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Single transferable vote (STV) is a type of ranked preferential
electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Political electoral systems are organized by governments, while non-political ele ...
which uses multiple-member
constituencies An electoral district, also known as an election district, legislative district, voting district, constituency, riding, ward, division, (election) precinct, electoral area, circumscription, or electorate, is a subdivision of a larger state Sta ...
where each voter casts a single ballot where they
rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked ...
candidates. The preferential or ranked voting allows transfer of votes to produce proportionality, to form consensus behind the most-popular candidates and to avoid the waste of votes prevalent under other voting systems. Another name for STV is multi-winner ranked-choice voting''.'' Under STV, each elector (voter) casts a single vote in a district election that elects multiple winners. Each elector marks their ballot for the most preferred
candidate A candidate, or nominee, is the prospective recipient of an award or honor, or a person seeking or being considered for some kind of position; for example: * to be elected to an office — in this case a candidate selection procedure occurs. * ...

and also marks secondary preferences. A vote goes to the voter's first preference if possible, but if the first preference is eliminated, instead of being thrown away, the vote is transferred to an alternate preference, with the vote being assigned to the voter's second, third, or lower choice if possible (or, under some systems, being apportioned fractionally to different candidates). As long as there are more candidates than seats, the least popular is eliminated and their votes transferred based on voters' marked subsequent preferences. A quota (the minimum number of votes that guarantees election) is calculated and candidates who accumulate that number of votes are declared elected. In some systems, surplus votes not needed by successful candidates are transferred proportionally, as described below. Elections and/or eliminations, and vote transfers where applicable, continue until enough candidates are declared elected 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 ). STV enables votes to be cast for individual candidates rather than for parties or party machine-controlled party lists. Compared to first-past-the-post (FPTP) voting, STV reduces the number of "wasted" votes, which are those cast for unsuccessful candidates and for successful candidates over and above those needed to secure a seat. STV avoids this waste by transferring a vote to another preferred candidate. STV also provides approximately proportional representation, ensuring that substantial minority factions have some representation. No one party or voting block can take all the seats in a district. The key to STV's achievement of proportionality is that each elector (voter) only casts a single vote in a district contest electing multiple winners. Under STV, district elections grow more proportionally representative in direct relation to increase in the number of seats to be elected in a constituencythe 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 $\left(\right) / \left(\right)$, a candidate or party with 33 percent of the votes is guaranteed to win a seat. In a seven-seat STV district, any candidate who can get the support of 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. Addtionally, a majority of voters see their vote used to elect the candidates who make up a majority of the district's elected members.
Instant runoff voting Instant-runoff voting (IRV), also sometimes referred to as the alternative vote (AV), preferential voting, or, in the United States, ranked-choice voting (RCV), though these names are also used for other systems, is a type of ranked preferential ...
(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.

# Terminology

When single transferable voting is used for single-winner elections, it produces a system that is formally called
instant-runoff voting Instant-runoff voting (IRV) is a type of ranked preferential vote counting method used in single-seat elections with more than two candidates. IRV is also sometimes referred to as the alternative vote (AV), preferential voting, single transfe ...
. 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 Ranked voting is any election voting system in which voters use a ranked (or preferential) ballot to select more than one candidate (or other alternative being voted on) and to ranking, rank these choices in a sequence on the Level of measurement#Or ...
. 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. "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 Tasmania (), abbreviated as TAS, is an island An island (or isle) is an isolated piece of habitat that is surrounded by a dramatically different habitat, such as water. Very small islands such as emergent land features on atol ...
and the
Australian Capital Territory The Australian Capital Territory (ACT), known as the Federal Capital Territory (FCT) until 1938, is a federal territory A federal territory is an area under the direct and usually exclusive jurisdiction of a federation's central or national ...
.

# Voting

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 STV

## The use of quota to fill seats

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. Another system, which used four-seat districts, set quota at 25 percent of the votes in a district. 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.

