Voters rank the candidates in order of preference, with "1" being the highes (most preferred) ranking. For example, if there are 3 candidates, the voter chooses 1 beside their first choice, 2 beside their second choice and 3 beside their third choice.
The difference between a regular preferential votes and STV is the number vacancies. The basic preferential vote has one vacancy ( single seat); when multiple vacancies exist, STV is used to tally the votes. With multiple vacancies, during the tally, surplus votes are "transferred", based on the ranking assigned to the candidates at the time of voting, in order to ensure that all vacancies are filled. To transfer votes, The Voting Vault uses the Meek's STV Method. This will be explained in more detail in "How the Results are Calculated".
Results are calculated throught the process of redistributing the votes and eliminating low ranked candidates in rounds to try and get a candidate across the quota of votes required to win. To generate a quota, the total number of submitted votes in an election is divided by the number of available vacancies for the position plus one. Then, 1/10 is added to that quotient, and the result is truncated to 9 decimals places. For example, if we have 115 votes cast in an election where the position up for election has three vacancies:
In the first round of tallying, first preference of each ballot count as a vote for that particular candidate. Any candidate who has at least the minimum number of votes required, as dictated by the quota, is automatically consider a "winner". In our above example, the candidate would need to have at least 28, 750000011 vote to win.
If there is at least one candidate who surpassed the quota, then their surplus votes are transferred. If no candidates surpass the quota, the candidate with the fewest votes is eliminated, and their votes are transferred to other candidates. If candidates are tied for last place, then a candidate is randomly selected for elimination.
The quota can change if a vote is "exhausted". A vote becomes exhausted in the event that the voter has not indicated a different candidate to transfer their vote to, or all of their vote to be transferred to, then once their final ranked candidate is eliminated, the vote's vote is eliminated with the candidate. This affects the quota because if affects the numerator of the quota formula: the total number of votes cast is decreasing.
No matter whether the votes are coming from an eliminated candidate, or from surplus votes from a candidate above quota, the transferring process is the same. Votes are transferred to the next highest-ranked candidate, as indicated by the voter. However, there is big difference between transferring surplus votes, and tranferring votes from an eliminated candidate. When a candidate is their votes are redistributed. Depending on which votes are consider "surplus", the outcome for other candidates can change: if two voters' ballots are consider "surplus". To solve this problem, fractions are used to determine the outcome, which keeps the vote distribution fair and unbiase for all candidates.
In the above example, imagine a candidate receive 32votes, over 3 greater than the quota of 28.750000001 votes. That candidate has a little over 3 surplus votes to be distributed (32-28.750000001=3.249999999). The surplus votes are transferred at 3.249999999/32, or 0.101562499, of their value. After all votes have been redistributed, 3.249999999 total votes were transferred.
The Voting Vault uses Meeks' STV to transfer votes. The candidate who have hit quota continue to be apart of the receiving and transferring of votes. Each candidate is assigned a keep factor that indentifies how much of the votes receive should be transferred away. So, any candidate under quota will have a keep factor of less than one, because their votes will always have a portion transferred away to keep them at quota, the voter's votes are always going to their intended candidates, even through a portion of that vote may be transferred away.