Single transferable vote


Single transferable vote (STV) is a multi-winner electoral system in which voters cast single votes in the form of ranked-choice ballots.[1] Voters have the option to rank candidates and their vote may be transferred according to their preferences, if their preferred candidate is eliminated, so that their vote still counts.

A single transferable vote ballot paper for the electorate of Brindabella in the 2016 Australian Capital Territory general election

STV aims to provide proportional representation based on votes cast in the district where it is used, so that most votes are used effectively to elect someone preferred by the voter and so that each vote is worth about the same as another. Unlike in plurality voting systems or majoritarian systems, no one party or voting bloc can take all the seats in a district under STV unless the number of seats is very small or one party takes almost all the votes cast, which is seldom the case.

Under STV, each voter casts a single, ranked-choice vote and the system selects multiple winners for a constituency (a multi-member district). Every sizeable 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, and the ranked voting allows voters to form consensus behind the most popular candidates.[2]

The main characteristics of STV are:

  • Compared to first-past-the-post (FPTP) voting, and instant-runoff voting (IRV), STV reduces the number of "wasted" votes (votes which are cast for unsuccessful candidates and for successful candidates over and above those needed to secure a seat) by electing multiple representatives for a district.
  • STV enables votes to be cast for individual candidates rather than for parties. Party lists are therefore not needed; it is the voters who create their own ordered list of candidates.
  • STV provides approximately proportional representation, ensuring that substantial minority factions have some representation. The key to STV's achievement of semi-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 approach proportionality.

How STV worksEdit

On their ballot, the voter ranks candidates in order of preference. A vote is initially allocated to the voter's first preference. If seats remain open after this first count, votes are transferred as per following steps.

If that candidate is eliminated, the vote is transferred to the next-preferred candidate rather than being discarded; if the second choice is eliminated, the procedure is iterated to lower-ranked candidates. Under some systems, the vote is apportioned fractionally to different candidates. As long as there are more candidates than seats, the least popular candidate is eliminated, and votes for them are transferred based on voters' subsequent preferences.

Before the election, a quota (the minimum number of votes that guarantees election) is calculated by a specified method, and candidates who accumulate that many votes are declared elected. In some systems, the quota is also used to determine surplus votes, the amount of votes received by successful candidates over and above the quota. Surplus votes are transferred to candidates ranked lower in the voters’ preferences, so they would not be wasted by remaining with a candidate who does not need them.

Transfer of surplus votes is done before any eliminations of candidates. This prevents a party from losing candidates in the early stages who might be elected later through transfers.[3]

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. The specific method of transferring votes varies in different systems (see § Vote transfers and quota).

District elections grow more proportionally representative in direct relation to the increase in the number of seats to be elected in a constituency – the more seats, the more the distribution of the seats in a district will be proportional. For example, in a three-seat STV election using the Hare Quota of  , a candidate or party with 33 percent of the votes is guaranteed to win a seat. In a seven-seat STV district, any candidate with approximately 14 percent of the vote (either first preferences alone, or a combination of first preferences and lower-ranked preferences transferred from other candidates) will win a seat. Because of this quota-based fairness, it is extremely rare for a party to take a majority of the seats in a district without a majority of the vote. Additionally, a large majority of voters (generally around 80 percent or more) see their vote used to elect someone. Thus under STV, the candidates who make up a majority of the district's elected members are supported directly by a majority of the voters in the district.

Example for a non-partisan electionEdit

Suppose an election is conducted to determine what three foods to serve at a party. There are five choices: Oranges, Pears, Chocolate, Strawberries, and Hamburgers. Only three of them will be served.

The hope is that each guest will be served at least one food that they are happy with. It is decided to use STV to make the decision, so each guest is given one vote and also allowed to cast one back-up preference to be used only if the first preference cannot select a food or to direct transfer of surplus votes if it does. The 23 guests at the party mark their ballots according to the table below, with first and second preferences marked by each voter.

# of guests x x x x x x x x x x x x
x x x x
x x x x x x x
1st preference            
2nd preference            
Step Candidates Result
Setting the quota x x x x x
x x x
x x x x
x x x x

x x x x
x x
First, the quota is calculated. Using the Droop quota, with 23 voters and 3 winners to be found, the number of votes required to be elected is:
Round 1 x x x x x x x x x x x x
x x x x

x x x x
x x x Chocolate is declared elected, since Chocolate has more votes than the quota (with six surplus votes).
Round 2 x x x x x x x x x x x x
x x
x x x x
x x x x Chocolate's surplus votes are transferred. Second preferences on the Chocolate votes are marked for Strawberry and Hamburgers. They receive votes in proportion to the Chocolate voters' second choice preferences, using the formula:

In this case, 8 of the 12 voters for Chocolate had the second preference of Strawberries, so (8/12)•6 = 4 of Chocolate's votes would transfer to Strawberries; meanwhile 4 of the 12 voters for Chocolate had Hamburgers as their second preference, so (4/12)•6 = 2 of Chocolate's votes will transfer to Hamburgers. Thus, Strawberries has 1 first-preference votes and 4 new votes, for an updated total of 1 + 4 = 5 votes; likewise, Hamburgers now has 2 + 2 = 4 votes; no other tallies change. The quota staying with Chocolate is proportional.

After the transfer of this surplus, no candidate has reached the quota. As there is no new surplus to be transferred, in the next count, the least-popular candidate is eliminated. Therefore, Pear, which now has the fewest votes (after the update), is eliminated.

Round 3 x x x x x
x x x
x x x x
x x
x x x x
x x x x Pear's votes are transferred in proportion to the second preferences marked by voters for Pear, i.e. only Oranges in this case, which gives Oranges 3 more votes. Oranges now totals 5 (original) + 3 (new) = 8 votes, exceeding the quota; so, Oranges is elected. Orange has two more votes than the required quota and therefore has surplus to transfer. But as the only second preferences marked are for Pear, which has already been eliminated, all votes are non-transferable. As there is no new surplus to be transferred and there are still one open seat, the vote count proceeds with the elimination of the current least-popular candidate.
Round 4 x x x x x
x x x
x x x x
x x
x x x x
x x x x Neither of the remaining candidates meets the quota, so again the lowest candidate (in this case Hamburgers) is eliminated. This leaves Strawberries as the only remaining candidate, so it wins the final seat (despite not having quota). This ends the count. Hamburger's votes are not transferred because such a transfer cannot change the election of Strawberries.

If there were still unfilled seats and remaining candidates, Hamburgers' votes would be transferred proportionately based on next preferences, if there were any indicated. But in this case, all are non-transferable anyway. Chocolate-then-Hamburgers votes cannot be transferred again as only two preferences were stated and both had been used already. And Hamburger-then-Pear votes that had gone to Hamburgers cannot be transferred as Pear has been eliminated.)