## Vote transfers and quota

STV systems primarily differ in how they transfer surplus votes and in the size of the quota. For this reason some have suggested that STV can be considered a family of voting systems rather than a single system. The quota, if used, must be set at a level where no more candidates can reach quota than there are seats to be filled. The quota is the minimum number of votes that ensures a candidate is elected. Any candidate that takes the quota is declared elected. It cannot be so small that more candidates can be elected than the number of open seats, but the smaller it is, the more fair is the result. If fair results are to be produced and the number of candidates are pre-set, a quota must be set whereby any candidate that receives it is declared elected. There are different quotas to choose from. The
Droop quota The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR ...
is the most commonly used quota. 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 The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR ...
is given by the
floor function In mathematics and computer science, the floor function is the function (mathematics), function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted \operatorname(x) or \lfloor x\rfloor ...

formula: :$\text = \operatorname \left\left(\frac \right\right) + 1$ The Droop quota is an extension of the
majoritarian Majoritarianism is a traditional political philosophy Political philosophy is the philosophical study of government, addressing questions about the nature, scope, and legitimacy of public agents and institutions and the relationships between t ...
principle of requiring a 50% + 1 majority in single-winner elections under
instant-runoff voting Instant-runoff voting (IRV) is a type of ranked preferential vote counting method used in single-seat elections with more than two candidates. IRV is also sometimes referred to as the alternative vote (AV), preferential voting, single transfe ...
. 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 The Hare quota (also known as the simple quota) is a formula used under some forms of the Single Transferable Vote The single transferable vote (STV) is a voting system designed to achieve or closely approach proportional representation Pr ...
was used in the original proposals by Thomas Hare. 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 who 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 voteIn electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Political electoral systems are organized by governments, while ...
s. 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 the case of transfers of surplus votes, if the number of transferable votes is less than the number of the surplus, no math is 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 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 $\left(\text\right) / \left(\text+1\right)$. Without fractional votes, the equivalent integer quota may be written: :$\text = \operatorname \left\left(\right\right)$ So, the quota for one seat is 50 of 100 votes, not 51. 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 typestransfers 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 candidates

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.

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:
:$\begin & \text \\$= & \left( \frac \right) \times \text \end 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. STV variants that look only to the next usable preference are used successfully in the Republic of Ireland (except Senate elections) and in Malta, and elsewhere. In these places, 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 The single transferable vote (STV) is a voting system based on proportional representation and Ranked voting systems, ranked voting. Under STV, an elector's vote is initially allocated to his or her most-preferred candidate. After candidates have b ...
(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 The single transferable vote The single transferable vote (STV) is a voting system designed to achieve or closely approach proportional representation Proportional representation (PR) characterizes electoral systems in which divisions in a ...
,
Warren's method The single transferable vote (STV) is a voting system based on proportional representation and Ranked voting systems, ranked voting. Under STV, an elector's vote is initially allocated to his or her most-preferred candidate. After candidates have b ...
and the
Wright system Wright is an occupational surname originating in England. The term 'Wright' comes from the circa 700 AD Old English word 'wryhta' or 'wyrhta', meaning worker or shaper of wood. Later it became any occupational worker (for example, a shipwright is ...
have been invented. 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. 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 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. This has subsequently (since 1998) been used by the
John Muir Trust The John Muir Trust (JMT) is a Scottish charity, established in 1983 to conserve wild land and wild places for the benefit of all. The Trust runs an environmental award scheme, manages several estates, mainly in the Highlands and Islands of Scotla ...
for electing its trustees.

# Demonstration STV election

Suppose an election is conducted to determine what three foods to serve at a party. There are 5 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 can not elect 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. 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: :$Q_ = \operatorname \left\left(\right\right) +1 = 6 \mbox$. When ballots are counted the election proceeds as follows: 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 In a first-past-the-post electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Political electoral systems are org ...
, 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 votesvotes 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.

# History and current use

## Origin

In 1896,
Andrew Inglis Clark Andrew Inglis Clark (24 February 1848 – 14 November 1907) was an Australian founding father and co-author of the Australian Constitution; he was also an engineer, barrister A barrister is a type of lawyer in common law jurisdiction (area), jur ...

Tasmanian House of Assembly The House of Assembly, or Lower House, is one of the two chambers of the Parliament of Tasmania In modern politics and history, a parliament is a legislature, legislative body of government. Generally, a modern parliament has three fu ...

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 Herbert George Wells"Wells, H. G."
Revised 18 May 2015. ''
was a strong advocate, calling it "Proportional Representation". 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. 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 In a first-past-the-post electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Political electoral systems are org ...
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.

