I've heard that some elections use single transferable vote. What is this and how does it work? How does it differ from a standard majority vote election?
The single transferable vote (STV) is a system where you can vote for more than one option at the same time, but in a ranked fashion.
Your vote is first allocated to your first preference but if that doesn't meet the threshold for the next round is then allocated to your next-highest preference that is still in the run.
Given the following situation: We have 5 candidates (A through E) and 20 voters that need to pick 3 winners.
The following votes have been casted:
Votes 4 2 8 4 1 1 Pref 1 A B C C D E Pref 2 / A D E / /
The first step is to calculate the threshold needed for a choice to be win. In this case this is ((20 votes cast/(3 winners + 1)) + 1) = 6.
We then get the following counting of the votes:
Candidate A B C D E Rnd 1 4 2 8 + 4 1 1 Candidate C is the first winner as 12 > 6 Rnd 2 4 2 6 5 3 The surplus votes from C to the second choices. As no candidate reaches 6, B with the fewest votes is eliminated. Rnd 3 6 / 6 5 3 B's votes are distributed to the second preference. A reaches the threshold exactly, thus leaving no surplus to distribute. Rnd 4 6 / 6 5 3 None of the remaining candidates D or E reach the threshold, so the 3rd winner is D with the most votes over E.
The result yields as winners: A, C and D
In a traditional standard majority system, you would have had to organize three distinctive election rounds while with STV you could do it all with one ballot and one voting round.
"Single transferable vote" is a fairly apt name -- you still get one vote, but the system attempts to maximize its efficiency by transferring the vote between candidates, instead of just sticking you with whomever your top choice was.
To do this, STV requires that you fill out a ranked ballot, sorting the candidates from most- to least-liked. To start with, everyone's #1 choice gets 1 vote, and the scores are summed. It's possible depending on the votes and the threshold for winning (which varies depending on the type of STV in use) that one person has enough votes to win. If they do and this is a single-seat election, that's it. If not:
If there is a winner but the election is for multiple seats, the person who is over the threshold wins one of the seats. However, they might have more votes than they needed, and STV doesn't like wasting votes. It takes as many votes as it can from the winner (without dropping them under the threshold) and redistributes them to the remaining candidates (how this redistribution is decided also varies depending on the type of STV). This is why the voters need to select multiple options. Then we go back to the top and see if another person has crossed the threshold
If there are still empty seats but nobody has enough votes to win one, we eliminate the person in last place and redistribute 100% of their votes to the remaining candidates, just like we do with the excess votes for the winner. Then we see if anybody has won
You can see many examples of STV on Stack Exchange itself -- Meek STV is used to decide moderator elections. STV avoids many of the problems with plurality voting (see What are the disadvantages of first-past-the-post electoral systems?), while still remaining relatively simple. It's not even necessary to fill out the entire ballot (Stack Exchange only requires you select your top three choices), although with a large enough election or poor enough choices you run the risk of your vote not counting because none of your candidates made it to the end