Result: The winners are Chocolate, Oranges and Strawberries.

This result differs from the one that would have occurred if the three winners were decided by first preference plurality rankings, in which case Pear would have been a winner, as opposed to Strawberry, for having a greater number of first preference votes.

If the voters had been able to choose only one food to serve (as in first-past-the-post), it is likely that Chocolate, the choice of only slightly more than half of the 23 party-goers, would have won and Chocolate would be the only food served at the party.

STV in this case produced a high level of effective votes – votes used to elect the successful candidates. 18 voters saw their first preference elected, and three more saw their second preference elected. Only two, those who voted for hamburgers with pears as their second preference, did not see any of their choices elected.

Example for an election with partiesEdit

There are five seats in a district. Party A runs five candidates, Party B runs three, and there is one independent in the race. The election is conducted under STV with the Hare quota, which for five candidates is 20% (100% divided by five).

First roundEdit

Candidate Party Votes

(first preferences)

Quota Elected? If elected: surplus votes
Candidate A1 Party A 1% 20%
Candidate A2 Party A 9%
Candidate A3 Party A 25% Yes 5%
Candidate A4 Party A 8%
Candidate A5 Party A 5%
Candidate I Independent 7%
Candidate B1 Party B 11%
Candidate B2 Party B 18%
Candidate B3 Party B 16%
TOTAL 100%

In the first round, the very popular candidate of Party A, Candidate A3 is above the quota, so they win a seat. Surplus votes are distributed; the voters of Candidate A3 have put another politician from their party, Candidate A4, as their second preference, so they now get 5% of the Candidate A3 votes.

Second and third roundsEdit

In the second and third rounds, the least popular candidates are eliminated (Candidates A1 and A5) and their votes transferred to their next preferences. Voters of Candidate A5 are not very partisan, they actually prefer the independent candidate over the other candidates of Party A still in the race.

Candidate Party Votes Quota Elected? If elected: surplus votes
Candidate A1 Party A 20%
Candidate A2 Party A 9%+1%=10%
Candidate A3 Party A already elected Yes
Candidate A4 Party A 8%+5%=13%
Candidate A5 Party A
Candidate I Independent 7%+5%=12%
Candidate B1 Party B 11%
Candidate B2 Party B 18%
Candidate B3 Party B 16%
TOTAL 80% (1 already elected)

Fourth roundEdit

In the next round, Candidate A2 is eliminated with all their votes going to the candidate A4, the last remaining candidate from Party A, who gets elected. All the voters who helped elect Candidate A4 prefer the independent candidate to the candidates of the other party so their vote will go to

Candidate Party Votes Quota Elected? If elected: surplus votes
Candidate A1 Party A 20%
Candidate A2 Party A
Candidate A3 Party A already elected Yes
Candidate A4 Party A 13%+10%=23% Yes 3%
Candidate A5 Party A
Candidate I Independent 12%
Candidate B1 Party B 11%
Candidate B2 Party B 18%
Candidate B3 Party B 16%
TOTAL 80% (1 already elected)

Fifth roundEdit

Finally Candidate B1 is also eliminated. There are now only three candidates in the race, so they automatically get the remaining seats regardless of whether they reached the quota.

Candidate Party Votes Quota Elected? If elected: surplus votes
Candidate A1 Party A 20%
Candidate A2 Party A
Candidate A3 Party A already elected Yes
Candidate A4 Party A already elected Yes
Candidate A5 Party A
Candidate I Independent 12+3%+5% Yes
Candidate B1 Party B
Candidate B2 Party B 18%+6% Yes
Candidate B3 Party B 16% Yes
TOTAL 60% (2 already elected)

Compared to other systemsEdit

Under STV, candidates A3, A4, I, B2 and B3 were elected. This is different than if all voters could only vote for their first preference, which is called the single non-transferable vote. In this case, the seemingly most popular five candidates would have been elected, which were candidates A3, B2, B3, B1 and A2, meaning even though Party B's candidates had less support together, they received 60% of seats, and Party A only 40%. In this case, Party A overextended themselves by fielding too many candidates, but even if they strategically nominated only three, they would not necessarily have been successful in gaining a seat, unless their voters used coordinated strategic voting.

If all voters could vote for five candidates (but not ranked) – which is called block voting, a type of multiple non-transferable vote – Party A could have won all seats, leaving Party B and voters of the independent candidate without representation. This is because if all voters of Party A voted for all 5 of their candidates, every Party A candidate could have received up to 48% of the votes, and some even up to 55% if voters of Candidate I also voted for some Party A candidates with their 4 other votes. At the same time, all of Party B's candidates could only get up to 45% or at best 52% with the same tactics. If the voters are partisan enough, the likely outcome is that one party can take all the seats (majoritarian representation) and all other votes are wasted.

STV meanwhile is roughly proportional (as much as the number of seats allows) and takes into account not just the first preferences of voters. In the example, it could be seen that some voters, who might like a candidate from a certain party best, might prefer an independent (or even a rival party candidate) before other candidates of that party. This means that even if it seems that some faction (based on first preferences) is overrepresented or underrepresented in the outcome, this could also be the outcome that follows from the voters' alternative preferences.

Party Popular vote

(based on 1st preference candidates)

Single transferable vote (STV)

(Hare quota)

Single non-transferable vote (SNTV)

(no tactical voting)

Block voting (BV)

(likely outcome)

Party-list PR (List-PR)

(based on 1st-preference candidates)

Seats % Seats % Seats % Seats %
Party A 48% 2 40% 2 40% 5 100% 3 60%
Party B 45% 2 40% 3 60% 0 0% 2 40%
Independent 7% 1 20% 0 0% 0 0% 0 0%

Related voting systemsEdit

Instant-runoff voting (IRV) is the single-winner analogue of STV. It is also called "single-winner ranked-choice voting". Its goal is representation of a majority of the voters in a district by a single official, as opposed to STV's goals of not only the representation of a majority of voters through the election of multiple officials but also of proportional representation of all the substantial voting blocks in the district.

Single non-transferable vote (SNTV) produces much the same representation as STV, without the work and complication of vote transfers. Single voting in a multiple-member district produces mixed roughly proportional representation, which STV's vote transfers sometimes does not alter. (An example was the election of Edmonton, Alberta, MLAs through STV in 1930. The winners were the same under STV as would have been elected under SNTV.)

