Single transferable vote
Encyclopedia
The single transferable vote (STV) is a voting system designed to achieve proportional representation
through preferential voting
. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or unused votes are transferred according to the voter's stated preferences. The system minimizes "wasted" votes
, provides approximately proportional representation, and enables votes to be explicitly cast for individual candidates rather than for closed party lists. It achieves this by using multi-seat constituencies
(voting districts) and by transferring votes to other eligible candidates that would otherwise be wasted on sure losers or sure winners.
A modified version of STV, known as the Hare-Clark system, is used in Australia
in lower house
elections in two states/territories: Tasmania
and the Australian Capital Territory
. The name is derived from Thomas Hare, who initially developed the system and the Tasmanian Attorney General
, Andrew Inglis Clark
, who worked to have a modified version introduced. Hare-Clark has been subsequently modified to introduce improvements, such as rotating ballot papers (the Robson Rotation
). The Upper Houses of the remaining Australian states, as well as the Upper House of the Parliament of Australia
, use conventional STV.
STV is the system of choice of groups such as the Proportional Representation Society of Australia
and the Electoral Reform Society
in the United Kingdom. Its critics contend that some specialists and 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' in an STV ballot paper (see 'Voting' below).
. , in government elections, STV is used for:
In British Columbia
, Canada
, STV was recommended
for provincial elections by the BC Citizens' Assembly on Electoral Reform. 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. In a second referendum on May 12th 2009
STV was defeated, 60.91% to 39.09%
STV has also been used historically in several other jurisdictions. For a more complete list, see History and use of the Single Transferable Vote
.
(alternative vote) method. To differentiate them, STV used for multi-winner elections is sometimes called proportional representation through the single transferable vote, or PR-STV. The term STV usually refers to the multi-winner version, as it does in this article. In Australia STV is known as the Hare-Clark Proportional method, while in the United States it is sometimes called choice voting, preferential voting or preference voting (note that preferential voting
can alternatively refer to a broader category of voting systems).
In STV, each voter ranks the list of candidates in order of preference. In other words (under 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 ballot paper submitted by the voter therefore contains an ordinal list of candidates. In the ballot paper shown in the image on the right, the preferences of the voter are as follows:
, given by the formula:
when the quota is an integer. When the quota is not an integer it is rounded down; that is, its fractional part is ignored.
The 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 so on.
There are variations in applying these STV rules, such as in how to transfer surplus votes from winning candidates and whether to transfer votes to already elected candidates. When the number of votes to transfer from a losing candidate is too small to change the ordering of remaining candidates, more than one candidate can be eliminated simultaneously.
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 vote
s.
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:
When ballots are counted the election proceeds as follows:
Result: The winners are Chocolate, Oranges and Strawberries.
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. As originally conceived STV used the Hare quota
, but this is now generally considered to be technically inferior. New Zealand uses a quota similar to the Droop quota — see: Electoral system of New Zealand
.
The simplest methods of transferring surpluses under STV involve an element of randomness; partially random systems are used in the Republic of Ireland (except Senate elections) and Malta, among other places. For this reason the Gregory method (also known as Newland-Britain or Senatorial rules) was invented, which eliminates randomness by allowing for the transfer of fractions of votes. Gregory is in use in Northern Ireland, Republic of Ireland (Senate elections) and Australia. Both Gregory and these earlier methods have the problem, however, 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. However, while simpler 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 currently used in STV local body elections in New Zealand.
The concept of transferable voting was first proposed by Thomas Wright Hill
in 1821. The system remained unused in real elections until 1855, when Carl Andræ proposed a transferable vote system for elections in Denmark
. Andræ's system was used in 1856 to elect the Danish Rigsraad, and by 1866 it was also adapted for indirect elections to the second chamber, the Landsting
, until 1915.
Although he was not the first to propose a system of 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 STV 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. This is unnecessary in modern STV elections, however, as an individual voter can discover how their vote was ultimately 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 noted political essayist, John Stuart Mill
, was a friend of Hare and an early proponent of STV, praising it at length in his essay Considerations on Representative Government, in which he writes, "Of all modes in which a national representation can possibly be constituted, this one affords the best security for the intellectual qualifications desirable in the representatives. At present... the only persons who can get elected are those who possess local influence, or make their way by lavish expenditure...." His contemporary, Walter Bagehot
, also praised the Hare system for allowing everyone to elect an MP, even ideological minorities, but also argued that the Hare system would create more problems than it solved: "[the Hare system] is inconsistent with the extrinsic independence as well as the inherent moderation of a Parliament - two of the conditions we have seen, are essential to the bare possibility of parliamentary government."