## Australia

Tasmania Tasmania (), abbreviated as TAS, is an island An island (or isle) is an isolated piece of habitat that is surrounded by a dramatically different habitat, such as water. Very small islands such as emergent land features on atol ...
first used STV for election of members of the
Tasmanian House of Assembly The House of Assembly, or Lower House, is one of the two chambers of the Parliament of Tasmania In modern politics and history, a parliament is a legislature, legislative body of government. Generally, a modern parliament has three fu ...

from 1896 to 1902. In 1909, it began to be used on a permanent basis for Assembly elections. (
Instant-runoff voting Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential electoral system, vote counting method used in single-seat elections with more than two candidates. IRV is also sometimes referred to as the alternative vote (AV), pre ...
was used for elections to the Tasmania Legislative Council (its upper house), with some of the members elected through
STV STV may refer to: Television * Satellite television ** Direct-broadcast satellite television (DBSTV) Channels and stations * STV (TV channel), the brand name of ITV broadcasters in central and northern Scotland ** Scottish Television, now legally ...
prior to 1946.) In 1948, single transferable vote
proportional representation#REDIRECT Proportional representation Proportional representation (PR) characterizes electoral systems in which divisions in an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical, and to ideolog ...

on a state-by-state basis became the method for electing Senators to the
Australian Senate The Senate is the upper house of the bicameral Parliament of Australia, the lower house being the House of Representatives (Australia), House of Representatives. The compositioned and powers of the Senate are established in Chapter I of the Con ...
. This change has led to the rise of a number of minor parties such as the Democratic Labor Party,
Australian Democrats The Australian Democrats is a centrist Centrism is a political Politics (from , ) is the set of activities that are associated with Decision-making, making decisions in Social group, groups, or other forms of Power (social and politica ...

and
Australian Greens The Australian Greens, commonly known as The Greens, are a confederation A confederation (also known as a confederacy or league) is a union of sovereign groups or states united for purposes of common action. Usually created by a treaty, ...
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 and a form of
optional preferential voting One of the ways in which ranked voting systems vary is whether an individual vote must express a minimum number of preferences to avoid being considered spoilt vote, invalid ("spoiled" or "informal"). Possibilities are: * Full 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 The Legislative Council, or upper house, is one of the two chambers of the Parliament of South Australia The Parliament of South Australia at Parliament House, Adelaide is the bicameral legislature of the Australian state of South Australia. It ...
in 1973, which initially used a
party list Poster for the European Parliament election 2004 in Italy, showing party lists Party-list proportional representation systems are a family of voting system An electoral system or voting system is a set of rules that determine how elections and r ...
system (replaced with STV in 1982), followed by the single transferable vote being introduced for the
New South Wales Legislative Council The New South Wales Legislative Council, often referred to as the upper house, is one of the two chambers of the parliament In modern politics and history, a parliament is a legislative A legislature is an assembly Assembly may r ...
in 1978, the
Western Australian Legislative Council The Western Australian Legislative Council is the upper house of the Parliament of Western Australia, a state of Australia. It is regarded as a house of review for legislation passed by the Western Australian Legislative Assembly, Legislative Ass ...
in 1987 and the
Victorian Legislative Council The Victorian Legislative Council (VLC) is the upper house of the bicameral Bicameralism is the practice of having a legislature divided into two separate Deliberative assembly, assemblies, chambers, or houses, known as a bicameral legislatu ...

in 2003. The single transferable vote was also introduced for the elections to the
Australian Capital Territory Legislative Assembly The Legislative Assembly for the Australian Capital Territory (known in short as the ACT Legislative Assembly) is the unicameral legislature of the Australian Capital Territory (ACT). It sits in the Legislative Assembly Building, Canberra, Le ...

after a 1992 referendum. The term ''STV'' in Australia refers to the Senate electoral system, a variant of ''Hare-Clark'' characterized by the "above the line"
group voting ticketA group voting ticket (GVT) is a simplified preferential voting system currently in use for elections to the Victorian Legislative Council and Western Australian Legislative Council The Western Australian Legislative Council is the upper house of ...
, a party list option. It is used in the Australian upper house, the
Senate The Curia Julia in the Roman Forum ">Roman_Forum.html" ;"title="Curia Julia in the Roman Forum">Curia Julia in the Roman Forum A senate is a deliberative assembly, often the upper house or Debating chamber, chamber of a bicameral legislatu ...
, most state upper houses, the
Tasmania Tasmania (), abbreviated as TAS, is an island An island (or isle) is an isolated piece of habitat that is surrounded by a dramatically different habitat, such as water. Very small islands such as emergent land features on atol ...
n 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 New South Wales (abbreviated as NSW) is a state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * The State (newspaper), ''The State'' (newspape ...
that meant writing 99 preferences on the ballot. Therefore, 95% and more of voters use the above-the-line option, making the system, in all but name, a party list system. 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. 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". 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 ( en, Splendour without diminishment) , image_map = British Columbia in Canada 2.svg , Label_map = yes , coordinates = , official_lang = None , Slogan = Beautiful British C ...