Indirect single transferable voting is a non-ranked-vote version of STV. Single voting in a multi-seat district is retained. Voters do not mark their ballots with rankings, but votes are transferred, as needed, based on the eliminated or elected candidate's pre-set instructions. This is a useful system to achieve many of the benefits of STV in districts where it is difficult to collect all the ballots in one central place to conduct STV transfers or where X voting is preferred over ranked voting due to voters' inability or disinterest in ranking candidates. Once known as the Gove system, or the schedule system of PR, it was invented by Massachusetts legislator William H. Gove of Salem and Archibald E. Dobbs of Ireland, author of Representative Reform for Ireland (1879).[4][5]


When single transferable voting is used for single-winner elections, it produces a system that is formally called instant-runoff voting.[6]

STV uses preferential votes cast in multi-seat districts, but some use the term "preferential voting" when they are talking only about instant-runoff voting. "Preferential voting" can also refer to a broader category, ranked voting systems. In the United States, STV is sometimes also called preferential voting, choice voting or preference voting.

STV used for multi-winner elections is sometimes called "proportional representation through the single transferable vote", or PR-STV or STV-PR (in Scotland). "STV" usually refers to the multi-winner version, as it does in this article.

Hare–Clark is the name given to PR-STV elections in Tasmania and the Australian Capital Territory.[7][8]


Simplified example of an STV ballot

In STV, each voter casts just one vote although multiple seats are to be filled in the district. They can provide alternate preferences to be used if needed by ranking the candidates in order of preference. In practice, the candidates' names are usually organized in columns so that voters are informed of the candidates' party affiliations or whether they are standing as independents.

An alternative way to mark preferences for candidates is to use columns for the voters' preference. One column shows first preference. An X there goes beside the most-preferred candidate. The next column is for the second preference. An X there marks the second-preference candidate, etc.

Filling seats under STVEdit

The use of quota to fill seatsEdit

In most STV elections, a quota is established to ensure that all elected candidates are elected with approximately equal numbers of votes. In some STV varieties, votes are totalled, and a quota (the minimum number of votes that guarantees election) is derived.[a] Another system, which used four-seat districts, set quota at 25 percent of the votes in a district.[9]

Once a quota is determined, candidates' vote tallies are consulted. If a candidate achieves the quota, they are declared elected. Then in some STV systems, any surplus vote is transferred to other candidates in proportion to the next-highest preference marked on the ballots received by that candidate. If more candidates than seats remain, the candidate with the fewest votes is eliminated, with their votes being transferred to other candidates as determined by the voters' next preference. Elections and eliminations, and vote transfers where applicable, continue until enough candidates are declared elected to fill the open seats or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected. These last candidates may be elected without surpassing quota, but their survival until the end is taken as proof of their general acceptability by the voters.

Finding winners using quotaEdit

An STV election count starts with a count of each voter's first choice, recording how many for each candidate, calculation of the total number of votes and the quota and then taking the following steps:

  1. A candidate who has reached or exceeded the quota is declared elected.
  2. If any such elected candidate has more votes than the quota, surplus votes are then transferred to other candidates proportionally based on their next-indicated choice on all the ballots that had been received by that candidate. There are several different ways to do this. (see § Quota and vote transfers ).
  3. If there are still seats to be filled after the surplus votes of all candidates elected in the first count have been transferred, if any new candidates have been elected, their surplus votes are transferred proportionally.
  4. If there are still seats to be filled after all surplus votes have been transferred, the candidate with the fewest votes is eliminated and their votes are transferred to the next candidate marked on each ballot. Candidates already elected or eliminated cannot receive votes in most systems.
  5. This process repeats until either every seat has been filled by candidates surpassing quota or until there are only as many remaining candidates as there are remaining seats, at which point the remaining candidates are declared elected.

There are variations in conducting transfers (see § Quota and vote transfers).

When the number of votes transferred from the losing candidate with the fewest votes is too small to change the ordering of remaining candidates, no transfer is made or more than one candidate is eliminated simultaneously.

Vote transfers and quotaEdit

STV systems primarily differ in how they transfer surplus votes and in the size of the quota. For this reason, it has been suggested that STV can be considered a family of voting systems rather than a single system.

If fair results are to be produced and the number of candidates is fixed, a quota must be set such that any candidate who receives that many votes is elected. The quota, if used, must be set at a level where no more candidates can reach quota than there are seats to be filled. It cannot be so small that more candidates can be elected than the number of open seats, but the smaller it is, the fairer the result. There are several ways to specify quotas.

The Droop quota is the one most commonly used. It is generally considered to be the absolute lowest number that elects the correct number of candidates to fill the available seats, at least based on the original number of votes cast.

The Droop quota is given by the floor function formula:


The Droop quota is an extension of the majoritarian principle of requiring a 50% + 1 majority in single-winner elections under instant-runoff voting. Using Droop means 25% plus 1 is the quota in a three-seat contest because no more than three people can each have 25% of the vote + 1; using Droop means 10% of the vote + 1 is the quota in a nine-seat district because no more than nine people can each have 10% of the vote + 1, and so on.

Droop being relatively low means that the largest party, if it has majority of votes, is likely to take the majority of the seats in a district.

The Hare quota was used in the original proposals by Thomas Hare.[10] It is larger than the Droop and sometimes ensures greater representation to less-popular parties within a district. But also, being larger than Droop, Hare presents more of an obstacle to small parties that hope to take just one seat. Being smaller than Hare, the Droop quota may give a seat to a small party that does not have the votes to take a seat under Hare.

There are variations in the conduct of transfers in different variations of STV, such as how to transfer surplus votes from winning candidates and whether to transfer votes to already-elected candidates. Under STV, votes cast for losing candidates and surplus votes cast for winning candidates are sometimes transferred to voters' next choice candidates. In these ways, STV minimizes wasted votes.

It can happen that a vote is eligible to be transferred but cannot be because it bears no subsequent preference for any remaining candidate. In the case of transfers of surplus votes, if the number of transferable votes is less than the number of the surplus, no calculations are needed to make the transfer. Transfer of the transferable votes is done simply by reference to subsequent preference on the votes.

If the variation of STV used allows transfers to candidates already elected, when a candidate is eliminated and the next preference on the ballot shows preference for a candidate already elected, votes are transferred to already victorious candidate. The new surplus votes for the victorious candidate (transferred from the eliminated candidate) are then transferred to the next preference of the victorious candidate, as happened with their initial surplus. However, any vote transfers from the victorious candidate to a candidate who was already eliminated are impossible, and reference must be made to the next marked preference, if any. See § Filling seats under STV for details.

A quota set lower than Droop is sometimes workable. If fractional votes are used in an STV method, the Droop quota may be modified so that the fraction is not rounded down.

Frank Britton, of the Election Ballot Services at the Electoral Reform Society, observed that the final plus one of the Droop quota is not needed; the exact quota is then simply  . Without fractional votes, the equivalent integer quota may be written:


So, the quota for one seat is 50 of 100 votes, not 51.[11]

In any case, in most STV elections the appearance of non-transferable votes means that the quota could be lowered significantly during the counting of the vote with no danger of having too many elected.

