The single transferable vote (STV) is a voting system designed to
achieve proportional representation through ranked voting in
multi-seat organizations or constituencies (voting districts).
Under STV, an elector (voter) has a single vote that is initially
allocated to their most preferred candidate and, as the count proceeds
and candidates are either elected or eliminated, is transferred to
other candidates according to the voter's stated preferences, in
proportion to any surplus or discarded votes. The exact method of
reapportioning votes can vary (see Counting methods).
The system provides approximately proportional representation, enables
votes to be cast for individual candidates rather than for parties,
and—compared to first-past-the-post voting—reduces "wasted" votes
(votes on sure losers or sure winners) by transferring them to other
STV is the system of choice of groups such as the Proportional
Representation Society of
1 Governments with STV 2 Terminology 3 Voting 4 Counting the votes
4.1 Simplest Method: Elimination Transfers Only 4.2 More Refined Method: Setting the Quota 4.3 Finding the winners 4.4 Example
5 Counting methods 6 History and current use 7 Issues
7.1 Degree of proportionality 7.2 Difficulty of implementation 7.3 Role of political parties 7.4 By-elections 7.5 Tactics 7.6 Elector confusion 7.7 Other
8 Analysis of results
8.1 Migration of preferences
9 See also 10 References
10.1 Notes 10.2 Bibliography
11 Further reading 12 External links
Governments with STV STV has had its widest adoption in the English-speaking world. As of 2018[update], in government elections, STV is used for:
Ireland Parliamentary elections (since 1921) European elections Local government elections
Malta Parliamentary elections (since 1921) European elections Local government elections
United Kingdom Northern Ireland National assembly elections European elections Local government elections
Scotland Local government elections (since May 2007)
Indirect elections -
Nepal Indirect elections - Upper house elections (by provinces and local assemblies) since 2018
Pakistan Indirect elections - Senate elections (by members of provincial assemblies, and direct vote by the population of territories)
Australia Federal (country-wide) Senate elections (Since 1948) (in the form of a group voting ticket from 1983 until 2016)
Australian Capital Territory Legislative Assembly elections (Since 1992)
New South Wales Legislative Council elections (since 1978) (in the form of a group voting ticket until 2003) Local government elections
South Australia Legislative Council elections (since 1985) (in the form of a group voting ticket until 2017) Local government elections
Tasmania House of Assembly elections (since 1896) Local government elections
Victoria Legislative Council elections (since 2006) (in the form of a group voting ticket) Local government elections
Western Australia Legislative Council elections (since 1987) (in the form of a group voting ticket)
Regional council elections: Wellington Regional Council
Unitary authority elections: Marlborough District Council
Territorial authority elections:
Palmerston North City Council,
Kapiti Coast District
United States City elections in Cambridge, Massachusetts At-large municipal board seats in Minneapolis, Minnesota
In British Columbia, Canada, STV was recommended for provincial
elections by the BC Citizens' Assembly on Electoral Reform (British
Columbia). In a 2005 provincial referendum, it received 57.69% support
and passed in 77 of 79 electoral districts. It was not adopted,
however, because it fell short of the 60% threshold requirement the
Liberal government had set for the referendum to be binding. In a
second referendum, on 12 May 2009, STV was defeated 60.91% to 39.09%
STV has also been used in several other jurisdictions, particularly in
provincial general elections in the cities of Edmonton and Calgary in
Alberta. For a more complete list, see History and use of the single
When STV is used for single-winner elections, it is equivalent to the
instant-runoff voting (alternative vote) method. 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. In the
In STV, each voter ranks the list of candidates in order of preference. In the most common ballot design, they place a '1' beside their most preferred candidate, a '2' beside their second most preferred, and so on. The completed ballot paper therefore contains an ordinal list of candidates. In the ballot paper in this image, the preferences of the voter are as follows:
John Citizen Mary Hill Jane Doe
Counting the votes Simplest Method: Elimination Transfers Only The most straightforward way to count a ranked ballot vote is simply to sequentially identify the candidate with the least support, eliminate that candidate, and transfer those ballots to the next-named candidate on each ballot. This process is repeated until there are only as many candidates left as seats available. This method was used for a period of time in several local elections in South Australia. In effect, it is identical to instant-runoff voting, which is commonly used in leadership contests, except that the transfer process is terminated when there are still several candidates remaining. More Refined Method: Setting the Quota In most STV elections, an additional step is taken that ensures that all elected candidates are elected with approximately equal numbers of votes. It can be shown that a candidate requires a minimum number of votes – the quota (or threshold) – to be elected. A number of different quotas can be used; the most common is the Droop quota, given by the floor function formula:
votes needed to win
valid votes cast
seats to fill
displaystyle mbox votes needed to win =operatorname floor left( rm mbox valid votes cast over rm mbox seats to fill +1 right)+1
Droop quota is an extension of requiring a 50% + 1 majority in
single-winner elections. For example, at most 3 people can have 25% +
1 in 3-winner elections, 9 can have 10% + 1 in 9-winner elections, and
If fractional votes can be submitted, then the
Droop quota may be
modified so that the fraction is not rounded down. Major Frank
Britton, of the
A candidate who has reached or exceeded the quota is declared elected. If any such elected candidate has more votes than the quota, the excess votes are transferred to other candidates. Votes that would have gone to the winner go to the next preference. This can be done in several ways (see the section on Counting Methods, below). If no-one new meets the quota, the candidate with the fewest votes is eliminated and those votes are transferred to each voter's next preferred candidate. This process repeats until either a winner is found for every seat or there are as many seats as remaining candidates.
