CGP Grey published an excellent explanation of Single Transferable Vote, as well as a walkthrough of an STV election. Single Transferable Vote allows a large number of variations, including quotas and transfer methods; we suggest the Meek transfer method, shown here using the typical Droop quota.
The Meek method involves highly-complex math to achieve a simple outcome: voters each begin with one vote to cast and essentially pool together to “pay” for any elected candidate. If they only need half of the votes to do so, then each voter retains one-half of one vote to continue down the election.
Meek uses a more-complex approach to achieve fairness and avoid election manipulation—an unfortunate necessity for voting methods which elect fairly and resist manipulation, and one extended further with Schulze STV. Other approaches include selecting the losing candidate by a Condorcet method such as Schulze, counting losses instead of wins to elect the worst loser each round.
To illustrate, let’s imagine an election selecting two winners from three candidates who we’ll call Bernie, Warren, and Clinton. Using ranked ballots, the initial tally shows the below:
Above, we see voters elect a candidate with one-third of the votes, as per the Droop quota. Warren receives a full half of the votes, and so is elected. Seen above, the second-ranked choices on all Warren’s ballots went 40% to Bernie and 60% to Clinton.
First, only two-thirds of the votes cast for Warren were necessary, and the other one-third are excess. Therefor the voters have each expended two-thirds of a vote to elect Warren, leaving them one-third of a vote unused. Those votes transfer to the next candidate on each voter’s ballot.
After this transfer, no candidate reaches the winning quota. The candidate receiving the fewest votes—in this case Bernie, who is similar to Warren but a little too extreme for those voters who simply want a more-progressive Clinton—is eliminated, and the votes all move directly to the next choice marked on each ballot.
Because the candidate did not win, the full voting power of each ballot transfers: Warren-Bernie ballots transfer their remaining third of a vote, while Bernie-Clinton and Bernie-Warren-Clinton ballots transfer a whole vote. Under Meek transfers, votes passing through Warren as an immediate next choice are slightly-diminished in voting power, and the threshold of votes required to win is similarly lowered so that more Warren votes transfer each round. This improves voter representation at the cost of some complex math.
As shown above, some Bernie voters simply ranked only Bernie, or ranked Bernie and then Warren; these ballots cast no vote for any other candidate: a vote for a losing candidate is not necessarily a vote for the winning candidate. Clinton receives the Bernie-Clinton ballots, and also receives the Bernie-Warren-Clinton ballots.
In this example, the same results occur with unaltered excess votes transferred in full: Clinton has enough votes to win a seat, while Bernie comes up short. The situation essentially reflects voter choice: a strong first-preference win transfers a large portion of the vote; while a first-preference split places full votes on each candidate and weakens the transferred votes from the first winner. The outcomes from either situation remain similar.
This property of effectively “spending” a portion of a vote makes STV with Meek transfers an excellent method for electing multiple candidates, such as State Delegates and Central Committee members. Voters retain much of their voting power when electing popular candidates; and their votes are essentially removed from the race after electing a candidate with weak plurality support—a candidate who would get the most votes in a single-seat election, but only barely enough to make the STV quota.
In this way, you get proportional results: a slim majority and a large minority will elect one candidate each, rather than two or three or five candidates all chosen by the narrowest majority even if the large minority strongly-opposes every candidate elected.
In single-seat elections, STV with Meek transfers provides an excellent way to ensure voter choice with Smith- and Condorcet-compliant rule sets. Because political parties may span a broad range of ideological views, voters are best served when each party may nominate two or three candidates. Primary elections using STV with Meek transfers tend to elect from the ideological span of the party, rather than selecting similar candidates to represent a diverse voting base. The general election then avoids an enormous list of candidates, while providing the diversity of choice required for voters to obtain broad consensus in representation.