In STV, vote transfers are of two types – transfers of votes of eliminated candidates and transfers of surplus votes of elected candidates. The first type happens more often than the second type. Surplus votes are transferred only after a candidate is elected and then only if there are still open seats to be filled and if the transfers may affect the ranking of the remaining candidates.

Transfers of votes of eliminated candidatesEdit

Transfers of votes of eliminated candidates is done simply, without the use of complex math. The next usable preference on the vote gives the destination for the transfer of the vote. If there is no usable preference on the ballot, the vote goes to the "exhausted" or non-transferable pile.

Transfers of surplus votesEdit

The transfer of surplus votes of an elected candidate may be very simply done or may be done more or less intricately, depending on the circumstances and the choice of the government or election officials.

It can happen that a vote is set to be transferred but cannot be because it bears no subsequent preference for any remaining candidate. In transfers of surplus votes, any non-transferable votes are left with the elected candidate.

If the number of transferable votes is less than the surplus, the transfer of surplus votes can be performed just as it is done in the case of transfer of eliminated candidates, the only difference being that non-transferable votes remain with the elected candidate. They do not go to the exhausted pile. Transfer of the transferable votes is done in these cases simply by reference to the next usable preference on the vote.

In cases where the number of transferable votes is more than the surplus, a more-involved method is needed in order to make the transfer proportional and to ensure that the quota left with the successful candidate is proportional as well. But election officials here have a choice of using a simpler method or more involved methods.

The basic formula for how to transfer surplus votes when there are more transferable votes than the surplus to be transferred is:


This can produce fractional votes, which are handled differently under different counting methods.

As well, not considering later preferences when transferring votes may influence later transfers and are thought of as being random, so instead some places use systems that break down the elected candidate's votes into many separate piles looking at all the permutation of preferences marked on the votes.

In some STV variants, such as those used in the Republic of Ireland (except Senate elections), Malta, and elsewhere, merely the next preference is examined. Votes are transferred as whole votes. Any randomness may arise from the later preferences, if any, that may have to be used later. But choosing the votes at random from the pile means that each transfer should be mixed and likely closely resembles the composition of the entire pile.

The Gregory method (also known as Newland–Britain or Senatorial rules) eliminates randomness by examining all the preferences marked on ballots, the later preferences dictate how later transfers, if any, will go. They transfer votes as fractions of votes. Gregory is in use in Northern Ireland, the Republic of Ireland (Senate elections) and in Australia. Both Gregory and earlier methods have the problem that in some circumstances they do not treat all votes equally. For this reason Meek's method, Warren's method and the Wright system have been invented.[12] While easier methods can usually be counted by hand, except in a very small election Meek and Warren require counting to be conducted by computer.[citation needed] The Wright system is a refinement of the Australian Senate system replacing the process of distribution and segmentation of preferences by a reiterative counting process where the count is reset and restarted on every exclusion. Meek is used in local body elections in New Zealand.

Meek in 1969[13] was the first to realize that computers make it possible to count votes in way that is conceptually simpler and closer to the original concept of STV. One advantage of Meek's method is that the quota is adjusted at each stage of counting when the number of votes decreases because some become non-transferable. Meek also considered a variant on his system which allows for equal preferences to be expressed.[14] This has subsequently (since 1998) been used by the John Muir Trust for electing its trustees.[15]


Carl Andræ


In 1896, Andrew Inglis Clark was successful in persuading the Tasmanian House of Assembly to be the first parliament in the world elected by what became known as the Hare-Clark electoral system, named after himself and Thomas Hare. H. G. Wells was a strong advocate, calling it "Proportional Representation".[16] The HG Wells formula for scientific voting, repeated, over many years, in his PR writings, to avoid misunderstanding, is Proportional Representation by the single transferable vote in large constituencies.[17]

STV in large constituencies and multiple-member districts permits an approach to the Hare-Mill-Wells ideal of mirror representation. The UK National Health Service used to elect, through the first-past-the-post system in local or regional elections, only white male general practitioners to the General Medical Council. In 1979, the UK National Health Service used STV to proportionally elect women and immigrant GPs, and specialists, to the General Medical Council.[18]


Australian Senate ballot paper used in Victoria for 2016

Tasmania first used STV for election of members of the Tasmanian House of Assembly from 1896 to 1902. In 1909, it began to be used on a permanent basis for Assembly elections. (Instant-runoff voting was used for elections to the Tasmania Legislative Council (its upper house), with some of the members elected through STV prior to 1946.)

In 1948, single transferable vote proportional representation on a state-by-state basis became the method for electing Senators to the Australian Senate. This change has led to the rise of a number of minor parties such as the Democratic Labor Party, Australian Democrats and Australian Greens who have taken advantage of this system to achieve parliamentary representation and the balance of power. From the 1984 election, group ticket voting was introduced to reduce a high rate of informal voting but in 2016, group tickets were abolished to avoid undue influence of preference deals amongst parties that were seen as distorting election results[19] and a form of optional preferential voting was introduced.

Beginning in the 1970s, Australian states began to reform their upper houses to introduce proportional representation in line with the Federal Senate. The first was the South Australian Legislative Council in 1973, which initially used a party list system (replaced with STV in 1982),[20] followed by the single transferable vote being introduced for the New South Wales Legislative Council in 1978,[21] the Western Australian Legislative Council in 1987[22] and the Victorian Legislative Council in 2003.[23] The single transferable vote was also introduced for the elections to the Australian Capital Territory Legislative Assembly after a 1992 referendum.[24]

The term STV in Australia refers to the Senate electoral system, a variant of Hare-Clark characterized by the "above the line" group voting ticket, a party list option. It is used in the Australian upper house, the Senate, most state upper houses, the Tasmanian lower house and the Capital Territory assembly. There is a compulsory number of preferences for a vote for candidates (below-the-line) to be valid: for the Senate a minimum of 90% of candidates must be scored, in 2013 in New South Wales that meant writing 99 preferences on the ballot.[25] Therefore, 95% and more of voters use the above-the-line option, making the system, in all but name, a party list system.[26][27][28] Parties determine the order in which candidates are elected and also control transfers to other lists and this has led to anomalies: preference deals between parties, and "micro parties" which rely entirely on these deals. Additionally, independent candidates are unelectable unless they form, or join, a group above-the-line.[29][30] Concerning the development of STV in Australia researchers have observed: "... we see real evidence of the extent to which Australian politicians, particularly at national levels, are prone to fiddle with the electoral system".[31]: 86 

As a result of a parliamentary commission investigating the 2013 election, from 2016 the system has been considerably reformed (see 2016 Australian federal election), with group voting tickets (GVTs) abolished and voters no longer required to fill all boxes.