, Canada, a type of STV called
BC-STVBC-STV is the proposed voting system recommended by the Citizens' Assembly on Electoral Reform (British Columbia), Citizens' Assembly on Electoral Reform in October 2004 for use in British Columbia, and belongs to the single transferable vote family ...
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 The British Columbia Liberal Party (also referred to as the BC Liberals) is a Centre-right politics, centre-right provincial political party in British Columbia, Canada. The party currently forms the Official Opposition. The leader of the Libera ...

government had set for the referendum to be binding. 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. 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 States

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 Cleveland ( ), officially the City of Cleveland, is a city in the U.S. The United States of America (USA), commonly known as the United States (U.S. or US), or America, is a country primarily located in North America North ...

,
Cincinnati Cincinnati ( ) is a city in the U.S. state In the , a state is a , of which there are currently 50. Bound together in a , each state holds al jurisdiction over a separate and defined geographic territory where it shares its with the ...

and New York City. As of January 2010, it is used to elect the city council and school committee in
Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, Middlesex County, Massachusetts, and part of the Greater Boston, Boston metropolitan area as a major suburb of Boston. , it was the fifth most populous city in the state, behind Boston, ...
, the park board in
Minneapolis, Minnesota Minneapolis () is a city in the U.S. state of Minnesota. With a population of 429,954 as of 2020 United States census, 2020, it is the most populous city in the state and the 46th most populous in the nation. The county seat of Hennepin County, ...

, and the board of assessors in
Arden, Delaware Arden is a village and art colony in New Castle County, Delaware Delaware ( ) is a U.S. state, state in the Mid-Atlantic (United States), Mid-Atlantic region of the United States, bordering Maryland to its south and west; Pennsylvania to i ...
. STV has also been adopted for student government elections at several American universities, including
Carnegie Mellon Carnegie may refer to: *Carnegie (surname), including a list of people with the name Institutions Named for Andrew Carnegie *The Carnegie Building (Troy, New York), Carnegie Building, on the campus of Rensselaer Polytechnic Institute *Carnegie ...
,
MIT Massachusetts Institute of Technology (MIT) is a private land-grant research university A research university is a university A university ( la, universitas, 'a whole') is an educational institution, institution of higher education, hi ...
,
OberlinOberlin may refer to: ; Places in the United States * Oberlin Township, Decatur County, Kansas ** Oberlin, Kansas, a city in the township * Oberlin, Louisiana, a town * Oberlin, Ohio, a city * Oberlin, Licking County, Ohio, a ghost town * Oberlin, P ...
,
Reed Reed or Reeds may refer to: Science, technology, biology, and medicine * Reed bird (disambiguation) Reed bird may refer to: * Reed bunting * Pallas's reed bunting * Eurasian reed warbler * Red nose flower bomb ... * Reed pen A reed pen ( ...

,
UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public In public relations Public relations (PR) is the practice of managing and disseminating information from an individual or an organization ...

,
UC Davis The University of California, Davis (UC Davis, UCD, or Davis) is a public In public relations Public relations (PR) is the practice of managing and disseminating information from an individual or an organization An organizati ...

, Vassar,
UCLA The University of California, Los Angeles (UCLA) is a public In public relations Public relations (PR) is the practice of managing and disseminating information from an individual or an organization An organization, or organ ...
, Whitman, and
UT Austin The University of Texas at Austin, shortened to UT Austin, UT, or Texas, is a Public university, public research university in Austin, Texas and the Flagship#Colleges and universities in the United States, flagship institution of the Universit ...
. The Fair Representation Act, introduced in Congress in June 2017, would establish STV for US House elections starting in 2022.

## Places using STV

English-speaking world Speakers of English English usually refers to: * English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval England, which has eventually become the Wo ...
. , in government elections, STV is used for:

# Benefits and drawbacks

## Benefits

Advocates 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), the
Electoral Reform Society The Electoral Reform Society (ERS) is an independent campaigning organisation based in the United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed. Th ...
in the United Kingdom and
FairVote FairVote, formerly the Center for Voting and Democracy, is a 501(c)(3) organization A 501(c)(3) organization is a corporation, trust, unincorporated association, or other type of organization exempt from federal income tax under section 501(c)( ...
in the USA (which refers to STV as fair representation voting and
instant-runoff voting Instant-runoff voting (IRV) is a type of ranked preferential vote counting method used in single-seat elections with more than two candidates. IRV is also sometimes referred to as the alternative vote (AV), preferential voting, single transfe ...
as "ranked-choice voting", although there are other preferential voting methods that use ranked-choice ballots).

