Single Transferable Votes - How do they work?
As ryano mentioned above, in a multi-seat constituency, the quota is calculated based on the number of seats and the actual valid (unspoiled) poll. When a candidate reaches this quota, he/she is deemed elected, and their surplus votes are redistributed according to the next preferences on the ballots.
Let's have a bit more detail. In Ireland, the ballot paper has a list of the candidates, in alphabetical order, along with their party affiliation and a mug shot (so it's easy to vote even if you're barely literate!), and a little box on the right-hand-side. To vote, you write "1" in the box corresponding to your first choice candidate, "2" in the box corresponding to your second choice, and so forth. You may fill in as many or as few as you like. When you cast your vote this way, you are telling the returning officer that if your number one candidate is elected or eliminated, your vote should be transferred to your number two candidate. Likewise, if your second choice candidate is elected/eliminated, your vote will be passed on to your third choice.
Bear with me now, this is where things get tricky.
When a candidate exceeds the given quota, his/her surplus votes may be redistributed according to the next preferences. This is done by firstly sorting all their votes into piles transferrable to the other candidates, and a separate pile for non-transferrables. If votes are transferrable to a candidate who has already been elected or eliminated, they are placed in the pile corresponding to the next preference, or the non-transferrables pile, where no next preference is stated. Next, each remaining candidate receives votes equivalent to the elected candidate's surplus (say S) divided by the total number of transferable votes (i.e. the total number of votes received by the elected candidate that can be transferred - say TT), all multiplied by the number of transferable votes that are for the given candidate (TC).
So, let's recap slightly.
The scenario is:
- Candidate A exceeds the quota, and is deemed elected.
- Candidate A exceeded the quota by S votes.
- Of Candidate A's votes, a total of TT are transferrable; i.e. the caster stated a preference for another candidate lower down than Candidate A.
- A total of TC of Candidate A's votes state Candidate B as their next preference.
- Therefore, Candidate B receives ( S / TT ) * TC transferred votes from Candidate A.
If a candidate is eliminated, all of his/her transferrable votes are transferred to their stated next preference. As can be imagined, all this counting is a fairly long and arduous task, as the counting is all still done by hand, apart from three constituencies in which electronic voting was implemented for the 2002 election
The counting of the votes is divided into separate counts. In the first count, the first preferences are counted; those candidates who exceed the quota are elected, and the bottom candidate is eliminated. If, following several counts, all seats are not filled, but the number of remaining candidates is equal to the number of vacant seats, they are deemed elected, even if they haven't reached the quota.
Some information taken from http://www.ireland.com/focus/election_2002/voting/voting1.htm