In British Columbia, Canada, a type of STV called BC-STV was recommended for provincial elections by the British Columbia Citizens' Assembly on Electoral Reform in 2004. In a 2005 provincial referendum, it received 57.69 percent support and passed in 77 of 79 electoral districts. It was not adopted, however, because it fell short of the 60 percent threshold requirement the BC Liberal government had set for the referendum to be binding.[32] In a second referendum, on 12 May 2009, BC-STV was defeated 60.91 percent to 39.09 percent.

STV has been used in several Canadian jurisdictions. The cities of Edmonton and Calgary elected their MLAs through STV from 1924 to 1956, when the Alberta provincial government changed those elections to use the first-past-the-post system. The city of Winnipeg elected its MLAs through STV from 1920 to 1955, when the Manitoba provincial government changed those elections to use first-past-the-post.[33]

Less well known is STV use at the municipal level in western Canada. Calgary and Winnipeg used STV for more than 50 years before city elections were changed to use the first-past-the-post system. Nineteen other municipalities, including the capital cities of the four western provinces, also used STV For elections in about 100 elections during the 1918 to 1931 period.

United StatesEdit

In the United States, the Proportional Representation League was founded in 1893 to promote STV, and their efforts resulted in its adoption by many city councils in the first half of the 20th century. More than twenty cities have used STV, including Cleveland, Cincinnati and New York City. As of January 2010, it is used to elect the city council and school committee in Cambridge, Massachusetts, the park board in Minneapolis, Minnesota, and the board of assessors in Arden, Delaware. STV has also been adopted for student government elections at several American universities, including Carnegie Mellon,[34][35] MIT, Oberlin, Reed, UC Berkeley, UC Davis, Vassar, UCLA, Whitman, and UT Austin. The Fair Representation Act, introduced in Congress in June 2017, would establish STV for US House elections starting in 2022.[36]

List of places using STVEdit

STV has had its widest adoption in the English-speaking world.

The table below lists countries that use a proportional electoral system to fill a nationally elected legislative body. Detailed information on electoral systems applying to the first chamber of the legislature is maintained by the ACE Electoral Knowledge Network.[37][38] Countries using PR as part of a parallel voting (mixed-member majoritarian) system are not included.

Country Legislative body Allocating formula Electoral threshold Constituencies Governmental system Notes
Australia Senate 4% States and territories of Australia Parliamentary system
Ireland Constituencies Parliamentary system
Malta Constituencies Parliamentary system
Australia Federal (country-wide) Senate elections (since 1948[b] – with the option of using a group voting ticket from 1983 until 2016)
Australian Capital Territory Legislative Assembly elections (since 1992)
Norfolk Island Local government elections (since 2016)
Northern Territory Local government elections (since 2011)
New South Wales Legislative Council elections (since 1978 – with the option of using a group voting ticket until 2003)
Local government elections (since 2012)
South Australia Legislative Council elections (since 1982 – with the option of using a group voting ticket from 1985 until 2017)
Local government elections (since 1999)
Tasmania House of Assembly elections (since 1896)
Local government elections (since 1993)
Victoria Legislative Council elections (since 2003 – with the option of using a group voting ticket)
Local government elections (since 2003)
Western Australia Legislative Council elections (since 1987 – with the option of using a group voting ticket until 2021)
India Indirect elections – presidential, vice-presidential, Rajya Sabha and Vidhan Parishad (in few states) elections.
Ireland Dáil general elections (lower house; since 1921[c])
Seanad general elections (upper house; since 1925)
European elections (since 1979)
Local government elections (since 1920[d])
Malta Parliamentary elections (since 1921)
European elections
Local government elections
Nepal Indirect elections – Upper house elections (by provinces and local assemblies) since 2018
New Zealand[39]

Regional council elections: Wellington Regional Council
Unitary authority elections: Marlborough District Council
Territorial authority elections:
Dunedin City Council, Kaipara District Council, Kapiti Coast District Council, New Plymouth District Council, Palmerston North City Council, Porirua City Council, Ruapehu District Council, Tauranga City Council, Wellington City Council[40]

Later additions – Hamilton City Council (2020)[41]
District health board elections: all 20 boards

Pakistan Indirect elections – Senate elections (by members of provincial assemblies,
and direct vote by the population of territories)
United Kingdom Northern Ireland Northern Ireland Assembly elections (since 1998)[e]
Local government elections
Scotland Local government elections (since May 2007)
United States City elections in Cambridge, Massachusetts (multi-member, at-large district), Eastpointe, Michigan, Palm Desert, California, Albany (NY), St. Paul (MN) and St. Louis Park (MN).[42]

At-large municipal board seats[43] in Minneapolis, Minnesota

Historically during the Progressive Era in 21 other cities between 1915 and 1960, including New York City for New York City Council from 1937 to 1947 (multi-winner districts)[44][45][46]

Benefits and drawbacksEdit


Advocates[who?] for STV argue it is an improvement over winner-take-all non-proportional voting systems such as first-past-the-post, where vote splits commonly result in a majority of voters electing no one and the successful candidate having support from just a minority of the district voters. STV prevents in most cases one party taking all the seats and in its thinning out of the candidates in the field prevents the election of an extreme candidate or party if it does not have enough overall general appeal.

STV is the system of choice of the Proportional Representation Society of Australia (which calls it quota-preferential proportional representation),[47] the Electoral Reform Society in the United Kingdom[48] and FairVote in the USA (which refers to STV as fair representation voting[49] and instant-runoff voting as "ranked-choice voting",[50] although there are other preferential voting methods that use ranked-choice ballots).


Critics[who?] contend that some voters find the mechanisms behind STV difficult to understand, but this does not make it more difficult for voters to rank the list of candidates in order of preference on an STV ballot paper (see § Voting).[51]


Degree of proportionalityEdit

The degree of proportionality of STV election results depends directly on the district magnitude (i.e. the number of seats in each district). While Ireland originally had a median district magnitude of five (ranging from three to nine) in 1923, successive governments lowered this. Systematically lowering the number of representatives from a given district directly benefits larger parties at the expense of smaller ones.

Supposing that the Droop quota is used: in a nine-seat district, the quota or threshold is 10% (plus one vote); in a three-seat district, it would be 25% (plus one vote).

A parliamentary committee in 2010 discussed the "increasing trend towards the creation of three-seat constituencies in Ireland" and recommended not less than four-seaters, except where the geographic size of such a constituency would be disproportionately large.[52]

STV provides proportionality by transferring votes to minimize waste, and therefore also minimizes the number of unrepresented or disenfranchised voters.

Difficulty of implementationEdit

A frequent concern about STV is its complexity compared with single-mark voting methods, such as plurality voting or party-list proportional representation. Before the advent of computers, this complexity made ballot-counting more difficult than for some other voting methods.

