Single transfer voting is a voting system designed to achieve proportional representation in multi-candidate elections. It is used, among other places, for all elections in the Republic of Ireland  and to elect the Australian senate  and the City Council in Cambridge, Massachusetts. The government of Tasmania calls single transfer voting the "Hare system" or the "Hare-Clark system" after Thomas Hare, an English solicitor who developed the system, and Andrew Inglis Clark, a Tasmanian Attorney-General who introduced single tranfer voting into State law .
Each voter ranks all candidates in order of preference. For example:
Setting The threshold
When all the votes have been cast, a winning threshold is set. The goal when setting the threshold is to find the minimum level of support a candidate needs in order to be elected while not allowing more candidates to be elected than there are seats to be filled. One common formula for the threshold is (Votes/(Seats+1))+1, but there are many others.
Counting The Votes
Process A: Top-preference votes are tallied. If one or more candidates have received more votes than the threshold, they are declared elected. After a candidate is elected, they may not receive any more votes.
The excess votes for the winning candidate are reallocated to the next-highest ranked candidates on the ballots for the elected candidate. There are different methods for determining how to reallocate the votes. Some versions use random selection, others count each ballot fractionally.
Process A is repeated until there are no more candidates who have reached their threshold.
Process B: The candidate with the least support is eliminated, and their votes are reallocated to the next-highest ranked candidates on the eliminated ballots. After a candidate is eliminated, they may not receive any more votes.
After each iteration of Process B is completed, Process A starts again, until all candidates have been elected or eliminated.
An example =
2 seats to be filled, four candidates: Andrea, Brad, Carter, and Delilah.
5 voters rank the candidates:
17 voters rank the candidates:
8 voters rank the candidates:
The threshold is: (30/(2+1))+1, or 11.
In the first round, Andrea recieves 22 votes and Delilah 8. Andrea is elected with 11 excess votes. Her votes are reallocated by lottery, and 8 of the reallocated votes are for Carter, 3 for Brad.
As none of the candidates have reached their threshold, Brad, the candidate with the fewest votes, is eliminated. All of his votes have Carter as the next-place choice, and are reallocated to Carter. This gives Carter 11 votes and he is elected.
Potential for Tactical Voting
Single Transfer voting eliminates much of the reason for tactical voting. A voter is "safe" voting for a candidate they fear won't be elected, because their vote will be reallocate in Process B. They are "safe" voting for a candidate they believe will receive overwhelming support, because their vote will get reallocated in Process A.
However, there are loopholes: candidates who have already been elected do not receive any more votes, so there is incentive to avoid voting for your top-ranked candidate until after they have already been elected. For example, a voter might make a tactical decision to rank their top-place candidate beneath a candidate they know will lose (perhaps a fictional candidate). If the voter's true top-place candidate has not been elected by the time their fake top candidate loses, the voter's full vote will count for their true top-place candidate. Otherwise, the voter will have avoided having had their ballot in the lottery to be "wasted" on their top-ranked candidate, and will continue on to lower-ranked candidates.