How a candidate is elected for one vacancy

If there is only one position available (e.g. a mayoralty) and there are only two candidates, the election will always be decided on the first preference votes, in just the same was as a first-past-the-post election.

If there is only one position available, and more than two candidates, STV works like this:

Setting the quota

The quota needed to get elected in an election for one position is half the votes being counted. (technically, half the votes, plus a fraction). The quota is recalculated whenever votes can’t be transferred (for example because the vote expresses only one preference, and the voting has progressed to second preferences).

Deciding an outcome on the count of first preferences

If a candidate gets more than half the first preference votes, that candidate will be elected. Votes will not need to be transferred to second and later preferences to decide the outcome because a candidate has already reached the quota.

Deciding an outcome if no one wins on the count of first preferences

If there are more than two candidates for a single position, it may be necessary to go only to second-preference candidates to decide a winner. This is done by eliminating the lowest-polling candidate and distributing the second-preference votes of those who supported that candidate to other candidates. After this is done, if the vote for one of the candidates is higher than the quota, that candidate is elected.

However, even after the second preferences of the lowest-polling candidate are distributed, it may be that no candidate has reached the quota. If this is the case, the next-lowest-polling candidate is eliminated, and the second-preference votes of that candidate are allocated to those who have not been eliminated. But some of those second-preference votes may be for the candidate who was eliminated first. In this case, these votes are allocated to the third preferences of those voters.

This continues until a candidate reaches the quota. The computer system used ensures that the order in which votes are counted does not affect the outcome.

Equal votes
If, on any count, two or more candidates have an equal number of votes and one of them has to be excluded, the electoral officer determines which candidate had the fewest votes the first time the candidates' totals were different and excludes the candidate with the lowest total votes.

Ties
If the candidates had an equal number of votes at all stages of the count, a random (or pseudo-random) process is used to choose which candidate is excluded.

Example one

One position
Two candidates
10,000 votes
5,500 first preferences for candidate A
4,500 first preferences for candidate B
the quota is
10,000 divided by (1+1) = 5,000
5,500 is greater than 5,000 therefore

Candidate A is elected. There is no need to include second preferences.

Example two

One position
Four candidates
10,000 votes
5,250 first preferences for candidate A
3,500 first preferences for candidate B
750 first preferences for candidate C
500 first preferences for candidate D
the quota is;
10,000 divided by (1+1) = 5,000
5,250 is greater than 5,000 therefore

Candidate A is elected. There is no need to include second preferences.

Example three

One position
Four candidates
10,000 votes
3,500 first preferences for candidate A
2,500 first preferences for candidate B
3,000 first preferences for candidate C
1000 first preferences for candidate D
the quota is
10,000 divided by (1+1) = 5,000
No candidate’s first preference vote is greater than 5,000 therefore
The lowest polling candidate (D) drops off and the second preferences of the 1000 voters who voted for that candidate are distributed among the 3 remaining candidates. This results in:

4,000 first preferences plus redistributed votes for candidate A
2,750 first preferences plus redistributed votes candidate B
3,250 first preferences plus redistributed votes for candidate C
0 for candidate D, as all votes for this candidate have been redistributed

No candidate’s first preference vote is greater than 5,000 therefore
The lowest polling candidate drops off and the second preferences of those who voted for that candidate are distributed among the 3 remaining candidates. Where the second preferences were for candidate D, who has already been excluded, third preferences are distributed. This results in

5,750 first preferences plus redistributed votes for candidate A
0 for candidate D, as all votes for this candidate have been redistributed
4,250 first preferences plus redistributed votes for candidate C
0 for candidate D, as all votes for this candidate have been redistributed

5,750 is more than 5,000, therefore:

Candidate A is elected.

NOTE: For elections with more than four candidates for a single position, the process continues in the same way until a candidate reaches the quota.