The algorithm is complicated. In large elections with many candidates, a computer may be required. (This is because after several rounds of counting, there may be many different categories of previously transferred votes, each with a different permutation of early preferences and thus each with a different carried-forward weighting, all of which have to be kept track of.)

Role of political partiesEdit

STV differs from other proportional representation systems in that candidates of one party can be elected on transfers from voters for other parties. Hence, STV may reduce the role of political parties in the electoral process and corresponding partisanship in the resulting government. A district only needs to have four members to be proportional for the major parties, but may under-represent smaller parties, even though they may well be more likely to be elected under STV than under first-past-the-post.


As STV is a multi-member system, filling vacancies between elections can be problematic, and a variety of methods have been devised:

  • The countback method is used in the Australian Capital Territory, Tasmania, Victoria, Malta, and Cambridge, Massachusetts. Casual vacancies can be filled by re-examining the ballot papers data from the previous election.
  • Another option is to have a head official or remaining members of the elected body appoint a new member to fulfill the vacancy.
  • A third way to fill a vacancy is to hold a single-winner by-election (effectively instant runoff); this allows each party to choose a new candidate and all voters to participate. This is the method used in the Republic of Ireland in national elections, and in Scotland's local elections.
  • Yet another option is to allow the party of the vacant member to nominate a successor, possibly subject to the approval of the voting population or the rest of the government. This is the method used in the Republic of Ireland in local elections.[53]
  • Another possibility is to have the candidates themselves create an ordered list of successors before leaving their seats. In the European Parliament, a departing member from the Republic of Ireland or Northern Ireland is replaced with the top eligible name from a replacement list submitted by the candidate at the time of the original election. This method was also used in the Northern Ireland Assembly, until 2009, when the practice was changed to allow political parties to nominate new MLAs in the event of vacancies. Independent MLAs may still draw up lists of potential replacements.[54]
  • For its 2009 European elections, Malta introduced a one-off policy to elect the candidate eliminated last to fill the prospective vacancy for the extra seat that arose from the Lisbon Treaty.


If there are not enough candidates to represent one of the priorities the electorate vote for (such as a party), all of them may be elected in the early stages, with votes being transferred to candidates with other views. On the other hand, putting up too many candidates might result in first preference votes being spread too thinly among them, and consequently several potential winners with broad second-preference appeal may be eliminated before others are elected and their second-preference votes distributed. In practice, the majority of voters express preference for candidates from the same party in order,[citation needed] which minimizes the impact of this potential effect of STV.

The outcome of voting under STV is proportional within a single election to the collective preference of voters, assuming voters have ranked their real preferences and vote along strict party lines (assuming parties and no individual independents participate in the election). However, due to other voting mechanisms usually used in conjunction with STV, such as a district or constituency system, an election using STV may not guarantee proportionality across all districts put together.

A number of methods of tactical or strategic voting exist that can be used in STV elections, but much less so than with first-past-the-post elections. (In STV elections, most constituencies will be marginal, at least with regard to the allocation of a final seat.)

Elector confusionEdit

STV systems vary, both in ballot design and in whether or not voters are obliged to provide a full list of preferences.

In jurisdictions such as Malta, Republic of Ireland and Northern Ireland, voters may rank as many or as few candidates as they wish. Consequently, voters sometimes, for example, rank only the candidates of a single party, or of their most preferred parties. A minority of voters, especially if they do not fully understand the system, may even "bullet vote", only expressing a first preference, or indicate a first preference for multiple candidates, especially when both STV and plurality are being used in concurrent elections.[55]

Allowing voters to rank only as many candidates as they wish grants them greater freedom, but can also lead to some voters ranking so few candidates that their vote eventually becomes "exhausted"– that is, at a certain point during the count, it can no longer be transferred and therefore loses an opportunity to influence the result. However the number found to be non-transferable under STV is less than are ignored or wasted under the first-past-the-post system. Some votes found to be non-transferable are that way because the choices marked have already been elected, so the voter may be pleased with the overall election result even though their first preference was not elected and their vote itself was not used to elect anyone. Even if a voter marks many alternate preferences, the vote will still be found to be non-transferable, if at any point the vote needs to be transferred and all the preferences listed next have already been eliminated or elected. But the number of non-transferable votes is fewer than the number of ignored votes under first-past-the-post and the number of effective votes, votes actually used to elect someone, is higher than under all but the most landslide first-past-the-post election contests.

The STV method can be confusing, and may cause some people to vote incorrectly with respect to their actual preferences.

STV ballots can also be long; having multiple pages increases the chances of people not marking multiple preferences and thus missing later opportunities to have their vote transferred. However, after a vote has been transferred a couple times and it now is at the end of the count and just three candidates remain in the running for the last seat, the voter may have little interest in the choice. None of them were the voter's first choice, nor their second or third preference. And perhaps the voter has already seen one or two of their earlier choices already elected. Many votes up for transfer are found to be non-transferable in the last vote transfers. Some at the end are elected with partial quotas, due to the number of non-transferable votes. But in STV elections a majority of votes are used to elect the members who are elected.


Some opponents[who?] argue that larger, multi-seat districts would require more campaign funds to reach the voters. Proponents argue that STV can lower campaign costs because like-minded candidates can share some expenses. Proponents reason that negative advertising is disincentivized in such a system, as its effect is diluted among a larger pool of candidates. In addition, candidates do not have to secure the support of at least 50% of voters, allowing candidates to focus campaign spending primarily on supportive voters.

As well, under STV, it is not necessary to be the most popular candidate in the district to be elected; it is only necessary to have quota (or survive to the end when the remaining candidates are declared elected). To have quota, you do not need support from across the district necessarily. If a corner of the district has a quota worth of votes and the voters there support a candidate, that candidate will be elected and there is nothing the others elsewhere in the district can do about it. So, at least theoretically, you would not need to campaign across the district.[56]

Analysis of resultsEdit

Academic analysis of voting systems such as STV generally centres on the voting system criteria that they pass. No preference voting system satisfies all the criteria in Arrow's impossibility theorem: in particular, STV fails to achieve independence of irrelevant alternatives (like most other vote-based ordering systems) and monotonicity.[citation needed]

Migration of preferencesEdit

The relative performance of political parties in STV systems is sometimes analysed in a different fashion from that used in other electoral schemes. For example, seeing which candidates are declared elected on first preference votes alone in the 2012 Scottish local elections, where 1223 members were elected, can be shown as follows:

2012 Scottish local elections[57]
Party Total elected Elected on 1st prefs alone
Total % % (2007)
Conservative 115 46 40.0 40.6
Labour 394 199 50.5 37.4
Liberal Democrats 71 20 28.2 21.7
SNP 425 185 43.5 56.5
Green 14 1 7.1
Independent 200 79 39.5 31.6
Other 4 2 50.0 14.3
Totals 1,223 532 43.5 39.7

