single transferrable vote

This form of proportional representation is also called preference voting and is practised in a few countries, including Australia and Ireland. In Ireland the system involves multi-seat constituencies, so it works on the basis of a quota rather than a simple majority. The quota for each constituency is calculated according to the following formula:

Quota = (Total Valid Poll / (Number of seats + 1) ) + 1

If no candidate reaches the quota, the lowest candidate(s) are eliminated as described above. However, if a candidate surpasses the quota, he/she is elected, and his/her surplus votes are distributed to the next choice on each ballot.

It takes forever to count, but allows for a truly representative democracy.

The following is a summary of the arguments in favour of PR/STV taken from http://www.electoral-reform.org.uk:

• STV does more than other systems to guarantee that everyone gets their views represented in parliament and that they have a say in what is done by their elected representatives. STV is the best option for:
  • Putting the power in the hands of the voters.
  • Keeping MPs linked to the people who voted for them. Most voters can identify a representative that they personally helped to elect and can feel affinity with. Such a personal link also increases accountability.
  • Making parliament reflect the views of the voters.
• Only a party or coalition of parties, who could attract more than 50% of the electorate could form a government. Any changes would have to be backed by a majority since public opinion is reflected fairly in elections under STV. This is far more important than that a government should be formed by only one political party.
• It enables the voters to express opinions effectively. Voters can choose between candidates within parties, demonstrating support for different wings of the party. Voters can also express preferences between the abilities or other attributes, of individual candidates.
• It is simple for voters to use.
• There is no need for tactical voting . Voters can cast a positive vote and know that their vote will not be wasted whatever their choice is.
• It produces governments that are strong and stable because they are founded on the majority support of the electorate.

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.

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