Advocacy of STV spread through the British Empire
, leading it to be sometimes known as British Proportional Representation. 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 system, named after himself and Thomas Hare.
Meek also considered a variant on his system which would have allowed for equal preferences to be expressed.
STV was also adopted in the first half of the 20th century to elect several city councils in the United States
. More than twenty cities used STV, including Cleveland
, Cincinnati
and New York. As of January 2010, it is used to elect the city council and school committee in Cambridge, Massachusetts
and the park board in Minneapolis, Minnesota
.
A frequent concern with STV among electorates considering its adoption is its relative complexity compared with plurality voting
methods. Before the advent of computers, this complexity could have made ballot-counting more difficult than some other voting methods.
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. In addition, unlike in at-large plurality elections, candidates do not have to secure the support of at least 50% of voters, allowing candidates to focus campaign spending primarily on supportive voters.
STV differs from all other proportional representation systems in use in that candidates of one party can be elected on transfers from voters for other parties. Hence, the use of 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, however they may well be more likely to be elected under STV than under First Past The Post. Also while small parties seen as a reasonable second preference by others (such as the Green Party in Ireland) more easily get elected, parties seen as more extreme by others (such as Sinn Féin in Ireland) find it harder to attract second preferences, and therefore find it harder to win seats.
As a multi-member system, filling vacancies between elections can be problematic, and a variety of responses have been devised. The countback method is used in the Australian Capital Territory
; Tasmania
; Victoria
; Malta
; and Cambridge, Massachusetts
. Casual vacancies are filled 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 fulfil the vacancy. A third alternative to fulfil 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. Another alternative 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 or Northern Ireland member 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
, however in 2009 this was changed to allow political parties to nominate new MLAs in the event of a vacancy. Independent MLAs may still draw up a list of potential replacements. For its 2009 European elections
, Malta set a one-off policy to elect the candidate eliminated last for filling the prospective vacancy for the extra seat to arise 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. 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 minimises 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.
STV systems in use in different countries vary, both in ballot design and in whether or not voters are obliged to provide a full list of preferences. In jurisdictions such as the 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. 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.
STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented or disenfranchised
voters.
According to the Gibbard-Satterthwaite theorem
tactical voting is possible in all non-dictatorial deterministic voting systems. A number of methods of tactical or strategic voting exist that can be used in elections conducted using STV. In general these methods are only effective in marginal districts and only affect the allocation of a single seat per district.
Academic analysis of voting systems such as STV generally centers on the voting system criteria that they pass. No preference voting system satisfies all the criteria described in Arrow's impossibility theorem
: in particular, STV fails to achieve independence of irrelevant alternatives
(like most other vote-based ordering systems) as well as monotonicity
.
Proportional representation
Proportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...
through preferential voting
Preferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or unused votes are transferred according to the voter's stated preferences. The system minimizes "wasted" votes
Wasted vote
In the study of electoral systems, a wasted vote may be defined in two different ways:# Any vote which is not for an elected candidate.# Any vote which does not help to elect a candidate....
, provides approximately proportional representation, and enables votes to be explicitly cast for individual candidates rather than for closed party lists. It achieves this by using multi-seat constituencies
Electoral district
An electoral district is a distinct territorial subdivision for holding a separate election for one or more seats in a legislative body...
(voting districts) and by transferring votes to other eligible candidates that would otherwise be wasted on sure losers or sure winners.
A modified version of STV, known as the Hare-Clark system, is used in Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
in lower house
Lower house
A lower house is one of two chambers of a bicameral legislature, the other chamber being the upper house.Despite its official position "below" the upper house, in many legislatures worldwide the lower house has come to wield more power...
elections in two states/territories: Tasmania
Tasmania
Tasmania is an Australian island and state. It is south of the continent, separated by Bass Strait. The state includes the island of Tasmania—the 26th largest island in the world—and the surrounding islands. The state has a population of 507,626 , of whom almost half reside in the greater Hobart...
and the Australian Capital Territory
Australian Capital Territory
The Australian Capital Territory, often abbreviated ACT, is the capital territory of the Commonwealth of Australia and is the smallest self-governing internal territory...