The data can also be analysed to find the proportion of voters who express only a single preference,[58] or those who express a minimum number of preferences,[59] to assess party strength. Where parties nominate multiple candidates in an electoral district, analysis can also be done to assess their relative strength.[60]

Other useful information can be found by analysing terminal transfers—i.e., when the votes of a candidate are transferred and no other candidate from that party remains in the count[59]—especially with respect to the first instance in which that occurs:

Average first terminal transfer rates (2012)[61]
Transferred from % non-transferable % transferred to
Con Lab LD SNP Ind/Other
Conservative 33.6 8.0 32.4 8.3 17.6
Labour 47.8 5.8 13.2 16.5 16.7
Liberal Democrats 23.1 21.8 20.4 15.5 19.3
SNP 44.2 6.0 18.1 14.1 17.8
Green 20.4 5.1 19.2 19.9 18.3 17.0

The transfers of votes under STV mean that candidates who did well on first-preference votes in the first count (but not well enough to be immediately declared elected) may not be elected in the end, and those who did poorly on the first count may be elected in the end. This is due to transfers made according to second and later preferences. This can also be analysed, again using the 1223 members elected in the Scottish local elections. Some of the leading candidates in the first count were not elected but, comparing the number to the total number of members elected in these elections, the successful candidates were mostly set in the first count (through the simple mechanics of single voting in multi-member districts), before any vote transfers are done. About ten percent or less of the front runners in the first count were not elected in the end.

Sixty-eight of the elected members, of the overall 1,223 successful candidates, were not already in winning position in the first count, thus showing that vote transfers merely put a polish on the first-count ranking of candidates established through single voting in multi-seat district.

Candidates not in a winning position on 1st preference who secured election, by party (2012)[62]
Political party Elected though
not in
top 3 or 4
Not elected
though in
top 3 or 4
Net gain/loss
2012 2007
Conservative 1 16 −15 −24
Labour 21 8 +13 −17
Liberal Democrats 4 3 +1 +29
SNP 19 29 −10
Green 1 1 +1
Independent 22 9 +13 +8
Other 2 −2 +3

See alsoEdit


  1. ^ In some implementations, a quota is simply set by law – any candidate receiving a given number of votes is declared elected. Under this system, used in New York City in the 1930s to 1940s, the number of representatives elected varies with voter turnout.
  2. ^ STV was previously used to elect the Tasmanian members of both the Senate and the House of Representatives in the inaugural 1901 federal election.
  3. ^ STV was previously used for the Dublin University constituency in the 1918 general election.
  4. ^ STV was previously used for the 1919 special election for Sligo Corporation.
  5. ^ STV was previously used for the 1921 and 1925 elections to the Northern Ireland parliament.


  1. ^ "Ranked Choice Voting / Instant Runoff". FairVote. Retrieved 12 April 2021.
  2. ^ "Single Transferable Vote". Electoral Reform Society.
  3. ^[bare URL PDF]
  4. ^[bare URL PDF]
  5. ^ Hoag, Effective Voting (1914)
  6. ^ "How RCV Works". FairVote.
  7. ^ Terry Newman, Hare-Clark in Tasmania
  8. ^ George Howatt, Democratic Representation under the Hare-Clark System - The Need for Seven-Member Electorates
  9. ^ Sandford Fleming, Essays on the Rectification of Parliament (1892)
  10. ^ Lambert & Lakeman 1955, p. 245.
  11. ^ Newland 1984.
  12. ^ Hill, Wichmann & Woodall 1987.
  13. ^ Meek 1994a.
  14. ^ Meek 1994b.
  15. ^ "Examples of STV elections".
  16. ^ Wells 1918, pp. 121–129.
  17. ^ HG Wells 1916: The Elements of Reconstruction. HG Wells 1918: In The Fourth Year.
  18. ^ Electoral Reform Society, 1979 audit, which records the gratitude of the British medical profession for introducing STV.
  19. ^ Anderson, Stephanie (25 April 2016). "Senate Voting Changes Explained in Australian Electoral Commission Advertisements". ABC News. Retrieved 30 August 2017.
  20. ^ Dunstan, Don (1981). Felicia: The political memoirs of Don Dunstan. Griffin Press Limited. pp. 214–215. ISBN 0-333-33815-4.
  21. ^ "Role and History of the Legislative Assembly". Parliament of New South Wales. Archived from the original on 23 April 2011. Retrieved 9 September 2014.
  22. ^ Electoral Reform expected to alter balance of power, The Australian, 11 June 1987, p.5
  23. ^ Constitution (Parliamentary Reform) Act 2003
  24. ^ "1992 Referendum". 6 January 2015.
  25. ^ "The Hare-Clark System of Proportional Representation". Melbourne: Proportional Representation Society of Australia. Retrieved 21 November 2014.
  26. ^ "Above the line voting". Perth: University of Western Australia. Retrieved 21 November 2014.
  27. ^ "Glossary of Election Terms". Sydney: Australian Broadcasting Corporation. Retrieved 21 November 2014.
  28. ^ Hill, I.D. (November 2000). "How to ruin STV". Voting Matters (12). Retrieved 10 August 2013.
  29. ^ Green, Anthony (20 April 2005). "Above or below the line? Managing preference votes". Australia: On Line Opinion. Retrieved 21 November 2014.
  30. ^ Terry, Chris (5 April 2012). "Serving up a dog's breakfast". London: Electoral Reform Society. Archived from the original on 7 October 2017. Retrieved 21 November 2014.
  31. ^ David M. Farrell; Ian McAllister (2006). The Australian Electoral System: Origins, Variations, and Consequences. Sydney: UNSW Press. ISBN 978-0868408583.
  32. ^ "Report of the Chief Electoral Office" (PDF).
  33. ^ A Report on Alberta Elections (1982)
  34. ^ "Elect@CMU | About single transferable voting". Carnegie Mellon University.
  35. ^ Gund, Devin. "CMU Fair Ranked Voting".
  36. ^ Donald, Beyer (14 July 2017). "H.R.3057 – 115th Congress (2017–2018): Fair Representation Act".
  37. ^ ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, World Map". Retrieved 24 October 2017.
  38. ^ ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, Table by Country". Retrieved 24 October 2017.
  39. ^ "Single Transferable Vote". Department of Internal Affairs. 2013. Retrieved 1 April 2016.
  40. ^ "STV Information". Retrieved 6 August 2020.
  41. ^ "Hamilton City Council switches to STV system for elections". Stuff. 6 August 2020. Retrieved 6 August 2020.
  42. ^ "Ranked-Choice Voting Commission Report ot the Amherst Town Council". Archived from the original on 4 November 2021. Retrieved 4 November 2021.
  43. ^ "What offices are elected using Ranked-Choice Voting?". What is Ranked-Choice Voting?. City of Minneapolis Elections & Voter Services. Retrieved 31 December 2017.
  44. ^ "Learning from the past to prepare for the future: RCV in NYC". FairVote. Retrieved 14 May 2019.
  45. ^ "History of RCV". Ranked Choice Voting Resource Center. Retrieved 14 May 2019.
  46. ^ "A short history of STV in the US".
  47. ^ "Proportional Representation and its Importance". Proportional Representation Society of Australia.
  48. ^ "Our mission". Electoral Reform Society. Archived from the original on 12 February 2013.
  49. ^ "Fair Representation Voting". FairVote.
  50. ^ "Ranked Choice Voting". FairVote.
  51. ^ Margetts 2003, p. 68.
  52. ^ Ireland 2010, p. 177.
  53. ^ "Local Elections Regulations, 1965. Section 87". S.I. No. 128/1965 – Local Elections Regulations, 1965.
  54. ^ "Change to the System for Filling Vacancies in the NI Assembly" (Press release). Northern Ireland Office. 10 February 2009. Archived from the original on 7 March 2012. Retrieved 5 October 2011.
  55. ^ Ombler 2006.
  56. ^ Hoag, Effective Voting, (1914)
  57. ^ Curtice 2012, p. 22.
  58. ^ Curtice 2012, p. 13.
  59. ^ a b Curtice 2012, p. 14.
  60. ^ Curtice 2012, pp. 17–18.
  61. ^ Curtice 2012, pp. 15–16.
  62. ^ Curtice 2012, p. 23.


