Single Transferable Vote

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The Single Transferable Vote, or STV, is a preference voting system designed to minimise wasted votes in multi-candidate elections while ensuring that votes are explicitly for candidates rather than party lists. STV systems achieve this by initially allocating an individual's vote to their most preferred candidate and then subsequently transferring wasted votes after candidates become either elected or eliminated according to the voter's ballot.

When promoted as a proportional representation method in multi-party multi-seat elections, it is generally known as Proportional Representation through the Single Transferable Vote or PR-STV; in Australia it is known as the Hare-Clark Proportional method, while the same system with parties able to indicate preferences is called STV. When STV methods are applied to single-seat elections, they simplify to instant-runoff voting and have different proportionality implications for a similar ballot due to the existence of only one winner.



Voting in STV is done with the goal of seeing that each elected representative has a number of distinct voters prefering him over other, unelected candidates. To ensure this, excess and unused votes from winning and losing candidates are transfered to remaining candidates according to the voter's preferences.

This method is sometimes approximated in elections among schoolchildren: the children line-up behind the candidate of their choice until enough members have a long enough line behind them. Since the children would all know that each candidate only needs a certain number of classmates' votes to be elected, those arriving last in line for a candidate who already has enough votes would choose to not waste their vote and instead move to another line to help someone else to win. Likewise, those children whose candidate obviously could not win would move to another line, and so on, until all the representatives are chosen.

Missing image

This process is automated in STV by use of the preferential ballot, a method for determining how to transfer votes, and a derived quota for determining winners. Each winning candidate represents a single quota's worth of votes analogous to the children lined up behind him, and voters are in turn automatically lined up and transfered according to how their preferences are listed on their ballots. Wasted votes, those that go to nonwinning candidates or candidates that have already won, are therefore effectively minimized in STV systems, simultaneously minimizing the number of unrepresented voters and providing proportionality. Depending on the method of STV used and the preference distribution of the voters, these wasted votes can either be completely localised within a small portion of the electorate (less than one quota) or fractionally spread out amongst a larger share (who have fractions of their votes transfer). Importantly, the more winners there are in a single constituency, the fewer votes that may be wasted under STV and therefore the more proportionate the outcome will be.

The preferential ballot

Voters in a Single Transferable Vote election cast a preferential ballot that is a ranked, ordinal listing of their preferred candidates. Voters in STV elections have a significant incentive to list their preferences honestly, as doing so improves the likelihood of the voter attaining representation amongst the winning candidates (see tactical voting, below).

Many STV systems allow voters to give a partial list of preferences by only ranking a subset of the candidates, however this leads to the possibility of "exhausted votes", where a vote is unable to be transfered because there are no more candidates indicated on the exhausted voter's ballot. To prevent exhausted ballots, some STV systems instead require voters to give a complete ordering of all the candidates in an election. However, when there is a large set of candidates this requirement may prove burdensome and can lead to voters ranking their final choices arbitrarily when they lack strong opinions ("Donkey voting"). To facilitate a complete ballot, STV ballots may provide the voter with the option of using group voting tickets rather than having to completely identify individual preferences.

Counting the ballots

<math>\left({{\rm votes} \over {\rm seats}+1}\right)+1<math>
The Droop Quota
Main article: Counting Single Transferable Votes

The quota (sometimes called the threshold) is the number of votes a candidate must receive to be elected. Votes are assumed to go to the top preference first, and are then transferred from eliminated candidates and the surpluses of winners until enough candidates meet the quota to fill the number of seats. If the STV system allows exhausted ballots and enough votes are exhausted to represent an entire quota, candidates are instead eliminated until the number of seats left to fill is the number of remaining candidates.

STV systems differ in how they transfer votes as well in as the exact size of the quota used for determining winners. The Droop quota, the most common, minimizes the size of the quota while still maintaining the condition that no more candidates can reach a quota than there are seats to be filled. While this still leaves nearly a quota's worth of votes unallocated (wasted), it is held that counting these votes would not alter the eventual outcome. Meek's method, the most common method of transfering votes adopted by new STV systems, utilizes a computer to evenly transfer portions of excess votes from winning candidates until they barely satisfy the quota. In Meek's method, initially different ballots that express the same preferences after particular candidates are eliminated are weighted exactly the same - there is no penalty for ballots arriving at a candidate in an earlier round than others.