. The name is derived from Thomas Hare, who initially developed the system and the Tasmanian Attorney General
Attorney General
In most common law jurisdictions, the attorney general, or attorney-general, is the main legal advisor to the government, and in some jurisdictions he or she may also have executive responsibility for law enforcement or responsibility for public prosecutions.The term is used to refer to any person...
, Andrew Inglis Clark
Andrew Inglis Clark
Andrew Inglis Clark was an Australian barrister, politician, electoral reformer and jurist. He initially qualified engineer, however he re-trained as a barrister in order to effectively fight for social causes which deeply concerned him...
, who worked to have a modified version introduced. Hare-Clark has been subsequently modified to introduce improvements, such as rotating ballot papers (the Robson Rotation
Robson Rotation
Robson Rotation is the method of printing multiple ballots for single transferable vote elections, with each having the candidates listed in a different order....
). The Upper Houses of the remaining Australian states, as well as the Upper House of the Parliament of Australia
Parliament of Australia
The Parliament of Australia, also known as the Commonwealth Parliament or Federal Parliament, is the legislative branch of the government of Australia. It is bicameral, largely modelled in the Westminster tradition, but with some influences from the United States Congress...
, use conventional STV.
STV is the system of choice of groups such as the Proportional Representation Society of Australia
Proportional Representation Society of Australia
The Proportional Representation Society of Australia is one of the main electoral reform organisations in Australia. It has branches in South Australia, Victoria-Tasmania, New South Wales, Western Australia and the Australian Capital Territory...
and the Electoral Reform Society
Electoral Reform Society
The Electoral Reform Society is a political pressure group based in the United Kingdom which promotes electoral reform. It is believed to be the oldest organisation concerned with electoral systems in the world.-Aims:...
in the United Kingdom. Its critics contend that some specialists and 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' in an STV ballot paper (see 'Voting' below).
Adoption
STV has had its widest adoption in the English-speaking worldEnglish-speaking world
The English-speaking world consists of those countries or regions that use the English language to one degree or another. For more information, please see:Lists:* List of countries by English-speaking population...
. , in government elections, STV is used for:
| Parliamentary elections (since 1921) European elections Local government elections |
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| Parliamentary elections European elections Local government elections |
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| Regional assembly elections European elections Local government elections |
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| Local government elections (since May 2007 Scottish local elections, 2007 The Scottish local elections, 2007 were held on 3 May 2007, the same day as Scottish Parliament elections and local elections in parts of England... ) |
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| Upper house of Parliament Rajya Sabha The Rajya Sabha or Council of States is the upper house of the Parliament of India. Rajya means "state," and Sabha means "assembly hall" in Sanskrit. Membership is limited to 250 members, 12 of whom are chosen by the President of India for their expertise in specific fields of art, literature,... elections (indirect election by state MLAs) |
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| Senate Senate of Pakistan The Senate of Pakistan is the upper house of the bicameral Parliament of Pakistan. Elections are held every three years for one half of the senate and each senator has a term of six years... elections (indirect election by members of provincial assemblies, and direct vote by the population of territories Federally Administered Tribal Areas The Federally Administered Tribal Areas are a semi-autonomous tribal region in the northwest of Pakistan, lying between the province of Khyber Pakhtunkhwa, Balochistan, and the neighboring country of Afghanistan. The FATA comprise seven Agencies and six FRs... ) |
||
| Country-wide | Senate elections Australian Senate The Senate is the upper house of the bicameral Parliament of Australia, the lower house being the House of Representatives. Senators are popularly elected under a system of proportional representation. Senators are elected for a term that is usually six years; after a double dissolution, however,... (in the form of a group voting ticket Group voting ticket Group voting tickets are a way to simplify preferential voting, usually in an election held under the single transferable vote or the alternative vote system.... ) |
|
 Australian Capital Territory |
Legislative Assembly Australian Capital Territory Legislative Assembly The Australian Capital Territory Legislative Assembly is the unicameral legislature of the Australian Capital Territory... elections |
|
 New South Wales |
Legislative Council New South Wales Legislative Council The New South Wales Legislative Council, or upper house, is one of the two chambers of the parliament of New South Wales in Australia. The other is the Legislative Assembly. Both sit at Parliament House in the state capital, Sydney. The Assembly is referred to as the lower house and the Council as... elections Local government elections |
|
 South Australia |
