Electoral methods
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Single transferable vote (STV) is a preferential voting system designed to minimize wasted votes and provide proportional representation while ensuring that votes are explicitly for candidates rather than party lists. It achieves this by using multi-seat constituencies (districts) and by transferring votes that would otherwise be wasted. STV initially allocates an individual's vote to their most preferred candidate, and then subsequently transfers unneeded or unused votes after candidates are either elected or eliminated, according to the voter's stated preferences.

As of 2007, STV is used for elections in the Republic of Ireland (since 1919), Northern Ireland (except elections to the British House of Commons) and Malta. It is also used for federal Senate and certain regional and local elections in Australia, local government elections in Scotland and some local government elections in New Zealand — see History and use of the Single Transferable Vote. In the United States, it is used for city elections in Cambridge, Massachusetts, and will be used for certain city elections in Minneapolis, Minnesota, starting in 2009. Under a bill before the Parliament of Canada, STV would be used for consultative elections of Senators. A variation of STV known as BC-STV came within three points of meeting the 60% threshold necessary for adoption in British Columbia in a 2005 referendum, but it will be put to the voters a second time in 2009. STV has been used for Scottish local elections since May 2007.

Terminology

When STV is used in a single-winner election, it is the same as instant-runoff voting. When used in multi-seat constituencies, it is also called proportional representation through the single transferable vote (PR-STV). Because instant-runoff is not a form of proportional representation, some scholars consider it a separate system from PR-STV. STV usually refers to PR-STV, and 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 and preference voting.

Voting

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:

1. John Citizen
2. Mary Hill
3. Jane Doe

Counting the votes

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 quota, given by the formula:

where:

• Votes = the total number of valid (unspoilt) votes cast
• Seats = the number of seats to be filled

Finding the winners

An STV election proceeds according to the following steps:

1. Any candidate who has reached or exceeded the required quota is declared elected.
2. If not enough candidates have been elected, the count continues.
3. If a candidate has more votes than the quota, then his or her surplus value is transferred to other candidates according to each voter's allocated preferences.
4. The candidate with the fewest votes is eliminated and his or her votes are transferred to remaining candidates according to voters' preferences.

This process repeats from step 1 until the required number of candidates have been elected.

Whether votes are transferred to elected candidates depends on the particular counting system chosen; systems that allow this subsequently redistribute the surplus, again.

A manual count is often halted when the number of seats to be filled equals the number of remaining candidates, instead of counting votes until all candidates have reached a quota. Also, if the number of votes transferred is insufficient to either elect a candidate or change the order of candidates in the ranking, then multiple candidates may be excluded at once or a surplus may be held instead of being transferred. These procedures are common if ballots which do not list a full ranking of candidates become exhausted, because it is then possible for an insufficient number of candidates to reach the quota.

Because in STV, candidates who receive excess votes and candidates who are excluded have their votes transferred to other candidates, it is said to minimise wasted votes.

There are two basic forms of counting an STV election: one is based on the number of ballot papers allocated to a candidate; the other, more accurate system, is based on the value of the vote as it progresses throughout the count. This variance is important in the calculation of a candidate's surplus. The paper-based formula (the surplus divided by the number of ballot papers) undermines proportionality and the "one vote, same value" principle due to some votes increasing in value at the expense of other votes. The value-based formula (the value of the vote divided by the surplus) avoids these shortcomings, ensuring proportionality and maintaining the "one vote, same value" principle.

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 Candy. The 20 guests at the party have the preferences marked on their ballots in the two tables below (the first is a numerical representation, the second is pictorial). In this election only the first one or two preferences of voters are shown, because in this case their lower preferences will not affect the result.

# 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 proportionately to Strawberry and candy according 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 barely meets the quota, 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, so Candy is eliminated. Strawberry is the only remaining candidate and so wins the final seat.

Result: The winners are Chocolate, Oranges and Strawberries.

Differing counting methods

Main article: Counting Single Transferable Votes

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 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. 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 and Warren's method have been invented.^[1] 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. Meek is currently used in STV local body elections in New Zealand.

The most recent refinements of STV involve attempting to remove the problem of sequential exclusions. Sequential exclusions mean that sometimes STV eliminates, at an early stage in the count, a candidate who might have gone on to be elected later had they been allowed to remain in the contest. Systems such as CPO-STV and Sequential STV have been invented to overcome this problem by incorporating elements of Condorcet methods into STV. A method known as BTR-STV deals with the problem differently and more simply than these systems by simply making sure no such candidate could possibly be eliminated. None of these new methods has yet been used in a government election.

Most of the systems that are currently in use were designed to facilitate a manual counting process. With the ever increasing use of computer technology, many of the processes are in need of review. For example, in calculating a candidate's surplus, some systems use the number of ballot papers (surplus/number of papers) as opposed to the allocated value of the ballot papers to determine the value of any candidates surplus (value of the vote/surplus). Computers make it feasible to use the more accurate allocated value method, which maintains the one vote one value principle. A paper-based formula distorts the vote, increasing the value of some votes at the expense of others.

Manual counting issues, like segmentation transfers, need to be further considered in a computerised count. Segmentation transfers are where votes are distributed according to either the order in which they were received, last bundle or the grouping of common value of ballot papers to be transferred from highest to lowest. To simplify the counting process in a computerised count there should be single transaction per candidate without segmentation.

History and current use

Main article: History and use of the Single Transferable Vote

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 Rigsdag, 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.^[2] 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.

The noted political essayist, John Stuart Mill, was a friend of Hare and an early proponent of STV, praising it in his essay Considerations on Representative Government.^[3] His contemporary, Walter Bagehot, also praised the Hare system for allowing everyone to elect an MP, even ideological minorities, but also added 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."^[4]

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.

Issues

Main article: Issues affecting the Single Transferable Vote

A frequent concern with STV among electorates considering its adoption is its relative complexity compared with plurality voting methods.

STV differs from all other proportional-representation systems in actual 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.

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 fulfill the vacancy. A third alternative to fulfill 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

Standing too few candidates may result in all of them being elected in the early stages, and votes being transferred to candidates of other parties. Standing too many candidates might result in first-preference votes being spread too thinly amongst 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 most voters will preference candidates from the same party in order which minimises the impact of this potential shortcoming 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. 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 as to ballot design and to 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 are permitted to 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/ 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.

See also

• Table of voting systems by nation
• Single Non-Transferable Vote
• Instant-runoff voting
• Voting system
• Proportional representation

References

External links

Information and summaries

• 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

Simulations and software

• 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
• 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

Articles and publications

• Voting Matters - a discussion paper, first published in 1994, normally published twice a year, that examines the technical issues of the single transferable vote and related electoral systems.
• P.R. in Ireland - by Proinsias Mac Aonghusa. A series of articles 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 Article by Brian Wichmann.
• Tie-Breaking with the Single Transferable Vote Article by Jeffrey C. O'Neill
• Single Transferable Vote with Borda Elimination: A New Vote Counting Systemalso Electoral Studies 24:2 June 2005. Article by Chris Geller.
• "Single Transferable Vote Resists Strategic Voting" by John J. Bartholdi, III and James B. Orlin.
• 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

• FairVote (USA, formerly the Center for Voting and Democracy)
• Proportional Representation Society of Australia
• Electoral Reform Society (United Kingdom) See also the Wikipedia article
• STV Action (United Kingdom)