The single transferable vote (STV) or proportional-ranked choice voting (P-RCV), also known as PR-STV and "proportional representation by means of the single transferable vote", is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
STV is a family of multi-winner proportional representation electoral systems. The proportionality of its results and the proportion of votes actually used to elect someone are equivalent to those produced by proportional representation election systems based on lists. STV systems can be thought of as allowing solid coalitions to cast voter-determined lists of individual candidates in elections using the largest remainders method to elect the winning candidates, rather than list-based proportional systems where voters cast their ballot for lists of already grouped candidates. Surplus votes belonging to winning candidates (those in excess of an electoral quota) may be thought of as remainder votes. Surplus votes may be transferred from a successful candidate to another candidate and then possibly used to elect that candidate.
Under STV, votes are transferred to a voter's subsequent preferences if necessary, and depending on how the voter marked their preferences, a vote may be transferred across party lines, to a candidate on a different party slate, if that is how the voter marked their preferences. This allows voters of parties with too few votes to win a seat for their own candidates to have an effect on which candidates of parties with more support are elected. Additionally, this means most voters' preferences contribute to the election of a candidate they supported rather than being wasted on candidates who were not elected or on candidates who received more votes than needed to achieve election.
Under STV, no one party or voting bloc can take all the seats in a district unless the number of seats in the district is very small or almost all the votes cast are cast for one party's candidates (which is seldom the case). This makes it different from other commonly used candidate-based systems. In winner-take-all or plurality systemssuch as first-past-the-post (FPTP), instant-runoff voting (IRV), and block votingone party or voting bloc can take all seats in a district.
The key to STV's approximation of proportionality is that each voter effectively only casts a single vote in a district contest electing multiple winners, while the ranked ballots (and sufficiently large districts) allow the results to achieve a high degree of proportionality with respect to partisan affiliation within the district, as well as representation by gender and other descriptive characteristics. The use of a quota means that, for the most part, each successful candidate is elected with the same number of votes. This equality produces fairness in the particular sense that a party taking twice as many votes as another party will generally take twice the number of seats compared to that other party.
Under STV, winners are elected in a multi-member constituency (district) or at-large, also in a multiple-winner contest. Every substantial group within the district wins at least one seat: the more seats the district has, the smaller the size of the group needed to elect a member. In this way, STV provides approximately proportional representation overall, ensuring that substantial minority factions have some representation.
There are several STV variants. Two common distinguishing characteristics are whether or not ticket voting is allowed and the manner in which surplus votes are transferred. In Australia, lower house elections do not allow ticket voting (where voters can simply mark the party of choice); some but not all state upper house systems do allow ticket voting. In Ireland and Malta, surplus votes are transferred as whole votes (there may be some randomness) and neither allows ticket voting. In Hare–Clark, used in Tasmania and the Australian Capital Territory, there is no ticket voting and surplus votes are fractionally transferred based on the last parcel of votes received by winners in accordance with the Gregory method.Terry Newman, Hare-Clark in TasmaniaGeorge Howatt, Democratic Representation under the Hare-Clark System – The Need for Seven-Member Electorates Systems that use the Gregory method for surplus vote transfers are strictly non-random. Other distinguishing features include district magnitude (number of members in the district, with all districts having the same DM or varying DM), how to fill casual vacancies (by-elections or other), and the number of preferences that the voter must mark (optional-preferential voting or other).
Unlike party-list proportional representation of the closed list variant, under STV voters vote for candidates rather than for parties. STV is also different from the single non-transferable vote election system, a semi-proportional system where candidates are not ranked and votes are not transferred.
Process
In a single transferable vote (STV) system, the voter ranks candidates in order of preference on their ballot. A vote is initially allocated to the voter's first preference.
A quota (the minimum number of votes that guarantees election) is calculated by a specified method (STV generally uses the Hare or Droop quota), and candidates who accumulate that many votes are declared elected. In many STV systems, the quota is also used to determine surplus votes, the number of votes received by successful candidates over and above the quota. Surplus votes are transferred to candidates ranked lower in the voters' preferences, if possible, so they are not wasted by remaining with a candidate who does not need them.
If seats remain open after the first count, any surplus votes are transferred. This may generate the necessary winners. As well, least popular candidates may be eliminated as a way to generate winners.