Legislative Council South Australian Legislative Council The Legislative Council, or upper house, is one of the two chambers of the Parliament of South Australia. Its central purpose is to act as a house of review for legislation passed through the lower house, the House of Assembly... elections Local government elections |
|
 Tasmania |
House of Assembly Tasmanian House of Assembly The House of Assembly, or Lower House, is one of the two chambers of the Parliament of Tasmania in Australia. The other is the Legislative Council or Upper House... elections Local government elections |
|
 Victoria (Australia) |
Legislative Council Victorian Legislative Council The Victorian Legislative Council, is the upper of the two houses of the Parliament of Victoria, Australia; the lower house being the Legislative Assembly. Both houses sit in Parliament House in Spring Street, Melbourne. The Legislative Council serves as a house of review, in a similar fashion to... elections Local government elections |
|
 Western Australia |
Legislative Council elections |
|
| Some local government elections such as Dunedin and the capital city of Wellington Local health board elections |
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| City elections in Cambridge, Massachusetts Cambridge, Massachusetts Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent... Certain city elections in Minneapolis, Minnesota Minneapolis, Minnesota Minneapolis , nicknamed "City of Lakes" and the "Mill City," is the county seat of Hennepin County, the largest city in the U.S. state of Minnesota, and the 48th largest in the United States... (starting in 2009) |
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| First used in Constitutional Assembly elections in 2010 | ||
In British Columbia
British Columbia
British Columbia is the westernmost of Canada's provinces and is known for its natural beauty, as reflected in its Latin motto, Splendor sine occasu . Its name was chosen by Queen Victoria in 1858...
, Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
, STV was recommended
BC-STV
BC-STV is a proposed voting system recommended by the Citizens' Assembly on Electoral Reform for use in British Columbia, and belongs to the Single Transferable Vote family of voting systems. BC-STV was supported by a majority of the voters in a referendum held in 2005 but the government had...
for provincial elections by the BC Citizens' Assembly on Electoral Reform. In a 2005 provincial referendum
British Columbia electoral reform referendum, 2005
A referendum was held in the Canadian province of British Columbia on May 17, 2005 to determine whether or not to adopt the recommendations of the Citizens' Assembly on Electoral Reform...
, 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. In a second referendum on May 12th 2009
British Columbia electoral reform referendum, 2009
A second referendum on electoral reform was held in conjunction with the provincial election on May 12, 2009. The BC-single transferrable vote electoral system was again voted on by the BC electorate. It would have required 60 per cent overall approval and 50 per cent approval in at least 60 per...
STV was defeated, 60.91% to 39.09%
STV has also been used historically in several other jurisdictions. For a more complete list, see History and use of the Single Transferable Vote
History and use of the Single Transferable Vote
The history and usage of the Single Transferable Vote voting system has been a series of relatively modest periods of usage and disusage throughout the world, however today it is seeing increasing popularity and proposed implementation as a method of electoral reform...
.
Terminology
When STV is used for single-winner elections, it is equivalent to the instant-runoff votingInstant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
(alternative vote) method. To differentiate them, STV used for multi-winner elections is sometimes called proportional representation through the single transferable vote, or PR-STV. The term STV usually refers to the multi-winner version, as it does in this article. In Australia STV is known as the Hare-Clark Proportional method, while in the United States it is sometimes called choice voting, preferential voting or preference voting (note that preferential voting
Preferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
can alternatively refer to a broader category of voting systems).
Voting
- John Citizen
- Mary Hill
- Jane Doe
Setting the quota
In an STV election, a candidate requires a certain 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 quotaDroop Quota
The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation . In an STV election the quota is the minimum number of votes a...
, given by the formula:
when the quota is an integer. When the quota is not an integer it is rounded down; that is, its fractional part is ignored.
The 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 so on.
Finding the winners
An STV election proceeds according to the following steps:- Any candidate who has reached or exceeded the quota is declared elected.
- If a candidate has more votes than the quota, that candidate's surplus votes are transferred to other candidates. Votes that would have gone to the winner instead go to the next preference listed on their ballot.
- If no one new meets the quota, the candidate with the fewest votes is eliminated and that candidate's votes are transferred.
- This process repeats until either a winner is found for every seat or there are as many seats as remaining candidates.
There are variations in applying these STV rules, such as in how to transfer surplus votes from winning candidates and whether to transfer votes to already elected candidates. When the number of votes to transfer from a losing candidate is too small to change the ordering of remaining candidates, more than one candidate can be eliminated simultaneously.
