The single transferable vote (STV) is a proportional representation system and also a ranked vote system that elects multiple winners. Under STV, an elector's vote is initially allocated to their first-ranked candidate. Candidates are elected (winners) if their vote tally exceeds the electoral quota. Surplus votes (those exceeding quota) may be transferred from winners to the remaining candidates (hopefuls) according to the surplus ballots' next usable back-up preference.
The system attempts to ensure factions are represented proportionally, without the need for official party lists, by having each winner elected with roughly the same number of votes. There are several variants of the single transferable vote. Each may produce different results.
Voting When using an STV ballot, the voter ranks candidates on the ballot. For example:
Andrea2Carter1Brad4Delilah3Sam
Some, but not all, single transferable vote systems require a preference to be expressed for every candidate, or for the voter to express at least a minimum number of preferences. Others allow a voter just to mark one preference if that is the voter's desire.
The vote will be used to elect just one candidate at the most, in the end.
Quota
The quota (sometimes called the threshold) is the number of votes that guarantees election of a candidate. Some candidates may be elected without reaching the quota, but any candidate who receives quota is elected.
The Hare quota and the Droop quota are the common types of quota.
The quota is typically set based on the number of valid votes cast, and even if the number of votes in play decreases through the vote count process, the quota remains as set throughout the process.
Meek's counting method recomputes the quota on each iteration of the count, as described below.
Hare quota
When Thomas Hare originally conceived his version of single transferable vote, he envisioned using the quota:
The Hare quota is mathematically simple. Its large size means that elected members have fewer surplus votes and thus other candidates do not benefit from as many vote transfers as they would in other systems. Some candidates may be eliminated in the process who may not have been eliminated under systems that transfer more surplus votes. Their elimination may cause a degree of disproportionality that would be less likely with a lower quota, such as the Droop quota.
Droop quota
The most common quota formula is the Droop quota, which is a number larger than this amount:
The Droop quota is always a smaller number of votes than computed by the Hare method.
Because of this difference, under Droop it is more likely that winners achieve the quota rather than being elected as the last remaining candidate after other candidates are eliminated or elected. But in real-life elections, if valid ballots do not require every candidate to be ranked, it is common even under Droop for one or two candidates to be elected with partial quota at the end, as the field of candidates is thinned to the number of remaining open seats and as the valid votes still in play become scarcer.
The use of Droop leaves out about a full quota's worth of votes, either declared exhausted or held by unsuccessful candidates, and thus to be ignored. Unlike a system using the Hare quota and mandatory full marking of the ballot, with STV variants that use optional preferential voting and the Droop quota, a certain percentage of ballots are not used to elect anyone. As a result, the Droop quota is said by some to tend towards disproportionality and to be biased in favor of large parties.
The Droop quota and Hare–Clark electoral system were designed to facilitate a manual counting system. With the introduction of computer-based counting systems, some consider them to be outdated and flawed, failing to reflect the intentions of voters. With the adoption of computer-based technology, a reiterative vote-counting system such as the Wright system may be preferred as it more accurately reflects voters' intentions. Under a reiterative system, there is no need or justification for the use of the Droop quota.
However, most STV systems used in the world use Droop. Many say it is more fair to large parties than Hare. Under Droop, a group consisting of at least half of all voters is guaranteed to win control of at least half of all seats, which is not always the case using the Hare quota. As well, Droopbeing smaller than Haremay give a seat to a smaller party, which is not achieved under Hare.
Counting rules Until all seats have been filled, votes are successively transferred to one or more "hopeful" candidates (those who are not yet elected or eliminated) from two sources: Surplus votes (i.e. those in excess of the quota) of elected candidates (whole votes or all votes at fractional values) All votes of eliminated candidates In either case, some votes may be non-transferable as they bear no marked back-up preferences for any non-elected, non-eliminated candidate.
The possible algorithms for effecting these transfer differ in detail, e.g., in the order of the steps. There is no general agreement on which is best, and the choice of method used may affect the outcome. The steps are:
Compute the quota. Assign votes to candidates by first preferences. Declare as winners all candidates who have achieved at least the quota. Transfer the excess votes from winners, if any, to hopefuls. Repeat 3–4 until no new candidates are elected. (Under some systems, votes could initially be transferred in this step to prior winners or losers. This might affect the outcome.) If these steps result in all the seats being filled, the process is complete. Otherwise: Eliminate one or more candidates, typically either the candidate with the fewest votes or all candidates whose combined votes are less than the votes attained by the next highest candidate. Transfer the votes of the eliminated candidates to remaining hopeful candidates. Return to step 3 and go through the loop until all seats are filled. (The last seat or seats might have to be filled by the few remaining candidates when the field of candidates thins to the number of remaining open seats, even if the remaining candidates have not achieved quota.)