There are variations, such as how to transfer surplus votes from winning candidates and whether to transfer votes to already-elected candidates. When the number of votes transferred from the losing candidate with the fewest votes is too small to change the ordering of remaining candidates, more than one candidate can be eliminated simultaneously. One simplistic formula for how to transfer surplus votes is:
transferred votes given to the next preference
votes for next preference belonging to the original candidate
total votes for the original candidate
surplus votes for original candidate
displaystyle mbox transferred votes given to the next preference =left( mbox votes for next preference belonging to the original candidate over mbox total votes for the original candidate right)* mbox surplus votes for original candidate
however, this can produce fractional votes. See Counting Methods for a discussion of how this is handled. If a candidate is eliminated and their votes are transferred to already victorious candidates, then the new excess votes for the victorious candidate (transferred from the eliminated candidate) will be transferred to the next preference of the victorious candidate, as happened with their initial excess. However, any votes which would transfer from the victorious candidate to one who was already eliminated must be reallocated. See the section on Counting Methods below for details. Because votes cast for losing candidates and excess votes cast for winning candidates are transferred to voters' next choice candidates, STV is said to minimize wasted votes. Example Suppose a food election is conducted to determine what to serve at a party. There are 5 candidates, 3 of which will be chosen. The candidates are: Oranges, Pears, Chocolate, Strawberries, and Sweets. The 20 guests at the party mark their ballots according to the table below. In this example, a second choice is made by only some of the voters.
# of guests 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 20 voters and 3 winners to be found, the number of votes required to be elected is:
(seats to fill)
+ 1 = 6
displaystyle Q_ operatorname Droop =operatorname floor left( 20 mbox (votes cast) over 3 mbox (seats to fill) +1 right)+1=6 mbox (votes required)
When ballots are counted the election proceeds as follows:
Round 1 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, to be precise).
Round 2 x x x x x x x x x x x x x x x x x x x x Chocolate's surplus votes transfer to Strawberry and Sweets in proportion to the Chocolate voters' second choice preferences, using the formula:
votes for second preference
total votes for Chocolate
displaystyle left( mbox votes for second preference over mbox total votes for Chocolate right)* mbox surplus votes
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 Sweets as their second preference, so (4/12)•6 = 2 of Chocolate's votes will transfer to Sweets. Thus, Strawberries has 1 first-preference votes and 4 new votes, for an updated total of 1+4 = 5 votes; likewise, Sweets now has 1 + 2 = 3 votes; no other tallies change. Even with the transfer of this surplus no candidate has reached the quota. 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 Pear's votes are transferred in proportion to the second-preference options of voters of Pear, i.e. only Oranges in this case, which gives Oranges 2 more votes. Oranges now totals 4 (original) + 2 (new) = 6 votes, reaching the quota; so, Oranges is elected. Orange meets the quota exactly, and therefore has no surplus to transfer.
Round 4 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. Strawberry has more votes, so Sweets are eliminated. Sweets' votes would be transferred proportionately, but only two preferences were selected, so Chocolate-then-Sweets votes cannot be reallocated; moreover, no-one who voted for Sweets originally gave a second preference. Therefore, all votes for Sweets disappear. Strawberries is the only remaining candidate, so it wins the final seat (despite not satisfying the quota).
Result: The winners are Chocolate, Oranges and Strawberries.
Main article: Counting single transferable votes
See also: Comparison of the Hare and Droop quotas
STV systems primarily differ in how they transfer 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
Droop quota is the most commonly used quota. This ensures majority
rule (except in rare cases) while maintaining the condition that no
more candidates can reach a quota than there are seats to be filled.
The Hare quota, which was used in the original proposals by Thomas
Hare, ensures greater proportionality, at the expense of having to
count more votes and not guaranteeing majority rule.