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 vote
Wasted vote
In the study of electoral systems, a wasted vote may be defined in two different ways:# Any vote which is not for an elected candidate.# Any vote which does not help to elect a candidate....
s.
An 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 have their ballots marked according to the table below. In this example, a second choice is needed by only some of the voters, however with a different vote distribution additional preferences may be needed.| # of Guests | x x x x | x x | x x x x x x x x |
x x x x | x | x |
|---|---|---|---|---|---|---|
| 1st Preference |  |
 |
 |
 |
||
| 2nd Preference | |
|
|
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:
When ballots are counted the election proceeds as follows:
| Candidate: | |
|
|
|
||
|---|---|---|---|---|---|---|
| Round 1 | x x x x | x x | x x x x x x x x x x x x |
x | x | Round 1: Chocolate is declared elected, since Chocolate has more votes than the quota |
| Round 2 | x x x x | x x | x x x x x x |
x x x x x |
x x x | Round 2: Chocolate's surplus votes transfer to Strawberry and Sweets in proportion to the Chocolate voters' second choice preferences. However, even with the transfer of this surplus no candidate has reached the quota. Therefore Pear, who has the fewest votes, is eliminated. |
| Round 3 | x x x x x x |
x x x x x x |
x x x x x |
x x x | Round 3: Pear's votes transfer to their second preference, Oranges, causing Orange to reach the quota and be 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 | Round 4: Neither of the remaining candidates meets the quota, but Strawberry has more votes, so Sweets are eliminated, and Strawberry wins the final seat. |
Result: The winners are Chocolate, Oranges and Strawberries.
Differing counting methods
STV systems differ in a number of ways, primarily in how they transfer votes as well as in the exact size of the quota used for determining winners. In fact, for this reason some have suggested that STV can be considered a family of voting systems rather than a single system. Today the Droop quotaDroop Quota
The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation . In an STV election the quota is the minimum number of votes a...
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. As originally conceived STV used the Hare quota
Hare quota
The Hare quota is a formula used under some forms of the Single Transferable Vote system and the largest remainder method of party-list proportional representation...
, but this is now generally considered to be technically inferior. New Zealand uses a quota similar to the Droop quota — see: Electoral system of New Zealand
Electoral system of New Zealand
In 1994 New Zealand officially adopted mixed member proportional representation as its electoral system for the House of Representatives after many years of first-past-the-post voting. The first MMP election was held in 1996....
.
The simplest methods of transferring surpluses under STV involve an element of randomness; partially random systems are used in the Republic of Ireland (except Senate elections) and Malta, among other places. For this reason the Gregory method (also known as Newland-Britain or Senatorial rules) was invented, which eliminates randomness by allowing for the transfer of fractions of votes. Gregory is in use in Northern Ireland, Republic of Ireland (Senate elections) and Australia. Both Gregory and these earlier methods have the problem, however, that in some circumstances they do not treat all votes equally. For this reason Meek's method, Warren's method and the Wright system
Wright system
The Wright system is a refinement of rules associated with proportional representation by means of the single transferable vote electoral system...
have been invented. However, while simpler 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 currently used in STV local body elections in New Zealand.
History and current use
The concept of transferable voting was first proposed by Thomas Wright Hill
Thomas Wright Hill
Thomas Wright Hill was a mathematician and schoolmaster. He is credited as inventing the single transferable vote in 1819...
in 1821. The system remained unused in real elections until 1855, when Carl Andræ proposed a transferable vote system for elections in Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
. Andræ's system was used in 1856 to elect the Danish Rigsraad, and by 1866 it was also adapted for indirect elections to the second chamber, the Landsting
Landsting (Denmark)
The Landsting was a house of the Rigsdag in Denmark from 1849 until 1953, when the bicameral system was abolished. The house had powers equal to the Folketing, which made the two houses of parliament hard to distinguish....
, until 1915.
Barrister
A barrister is a member of one of the two classes of lawyer found in many common law jurisdictions with split legal professions. Barristers specialise in courtroom advocacy, drafting legal pleadings and giving expert legal opinions...
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 STV 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. This is unnecessary in modern STV elections, however, as an individual voter can discover how their vote was ultimately 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 noted political essayist, John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...
