The core principles of the Single Transferable Vote system were invented independently by Thomas Hare in England and Carl Andrae in Denmark, where it was first used in 1855. In theory a system where votes are transferable means no votes can be wasted. STV is a system of proportional representation and allows voters to vote for an individual candidate rather than party lists. STV is also a form of preferential voting, which means that the voter states their preference for candidates by putting a one beside their favourite candidate, and two beside their second favourite candidate, and so on until all the voter's preferences have been expressed.
A quota will have been set which will state the number of votes any one candidate has to achieve to be elected. Votes are calculated according to voters' first preferences and anyone who achieves the set quota is elected.
If there is still a number of seats to be filled votes are transferred from candidates who have already achieved the quota and the candidate with the least amount of votes. The second preference vote then comes into play. This process of transferring votes then continues until the required number of candidates has been elected.
This system means that if a voter's first preference is not elected, their vote is not wasted, but is moved to their second preference, and if their second preference is not elected, their vote moves to their third preference, so a person's individual vote, in theory, always counts. In Hare's original proposal each voter would have been able to discover which candidate their vote would have ultimately been used for; it was thought that this would help foster a connection between the voters and candidates.
The STV system is now used all over the world, in the US, Canada, Australia, Malta, India and of course, most recently in Scotland's elections in May.