The specific method of transferring votes varies in different systems (see ). Transfer of any existing surplus votes is done before eliminations of candidates. This prevents a party from losing a candidate in the early stage who might be elected later through transfers. When surplus votes are transferred under some systems, some or all of the votes held by the winner are apportioned fractionally to the next marked preference on the ballot. In others, the transfers to the next available marked preference is done using whole votes.
When seats still remain to be filled and there are no surplus votes to transfer (none of the remaining candidates have surplus votes needing to be transferred), the least popular candidate is eliminated. The eliminated candidate's votes are transferred to the next-preferred candidate rather than being discarded; if the next-preferred choice has already been eliminated or elected, the procedure is iterated to lower-ranked candidates.
Counting, eliminations, and vote transfers continue until enough candidates are declared elected (all seats are filled by candidates reaching the quota) or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected.Humphreys, Proportional Representation, p. 136-137
Example for a non-partisan election Suppose an election is conducted to determine what three foods to serve at a party. There are seven choices: Oranges, Pears, Strawberries, Cake (of the strawberry/chocolate variety), Chocolate, Hamburgers and Chicken. Only three of these may be served to the 23 guests. STV is chosen to make the decision, with the whole-vote method used to transfer surplus votes. The hope is that each guest will be served at least one food that they are happy with.
To select the three foods, each guest is given one votethey each mark their first preference and are also allowed to cast two alternate preferences to be used only if their first-preference food cannot be selected or to direct a transfer of their vote if the first-preference food is chosen with a surplus of votes. The 23 guests at the party mark their ballots: some mark first, second and third preferences; some mark only two preferences. The alternate preferences are used as needed in successive rounds of counting.
When the ballots are counted, it is found that the ballots are marked in seven distinct combinations, as shown in the table below:
1st preference 2nd preference 3rd preference # of votes with combination 3 8 1 3 1 4 3
The election round by round: StepVotes for each option Quota The Droop quota is used. 23 divided by 4 is 5.75, which in this case is rounded up to 6. 1st round First-preference votes are counted. Pears reaches the quota with 8 votes and is therefore elected in the first round, with 2 surplus votes. 3 8 (ELECTED) 1 3 1 4 3 2nd round All of the voters who gave first preference to Pears preferred Strawberry next, so both of its surplus votes are transferred to Strawberry. 3 ELECTED 3 3 1 4 3 3rd round Chocolate has the fewest votes and is eliminated. According to its sole voter's next preference, this vote is transferred to Cake. No option has reached the quota and there are still more spots left than food candidates, so the elimination of options will continue. 3 ELECTED 3 4 eliminated 4 3 4th round Of the remaining options, Oranges, Strawberry and Chicken now are tied for the fewest votes. Strawberry had the fewest first preference votes, so its first-preference vote is transferred to Oranges. Its two surplus votes (from Pear–Strawberry–Cake voters) are transferred to Cake, which reaches the quota and is elected. 4 ELECTED eliminated 6 (ELECTED) eliminated 4 3 Final round Chicken has the fewest votes and is eliminated. As Chocolate has already been eliminated, its three votes are transferred to Hamburgers. Hamburgers is elected with 7 votes in total. (Its surplus vote is immaterial, as the election is over.)4ELECTEDeliminatedELECTEDeliminated7 (ELECTED)eliminated
The winners are Pears, Cake, and Hamburgers.
STV in this case produced a large number of effective votes: 19 votes were used to elect the successful candidates. (Only the votes for Oranges at the end were not used to select a food. The Orange voters have satisfaction of seeing their second choice – Pears – selected, even if their votes were not used to select any food.)
Also, there was general satisfaction with the choices selected. Nineteen voters saw either their first or second choice elected, although four of them did not actually have their vote used to achieve the result. Four saw their third choice elected. Fifteen voters saw their first preference chosen; eight of these 15 saw their first and third choices selected. Four others saw their second preference chosen, with one of them having their second and third choice selected.
Note that if Hamburger had received only one vote when Chicken was eliminated, it still would have won because the only other remaining candidate, Oranges, had fewer votes, so would have been declared defeated in the next round. This would have left Hamburger as the last remaining candidate to fill the last open seat, even if it did not have quota.