, was a friend of Hare and an early proponent of STV, praising it at length in his essay Considerations on Representative Government, in which he writes, "Of all modes in which a national representation can possibly be constituted, this one affords the best security for the intellectual qualifications desirable in the representatives. At present... the only persons who can get elected are those who possess local influence, or make their way by lavish expenditure...." His contemporary, Walter Bagehot
Walter Bagehot
Walter Bagehot was an English businessman, essayist, and journalist who wrote extensively about literature, government, and economic affairs.-Early years:...
, also praised the Hare system for allowing everyone to elect an MP, even ideological minorities, but also argued that the Hare system would create more problems than it solved: "[the Hare system] is inconsistent with the extrinsic independence as well as the inherent moderation of a Parliament - two of the conditions we have seen, are essential to the bare possibility of parliamentary government."
Advocacy of STV spread through the British Empire
British Empire
The British Empire comprised the dominions, colonies, protectorates, mandates and other territories ruled or administered by the United Kingdom. It originated with the overseas colonies and trading posts established by England in the late 16th and early 17th centuries. At its height, it was the...
, leading it to be sometimes known as British Proportional Representation. In 1896, Andrew Inglis Clark
Andrew Inglis Clark
Andrew Inglis Clark was an Australian barrister, politician, electoral reformer and jurist. He initially qualified engineer, however he re-trained as a barrister in order to effectively fight for social causes which deeply concerned him...
was successful in persuading the Tasmanian House of Assembly
Tasmanian House of Assembly
The House of Assembly, or Lower House, is one of the two chambers of the Parliament of Tasmania in Australia. The other is the Legislative Council or Upper House...
to be the first parliament in the world elected by what became known as the Hare-Clark system, named after himself and Thomas Hare.
Meek also considered a variant on his system which would have allowed for equal preferences to be expressed.
STV was also adopted in the first half of the 20th century to elect several city councils in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. More than twenty cities used STV, including Cleveland
Cleveland, Ohio
Cleveland is a city in the U.S. state of Ohio and is the county seat of Cuyahoga County, the most populous county in the state. The city is located in northeastern Ohio on the southern shore of Lake Erie, approximately west of the Pennsylvania border...
, Cincinnati
Cincinnati, Ohio
Cincinnati is a city in the U.S. state of Ohio. Cincinnati is the county seat of Hamilton County. Settled in 1788, the city is located to north of the Ohio River at the Ohio-Kentucky border, near Indiana. The population within city limits is 296,943 according to the 2010 census, making it Ohio's...
and New York. As of January 2010, it is used to elect the city council and school committee in Cambridge, Massachusetts
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
and the park board in Minneapolis, Minnesota
Minneapolis, Minnesota
Minneapolis , nicknamed "City of Lakes" and the "Mill City," is the county seat of Hennepin County, the largest city in the U.S. state of Minnesota, and the 48th largest in the United States...
.
Issues
The degree of proportionality of STV election results depends directly on the district magnitude. While Ireland originally had a median district magnitude of five (range three to nine) in 1923, successive governments lowered this. 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. When Northern Ireland adopted STV, they found five-seaters not sufficiently proportional and chose six-seaters.A frequent concern with STV among electorates considering its adoption is its relative complexity compared with plurality voting
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
methods. Before the advent of computers, this complexity could have made ballot-counting more difficult than some other voting methods.
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. In addition, unlike in at-large plurality elections, candidates do not have to secure the support of at least 50% of voters, allowing candidates to focus campaign spending primarily on supportive voters.
STV differs from all other proportional representation systems in use in that candidates of one party can be elected on transfers from voters for other parties. Hence, the use of STV may reduce the role of political parties in the electoral process and corresponding partisanship
Partisan (political)
In politics, a partisan is a committed member of a political party. In multi-party systems, the term is widely understood to carry a negative connotation - referring to those who wholly support their party's policies and are perhaps even reluctant to acknowledge correctness on the part of their...
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, however they may well be more likely to be elected under STV than under First Past The Post. Also while small parties seen as a reasonable second preference by others (such as the Green Party in Ireland) more easily get elected, parties seen as more extreme by others (such as Sinn Féin in Ireland) find it harder to attract second preferences, and therefore find it harder to win seats.
As a multi-member system, filling vacancies between elections can be problematic, and a variety of responses have been devised. The countback method is used in the Australian Capital Territory
Australian Capital Territory
The Australian Capital Territory, often abbreviated ACT, is the capital territory of the Commonwealth of Australia and is the smallest self-governing internal territory...