Surplus vote transfers To minimize wasted votes, surplus votes are transferred to other candidates if possible. The number of surplus votes is known, but none of the various allocation methods is universally preferred. Alternatives exist for deciding which votes to transfer, how to weight the transfers, who receives the votes and the order in which surpluses from two or more winners are transferred. Transfers are attempted when a candidate receives more votes than the quota. Excess votes are transferred to remaining candidates, where possible.
A winner's surplus votes are transferred according to their next usable marked preference. Transfers are only done if there are still seats to fill. In some systems, surplus votes are transferred only if they could possibly re-order the ranking of the two least-popular candidates.
In systems where exhausted votes can exist, such as optional preferential voting, if the number of votes bearing a next usable marked preference are fewer than the surplus votes, then the transferable votes are simply transferred based on the next usable preference.
If the transferable votes surpass the surplus, then the transfer is done using a formula (p/t)*s, where s is a number of surplus votes to be transferred, t is a total number of transferable votes (that have a usable next preference) and p is a number of usable next preferences for the given candidate. This is the whole-vote method used in the national elections of Ireland and Malta. Transfers are done using whole votes, with some of the votes that are directed to another candidate left behind with the winner and others of the same sort of votes moved in whole to the indicated candidate. Lower preferences piggybacked on the ballots may not be perfectly random and this may affect later transfers. This method can be made easier if only the last incoming parcel of votes is used to determine the transfer, rather than all of the successful candidate's votes. Such a method is used to elect the lower houses in the Australian Capital Territory (ACT) and in Tasmania.
Under some systems, a fraction of the vote is transferred, with a fraction left behind with the winner. As all votes are transferred (but at fractional value), there is no randomness and exact reduction of the successful candidate's votes are guaranteed. However the fractions may be tedious to work with.
Hare STV and the whole-vote method of transferring surplus votes If the transfer is of surplus received in the first count, transfers are done in reference to all the votes held by the successful candidate.
If the transfer is of surplus received after the first count through transfer from another candidate, transfers are done in reference to all the votes held by the successful candidate or merely in reference to the most recent transfer received by the successful candidate.
Reallocation ballots are drawn at random from those most recently received. In a manual count of paper ballots, this is the easiest method to implement.
Votes are transferred as whole votes. Fractional votes are not used.
This system is close to Thomas Hare's original 1857 proposal. It is used in elections in the Republic of Ireland to Dáil Éireann (the lower chamber), to local government, to the European Parliament, and to the university constituencies in Seanad Éireann (the upper chamber).
This is sometimes described as "random" because it does not consider later back-up preferences but only the next usable one. Through random drawing of the votes to make up the transfer, statistically the transfers often reflect the make-up of the votes held by the successful candidate.
Sometimes, ballots of the elected candidate are manually mixed. In Cambridge, Massachusetts, votes are counted one precinct at a time, imposing a spurious ordering on the votes. To prevent all transferred ballots coming from the same precinct, every th ballot is selected, where is the fraction to be selected.
Wright system The Wright system is a reiterative linear counting process where on each candidate's exclusion, the quota is reset and the votes recounted, distributing votes according to the voters' nominated order of preference, excluding candidates removed from the count as if they had not been nominated.
For each successful candidate that exceeds the quota threshold, calculate the ratio of that candidate's surplus votes (i.e., the excess over the quota) divided by the total number of votes for that candidate, including the value of previous transfers. Transfer that candidate's votes to each voter's next preferred hopeful. Increase the recipient's vote tally by the product of the ratio and the ballot's value as the previous transfer (1 for the initial count.)
Every preference continues to count until the choices on that ballot have been exhausted or the election is complete. Its main disadvantage is that given large numbers of votes, candidates, or seats, counting is administratively burdensome for a manual count due to the number of interactions. This is not the case with the use of computerized distribution of preference votes.
Hare–Clark
This variation is used in Tasmanian and ACT lower house elections in Australia. The Gregory method (transferring fractional votes) is used, but the allocation of transfers is based just on the next usable preference marked on the votes of the last bundle transferred to the successful candidate.