Counting Single Transferable Votes

The single transferable vote (STV) is a voting system based on proportional representation and preferential voting. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or unused votes are transferred according to the voter's stated preferences. The system minimizes "wasted" votes, provides approximately proportional representation, and enables votes to be explicitly cast for individual candidates rather for than closed party lists.There are many ways to count votes in Single Transferable Vote elections.

There are a variety of algorithms (methods) which can be used to carry out these transfers. This article explores these methods.

Voting

When using an STV ballot, the voter's preferences are set out on the ballot paper.

Each voter ranks all candidates (or some of them) in order of preference. For example:

Choice of quota

The quota (sometimes called the threshold) is the number of votes a candidate must receive to be elected. Two common formulae used to determine the quota are the Hare quota and the Droop quota.

Hare quota

When Thomas Hare originally conceived his version of Single Transferable Vote, he envisioned using the quota:



It will be seen that (except in the extremely unlikely event that each successful candidate receives exactly the same number of votes) there will not be enough candidates who meet the quota to fill the available seats....
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