; Tasmania
Tasmania
Tasmania is an Australian island and state. It is south of the continent, separated by Bass Strait. The state includes the island of Tasmania—the 26th largest island in the world—and the surrounding islands. The state has a population of 507,626 , of whom almost half reside in the greater Hobart...
; Victoria
Victoria (Australia)
Victoria is the second most populous state in Australia. Geographically the smallest mainland state, Victoria is bordered by New South Wales, South Australia, and Tasmania on Boundary Islet to the north, west and south respectively....
; Malta
Malta
Malta , officially known as the Republic of Malta , is a Southern European country consisting of an archipelago situated in the centre of the Mediterranean, south of Sicily, east of Tunisia and north of Libya, with Gibraltar to the west and Alexandria to the east.Malta covers just over in...
; and Cambridge, Massachusetts
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
. Casual vacancies are filled 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 fulfil the vacancy. A third alternative to fulfil 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. Another alternative is to have the candidates themselves create an ordered list of successors before leaving their seat. In the European Parliament
European Parliament
The European Parliament is the directly elected parliamentary institution of the European Union . Together with the Council of the European Union and the Commission, it exercises the legislative function of the EU and it has been described as one of the most powerful legislatures in the world...
, a departing Republic of Ireland or Northern Ireland member 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
Northern Ireland Assembly
The Northern Ireland Assembly is the devolved legislature of Northern Ireland. It has power to legislate in a wide range of areas that are not explicitly reserved to the Parliament of the United Kingdom, and to appoint the Northern Ireland Executive...
, however in 2009 this was changed to allow political parties to nominate new MLAs in the event of a vacancy. Independent MLAs may still draw up a list of potential replacements. For its 2009 European elections
European Parliament election, 2009 (Malta)
The European Parliament election of 2009 in Malta was the election of the delegation from Malta to the European Parliament in 2009. The elections were held on June 6 on the same day as the Maltese local council elections, 2009....
, Malta set a one-off policy to elect the candidate eliminated last for filling the prospective vacancy for the extra seat to arise 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. 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 minimises 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.
STV systems in use in different countries vary, both in ballot design and in whether or not voters are obliged to provide a full list of preferences. In jurisdictions such as the 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. 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.
STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented or disenfranchised
Disfranchisement
Disfranchisement is the revocation of the right of suffrage of a person or group of people, or rendering a person's vote less effective, or ineffective...
voters.
According to the Gibbard-Satterthwaite theorem
Gibbard-Satterthwaite theorem
The Gibbard–Satterthwaite theorem, named after Allan Gibbard and Mark Satterthwaite, is a result about the deterministic voting systems that choose a single winner using only the preferences of the voters, where each voter ranks all candidates in order of preference...
tactical voting is possible in all non-dictatorial deterministic voting systems. A number of methods of tactical or strategic voting exist that can be used in elections conducted using STV. In general these methods are only effective in marginal districts and only affect the allocation of a single seat per district.
Academic analysis of voting systems such as STV generally centers on the voting system criteria that they pass. No preference voting system satisfies all the criteria described in Arrow's impossibility theorem
Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
: in particular, STV fails to achieve independence of irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
(like most other vote-based ordering systems) as well as monotonicity
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
.
See also
- Table of voting systems by nationTable of voting systems by nationThis table deals with voting to select candidates for office, not for the passing of legislation.- Voting systems by country :- Key :Seats per district : Most elections are split into a number of electoral districts. In some elections, there is one person elected per district. In others, there are...
- Alternative vote
- Single Non-Transferable VoteSingle non-transferable voteThe single non-transferable vote or SNTV is an electoral system used in multi-member constituency elections.- Voting :In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes...
- Counting Single Transferable VotesCounting Single Transferable VotesThe single transferable vote is a voting system based on proportional representation and preferential voting. Under STV, an elector's vote is initially allocated to his or her most-preferred candidate...
- Electoral Reform SocietyElectoral Reform SocietyThe Electoral Reform Society is a political pressure group based in the United Kingdom which promotes electoral reform. It is believed to be the oldest organisation concerned with electoral systems in the world.-Aims:...
- Instant-runoff votingInstant-runoff votingInstant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
- Range VotingRange votingRange voting is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.A form of range voting was apparently used in...
- Tally (voting)Tally (voting)A tally is an unofficial private observation of an election count carried out under Proportional Representation using the Single Transferable Vote. Tallymen, predominantly a feature of the Irish electoral process, are appointed by political candidates and parties. They observe the opening of...