The easiest methods of transferring surpluses involve an element of
randomness; partially random systems are used in the Republic of
Ireland (except Senate elections) and in Malta, among other places.
Gregory method (also known as Newland-Britain or Senatorial rules)
eliminates randomness by allowing for the transfer of 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
The concept of transferable voting was first proposed by Thomas Wright
Hill in 1819. The system remained unused in public elections until
Although he was not the first to propose transferable votes, the
English barrister Thomas Hare is generally credited with the
conception of STV, and he may have independently developed the idea in
1857. Hare's view was that STV should be a means of "making the
exercise of the suffrage a step in the elevation of the individual
character, whether it be found in the majority or the minority." In
Hare's original system, he further proposed that electors should have
the opportunity of discovering which candidate their vote had
ultimately counted for, to improve their personal connection with
voting. It should be noted that at the time of Hare's original
proposal the UK did not use the secret ballot, so not only could the
voter determine the ultimate role of their vote in the election, the
elected MPs would have been able to determine who had voted for them.
As Hare envisaged that the whole House of Commons be elected "at
large" this would have replaced geographical constituencies with what
Hare called "constituencies of interest" - those people who had
actually voted for each MP. In modern elections, held by secret
ballot, a voter can discover how their vote was distributed by viewing
detailed election results. This is particularly easy to do using
Meek's method, where only the final weightings of each candidate need
to be published. The elected member is, however, unable to verify who
their supporters are.
The noted political essayist
John Stuart Mill
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
The countback method is used in the Australian Capital Territory,
Tasmania, Victoria, Malta, and Cambridge, Massachusetts. Casual
vacancies could 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.
Yet another option would be 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.
Another possibility is to have the candidates themselves create an
ordered list of successors before leaving their seat. In the European
Parliament, a departing
Republic of Ireland
See also: Tactical voting § Single transferrable vote
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.
(In STV elections, most constituencies will be marginal, at least with
regard to the allocation of a final seat.)
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
Scottish local elections, 2012
Party Total elected Elected on 1st prefs
Total % % (2007)
Conservative 115 46 40.0 40.6
Labour 394 199 50.5 37.4
Liberal Democrat 71 20 28.2 21.7
SNP 425 185 43.5 56.5
Scottish 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, or those who express a minimum number of preferences, in order 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 transfers—i.e., when the votes of a candidate are transferred and no other candidate from that party remains in the count—especially with respect to the first instance in which that occurs:
Average first terminal transfer rates (2012)
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 Democrat 23.1 21.8 20.4 – 15.5 19.3
SNP 44.2 6.0 18.1 14.1 – 17.8
Scottish Green 20.4 5.1 19.2 19.9 18.3 17.0
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:
Candidates not in a winning position on 1st preference who secured election, by party (2012)
Political party Elected though not in top 3 or 4 Not elected though in top 3 or 4 Net gain/loss
Conservative 1 16 −15 −24
Labour 21 8 +13 −17
Liberal Democrat 4 3 +1 +29
SNP 19 29 −10 –
Scottish Green 1 1 – +1
Independent 22 9 +13 +8
Other – 2 −2 +3
Political science portal
Tally (voting) None of the above Approval Voting Single non-transferable vote Table of voting systems by country Voting matters, a journal concerned with the technical aspects of STV
^ "Single Transferable Vote". Electoral Reform Society.
^ "Proportional Representation and its Importance". Proportional
Representation Society of Australia.
^ "Our mission". Electoral Reform Society. Archived from the original
on 12 February 2013.
^ "Ranked Choice Voting". FairVote.
^ Margetts 2003, p. 68.
^ "Single Transferable Vote". Department of Internal Affairs. 2013.
Retrieved 1 April 2016.
^ "What offices are elected using Ranked-Choice Voting?". What is
Ranked-Choice Voting?. City of
Bagehot, Walter (1894) . The English Constitution (7th
ed.). London: Kegan Paul, Trench, Trübner & Co..
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 .
Ireland. Oireachtas. Joint Committee on the Constitution (2010).
"Article 16 of the Constitution: Review of the Electoral System for
Bartholdi, John J., III; Orlin, James B. (1991). "Single Transferable Vote Resists Strategic Voting" (PDF). Social Choice and Welfare. Springer-Verlag. 8 (4): 341–354. doi:10.1007/BF00183045. ISSN 0176-1714. JSTOR 41105995. Retrieved 30 August 2017. 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. Oxford: Elsevier. 24 (2). 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. London: McDougall Trust (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. Department of the Senate. ISBN 0-642-71061-9.
ACE Project A concise STV analogy – from Accurate Democracy Accurate Democracy lists a dozen programs for computing the single transferable vote.
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