and majority voices both gain representation, instead of “winner takes all.”

Dunstan Regional Constituency – STV Quota Calculation

There are 3 vacancies (seats to be filled), and the total number of valid votes is the key starting point.

Provided Numbers:

Step 1: Calculate Valid Votes

To calculate the quota, we must exclude informal and blank votes.

Valid votes = Total votes − Informal − Blank
Valid votes = 46,596 − 102 − 1,439 = 45,055

Step 2: Apply the Droop Quota Formula

The Droop Quota formula used in STV is:

Plug in the values:

Now we round down to the nearest whole number, as per STV rules.

Quota = 11,264

Conclusion:

To be elected in this STV election for Dunstan Constituency, a candidate must receive at least 11,264 valid votes.

Rounding:

The Droop formula always uses the floor function, meaning:

Round down to the nearest whole number, even if it's .999.