# Single transferable vote

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Single transferable vote

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,[1] 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).

## Contents

STV has had its widest adoption in the English-speaking world. As of 2010, in government elections, STV is used for:

 Ireland Parliamentary elections (since 1921) European elections Local government elections Malta Parliamentary elections European elections Local government elections United Kingdom Northern Ireland Regional assembly elections European elections Local government elections Scotland Local government elections (since May 2007) India Upper house of Parliament elections (indirect election by state MLAs) Pakistan Senate elections (indirect election by members of provincial assemblies, and direct vote by the population of territories) Australia Country-wide Senate elections (in the form of a group voting ticket) Australian Capital Territory Legislative Assembly elections New South Wales Legislative Council elections Local government elections South Australia Legislative Council elections Local government elections Tasmania House of Assembly elections Local government elections Victoria Legislative Council elections Local government elections Western Australia Legislative Council elections New Zealand Some local government elections such as Dunedin and the capital city of Wellington Local health board elections United States City elections in Cambridge, Massachusetts Certain city elections in Minneapolis, Minnesota (starting in 2009) Iceland First used in Constitutional Assembly elections in 2010

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.

## Terminology

When STV is used for single-winner elections, it is equivalent to the instant-runoff voting (alternative vote) method.[2]   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).

## 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:

$\mbox{votes needed to win} = \left({{\rm \mbox{valid votes cast}} \over {\rm \mbox{seats to fill}}+1}\right) + 1$

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:

1. Any candidate who has reached or exceeded the quota is declared elected.
2. 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.
3. If no one new meets the quota, the candidate with the fewest votes is eliminated and that candidate's votes are transferred.
4. 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 votes.

## 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:

$\left({\mbox{20 votes cast} \over {\mbox{3 seats to fill}+1}}\right) +1 = \mbox{6 votes required}$

When ballots are counted the election proceeds as follows:

Candidate: Round 1: Chocolate is declared elected, since Chocolate has more votes than the quota 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: 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: 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 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[citation needed]. 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.[3] 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

Carl Andræ

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,[4] and by 1866 it was also adapted for indirect elections to the second chamber, the Landsting, until 1915.

Thomas Hare

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.[5] 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...."[6] 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."[7]

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.

## 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.[8] 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 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.[citation needed]

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.[9] 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,[citation needed] 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.

## References

1. ^ Justin Fisher, D. T. Denver and John Benyon, Central debates in British politics (2003), Pearson Education, ISBN 9780582437272, p. 68.
2. ^ "Q&A: Electoral reform and proportional representation". BBC. 2010-05-11. Retrieved 13 May 2010.
3. ^ Hill, I.D. (1987). "Algorithm 123 — Single Transferable Vote by Meek’s method".
4. ^ AndrĂŚs metode | Gyldendal - Den Store Danske
5. ^ Lambert & Lakeman (1955). "Voting in democracies". London : Faber, p. 245.
6. ^ Mill, J.S. "Considerations on Representative Government." Online at http://www.gutenberg.org/dirs/etext04/conrg10h.htm. Accessed 25 May 2007.
7. ^ Bagehot, Walter. "English Constitution".
8. ^ Joint Committee on the Constitution, Fourth Report, p. 177. "[1]".
9. ^ Goggins, Paul. "Change to the system for filling vacancies in the NI Assembly". Northern Ireland Office Website. Northern Ireland Office. Retrieved 5 October 2011.

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