- Voting systemVoting systemA voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
- Proportional representationProportional representationProportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...
- None of the aboveNone of the aboveNone of the Above or against all is a ballot option in some jurisdictions or organizations, designed to allow the voter to indicate disapproval of all of the candidates in a voting system...
(NOTA) or Re-Open Nominations (RON) - Voting mattersVoting mattersVoting matters is a peer-reviewed academic journal whose purpose is "To advance the understanding of preferential voting systems". Originally published by the Electoral Reform Society , Voting matters is now a publication of the McDougall Trust...
, a journal concerned with the technical aspects of STV
Information and summaries
- Easy to understand Flash animation produced for the British Columbia referendum
- Advantages and Disadvantages of STV - from the ACE Project
- Malta: STV with some twists - from the ACE Project
- Ireland: The archetypal STV system - from the ACE Project
- Electoral Systems and Conflict Management: Comparing STV and AV Systems - from the ACE Project
- A concise STV analogy - from Accurate Democracy
- Visualising the Hare-Clark Electoral System by Antony GreenAntony GreenAntony John Green is an Australian psephologist and commentator for the Australian Broadcasting Corporation.-Early years and background:...
(Australian Broadcasting CorporationAustralian Broadcasting CorporationThe Australian Broadcasting Corporation, commonly referred to as "the ABC" , is Australia's national public broadcaster...
) - Ideal Majority STV - modification to ensure provide a majority result proportional to mandate
Simulations and software
- Single Transferable Vote Simulator Interactive Flash program that lets the user assign votes and see the results as per STV.
- Flash animation providing a short overview of STV
- Guth an Phobail - a Java animation of all recent STV elections in Ireland (in Irish)
- / election polarbears - a Java animation of STV elections in Ireland 1982-2007 in English
- PoliticalSim — uses Excel scatter plots of voter and candidate positions to explain transferring votes.
- ChoicePlus — software for computing the single transferable vote
- OpenSTV — software for computing the single transferable vote
- BC DemoChoice Simulating 2005 BC Election if STV was used
- Single Transferable Vote Animation (BC-STV) detailed flash animation explaining the process of Single Transferable Vote.
- Joey's STV free Excel spreadsheet for computing simple STVs without additional software.
- Accurate Democracy lists a dozen programs for computing the single transferable vote.
- Flash animation of how Meek's method is used to count votes in New Zealand STV
- Indaba.org -- Ranked Choice Ballot Demo, including visualizations of an STV Runoff
Articles and publications
- P.R. in Ireland. A series of articles by Proinsias Mac AonghusaProinsias Mac AonghusaProinsias Mac Aonghusa was a vice-chairman of Ireland's Labour Party. He was a broadcaster for Radio Éireann , and for RTÉ, UTV and the BBC...
explaining the history and workings of the P.R. system in Ireland, published in 1959. - The Single Transferable Vote procedure in Ireland
- Information on BC-STV. British Columbia's Referendum on STV.
- A Technical Description of the Single Transferable Vote. Paper by Brian Wichmann.
- Tie-Breaking with the Single Transferable Vote. Paper by Jeffrey C. O'Neill, Voting mattersVoting mattersVoting matters is a peer-reviewed academic journal whose purpose is "To advance the understanding of preferential voting systems". Originally published by the Electoral Reform Society , Voting matters is now a publication of the McDougall Trust...
. - Single Transferable Vote with Borda Elimination: A New Vote Counting System, also Electoral Studies 24:2 June 2005. Article by Chris Geller.
- List of Organisations using STV for their Elections
- "Single Transferable Vote Resists Strategic Voting", by John J. Bartholdi, III and James B. OrlinJames B. OrlinJames Berger Orlin is an American operations researcher, the Edward Pennell Brooks Professor in Management and Professor of Operations Research at the MIT Sloan School of Management....
. - Detailed Description of the STV Count in accordance with the Rules in the Scottish Local Government Elections Order 2007. Article by James Gilmour.
Proponent groups
- Fair Voting BC (Canada)
- FairVote (USA, formerly the Center for Voting and Democracy)
- Proportional Representation Society of Australia
- Electoral Reform Society (United Kingdom) See also the Wikipedia articleElectoral Reform SocietyThe Electoral Reform Society is a political pressure group based in the United Kingdom which promotes electoral reform. It is believed to be the oldest organisation concerned with electoral systems in the world.-Aims:...
- STV Action (United Kingdom)
- The Center for Range Voting