## Drawbacks

Critics 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 ). Critics also see a vote transfer process that is more time-consuming than in first-past-the-post elections where the result is known within a few hours and say it is not worth using STV just to have more proportional results. However, STV's supporters say that some winners are known in the same period as under FPTP, and that with delays under FPTP caused by mail-in or absentee ballots, any delays in an STV scenario are not noticeable or are no great hardship.

# Issues

## Degree of proportionality

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. STV provides proportionality by transferring votes to minimize waste, and therefore also minimizes the number of unrepresented or
disenfranchisedDisfranchisement, also called disenfranchisement, or voter disqualification is the revocation of suffrage Suffrage, political franchise, or simply franchise is the right to vote in public, political elections (although the term is sometimes use ...
voters.

## Difficulty of implementation

A frequent concern about STV is its complexity compared with
plurality voting Plurality voting is an electoral system An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Political electoral systems are organized by gover ...
methods. 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 parties

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 A partisan is a committed member of a political party A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about po ...
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.

## By-elections

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 The Australian Capital Territory (ACT), known as the Federal Capital Territory (FCT) until 1938, is a federal territory A federal territory is an area under the direct and usually exclusive jurisdiction of a federation's central or national ...
,
Tasmania Tasmania (), abbreviated as TAS, is an island An island (or isle) is an isolated piece of habitat that is surrounded by a dramatically different habitat, such as water. Very small islands such as emergent land features on atol ...
, Victoria, Malta, and
Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, Middlesex County, Massachusetts, and part of the Greater Boston, Boston metropolitan area as a major suburb of Boston. , it was the fifth most populous city in the state, behind Boston, ...
. 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. * Another possibility is to have the candidates themselves create an ordered list of successors before leaving their seats. In the
European Parliament The European Parliament (EP) is one of three Legislature, legislative branches of the European Union and one of its seven Institutions of the European Union, institutions. Together with the Council of the European Union, it adopts European legi ...

, 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 The Northern Ireland Assembly ( ga, Tionól Thuaisceart Éireann; Ulster Scots: ''Norlin Airlan Assemblie'') often referred to by the metonym Metonymy () is a figure of speech A figure of speech or rhetorical figure is a word or phrase ...
, 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. * 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 The Treaty of Lisbon (initially known as the Reform Treaty) is an international agreement that amends the two treaties A treaty is a formal, legally binding written agreement between actors in international law International law, als ...
.

## Tactics

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, 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 confusion

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 Plurality may refer to: Voting * Plurality (voting), the most votes for any choice in an election, but not necessarily a majority ** Plurality voting, system in which each voter votes for one candidate and the candidate with a plurality is elected ...

## Other

Some opponents 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.

# Analysis of results

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#REDIRECT Arrow's impossibility theorem#REDIRECT Arrow's impossibility theorem {{Redirect category shell, 1= {{R from other capitalisation ...
{{Redirect category shell, 1= {{R from other capitalisation ...
: in particular, STV fails to achieve
independence of irrelevant alternatives The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom An axiom, postulate or assumption is a statement that is taken to be , to serve as a or starting point for further rea ...
(like most other vote-based ordering systems) and
monotonicity Figure 3. A function that is not monotonic In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus ...
.

## Migration of preferences

The relative performance of political parties in STV systems is 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 can be shown as follows: The data can also be analysed to find the proportion of voters who express only a single preference, or those who express a minimum number of preferences, to assess party strength. Where parties nominate multiple candidates in an electoral district, analysis can also be done to assess their relative strength. Other useful information can be found by analysing terminal transfersi.e., when the votes of a candidate are transferred and no other candidate from that party remains in the countespecially with respect to the first instance in which that occurs: Another effect of STV is that candidates who did well on first preference votes may not be elected, and those who did poorly on first preferences can be elected, because of differences in second and later preferences. This can also be analysed:

* Tally (voting) *
None of the above #REDIRECT None of the above "None of the above", or NOTA for short, also known as "against all" or a "scratch" vote, is a ballot option in some jurisdictions or organizations, designed to allow the voter to indicate disapproval of the candidat ...
*
Approval voting Approval voting is a single-winner electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Political electoral syste ...
*
Single non-transferable vote#REDIRECT Single non-transferable vote {{Redirect category shell, 1= {{R from other capitalisation ...
* Table of voting systems by country * ''Voting matters'', a journal concerned with the technical aspects of STV

# References

## Bibliography

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