  • Bagehot, Walter (1894) [1867]. The English Constitution  (7th ed.). London: Kegan Paul, Trench, Trübner & Co. – via Wikisource.
  • Curtice, John (2012). "2012 Scottish Local Government Elections" (PDF). London: Electoral Reform Society. Archived from the original (PDF) on 15 September 2015. Retrieved 30 August 2017.
  • Hill, I. D.; Wichmann, B. A.; Woodall, D. R. (1987). "Algorithm 123: Single Transferable Vote by Meek's Method". The Computer Journal. 30 (3): 277–281. doi:10.1093/comjnl/30.3.277. ISSN 1460-2067.
  • Ireland. Oireachtas. Joint Committee on the Constitution (2010). Article 16 of the Constitution: Review of the Electoral System for the Election of Members to Dáil Éireann (PDF). Dublin: Stationery Office. ISBN 978-1-4064-2501-7. Archived from the original (PDF) on 18 January 2012. Retrieved 20 November 2010.
  • Lambert, Enid; Lakeman, James D. (1955). Voting in Democracies. London: Faber and Faber.
  • Margetts, Helen (2003). "Electoral Reform". In Fisher, Justin; Denver, David; Benyon, John (eds.). Central Debates in British Politics. Abingdon, England: Routledge (published 2014). pp. 64–82. ISBN 978-0-582-43727-2.
  • Meek, B. L. (1994a). "A New Approach to the Single Transferable Vote. Paper I: Equality of Treatment of Voters and a Feedback Mechanism for Vote Counting". Voting Matters (1): 1–7. ISSN 1745-6231. Retrieved 30 August 2017.
  •  ———  (1994b). "A New Approach to the Single Transferable Vote. Paper II: The Problem of Non-transferable Votes". Voting Matters (1): 7–11. ISSN 1745-6231. Retrieved 30 August 2017.
  • Mill, John Stuart (1861). Considerations on Representative Government. London: Parker, Son, and Bourn. ISBN 9781414254685. Retrieved 20 June 2014 – via Google Books.
  • Newland, Robert A. (1984). "The STV Quota". Representation. 24 (95): 14–17. doi:10.1080/00344898408459347. ISSN 0034-4893.
  • Ombler, Franz (2006). "Booklet Position Effects, and Two New statistics to Gauge Voter Understanding of the Need to Rank Candidates in Preferential Elections" (PDF). Voting Matters (21): 12–21. ISSN 1745-6231. Retrieved 30 August 2017.
  • Wells, H. G. (1918). In the Fourth Year: Anticipation of a World Peace. London: Chatto & Windus. Retrieved 6 May 2016 – via Internet Archive.
  • Bach, Stanley (2003). Platypus and Parliament: The Australian Senate in Theory and Practice. Department of the Senate. ISBN 978-0-642-71291-2.
  • Ashworth, H.P.C.; Ashworth, T.R. (1900). Proportional Representation Applied to Party Government. Melbourne: Robertson and Co.

Further readingEdit

  • Bartholdi, John J., III; Orlin, James B. (1991). "Single Transferable Vote Resists Strategic Voting" (PDF). Social Choice and Welfare. 8 (4): 341–354. CiteSeerX doi:10.1007/BF00183045. ISSN 0176-1714. JSTOR 41105995. S2CID 17749613. Retrieved 30 August 2017.
  • Benade, Gerdus; Buck, Ruth; Duchin, Moon; Gold, Dara; Weighill, Thomas (2021). "Ranked Choice Voting and Minority Representation" (PDF). SSRN. doi:10.2139/ssrn.3778021. S2CID 234062227. Retrieved 2 March 2021.
  • Geller, Chris (2002). "Single Transferable Vote with Borda Elimination: A New Vote-Counting System" (PDF). Deakin University, Faculty of Business and Law.
  •  ———  (2004). "Single Transferable Vote with Borda Elimination: Proportional Representation, Moderation, Quasi-chaos and Stability". Electoral Studies. 24 (2): 265–280. doi:10.1016/j.electstud.2004.06.004. ISSN 1873-6890.
  • O'Neill, Jeffrey C. (2004). "Tie-Breaking with the Single Transferable Vote" (PDF). Voting Matters (18): 14–17. ISSN 1745-6231. Retrieved 30 August 2017.
  • Sawer, Marian & Miskin, Sarah (1999). Papers on Parliament No. 34 Representation and Institutional Change: 50 Years of Proportional Representation in the Senate (PDF). Department of the Senate. ISBN 0-642-71061-9.
  • Stone, Bruce (2008). "State legislative councils: designing for accountability." In N. Aroney, S. Prasser, & J. R. Nethercote (Eds.), Restraining Elective Dictatorship (PDF). UWA Publishing. pp. 175–195. ISBN 978-1-921401-09-1.

External linksEdit

  • ACE Project
  • A concise STV analogy – from Accurate Democracy
  • Accurate Democracy lists a dozen programs for computing the single transferable vote.
  • Australia's Upper Houses – ABC Rear Vision A podcast about the development of Australia's upper houses into STV elected chambers.