An example

Suppose we conduct an STV election using the Droop quota where there are two seats to be filled and four candidates: Andrea, Brad, Carter, and Delilah. Also suppose that there are 57 voters who cast their ballots with the following preference orderings:

16 Votes 24 Votes 17 Votes
With 57 voters and 2 winners, the quota is therefore:
<math>\left({57 \over (2+1)}\right) +1 = 20<math>
1st Andrea Andrea Delilah
2nd Brad Carter Andrea
3rd Carter Brad Brad
4th Delilah Delilah Carter

In the first round, Andrea receives 40 votes and Delilah 17. Andrea is elected with 20 excess votes - twice as many as she needs. Each of her supporter's votes are then split, half going to Andrea, and half going to their second preferences. 12 of these reallocated votes go to Carter, 8 to Brad.

As none of the remaining candidates have reached the quota and there is still one seat to fill, Brad, the candidate with the fewest votes, is eliminated. All of his votes have Carter as the next-place choice, and are reallocated to Carter. This gives Carter 20 votes and he is elected, filling the second seat.


Round 1 Round 2 Round 3
Andrea 40 20 20 Elected in round 1 since she has more votes than the quota
Brad 0 8 0 Eliminated in round 2 since he has the fewest votes and no one meets the quota
Carter 0 12 20 Elected in round 3 since he has enough votes to meet the quota
Delilah 17 17 17 Defeated in round 3 since both seats are filled

In this sample election, the number of wasted votes is 17 - those of Delilah's supporters. Note that by necessity this represents less than one quota's worth of the electorate - 17/57, or just under 30% - significantly less than the minimum 50% expected of simple plurality elections.


As with all voting systems, there are a number of areas of controversy surrounding 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. 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). For example, in STV elections to the Australian Senate, states with vastly different populations have the same number of seats, and so while the results for individual states are proportional, the nationwide result is not, giving greater voting power to individual voters in less populated states; the lack of proportionality is derived from unequal representation rather than any deficiency in STV. The New South Wales Legislative Council, where the whole state votes as a single electorate for 21 members, produces results that are proportional to the final allocation of preferences.

Because STV is a preference voting system, whereby voting is done by ranking a list of candidates, the type of proportionality obtained by STV contrasts with many other proportional voting systems such as party-lists. Under these systems, seats are apportioned as a percentage of single-preference-only votes for each candidate or party. By contrast, in STV each voter has a single (transferable) vote, regardless of whether there is one vacancy or several. STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented voters. Votes are said to be wasted when they have no effect on the outcome of an election, either because they go to a losing candidate or to a winning candidate who does not need them. For example, in an STV election using the Droop quota method for 9 seats, at most only 10% of the vote will be wasted. Depending on the method of STV used and the preference distribution of the voters, this share of wasted votes can either be completely localised within 10% of the electorate (who would get no representation) or fractionally spread out amongst a larger share. Importantly, the more winners there are in a single constituency, the fewer votes that may be wasted under STV and therefore the more proportionate the outcome will be.

There is some difficulty in determining whether election results from STV actually meet the expectations of proportional representation or not. Unlike party list or mixed member proportional voting systems, voters in STV do not explicitly select whom their preferred party, if any, is. Even when no tactical voting has occured, determining the partisan makeup of the electorate based on the order of candidates given on preferential ballots is a problem that may be unsolvable. Nonpartisan voters, swing voters, and voters with only weak leanings towards a particular party complicate the determination of the partisan makeup of the electorate, making truly accurate estimates of whether the parties elected by STV are in proportion to their popular support impossible.

One common method of estimating the party identification of voters is to assume their top-preference on their ballot represents a candidate from their preferred party. This method overlooks the possibility of independant voters and candidates, however, as well as the possibility of cross-party voting. Furthermore, this assumption that a voter's party identification matches his top vote choice exactly is frequently inaccurate in examinations of single winner plurality-based electoral systems like the United States, where cross-party voting is visibly common when comparing party registration data and opinion polls.

Nevertheless, failures to produce partisan proportionality exactly analogous to the party affiliations of top choice candidates in elections can be controversial. For example, the Northern Ireland elections in 1998 led to the Ulster Unionists' winning more seats than the Social Democratic and Labour Party, despite winning a smaller share of first-preference votes. A similar discrepancy in 1981 resulted in a constitutional crisis in Malta: see below. By constrast, in the Republic of Ireland, predicting the impact of lower-preference transfers on seat allocation is considered part of the fun of election night punditry.

Tactical voting

The single transferable vote eliminates much of the reason for tactical voting. Voters are "safe" ranking candidates they fear may not be elected, because their votes will be transfered after they are eliminated. Similarly, voters are also "safe" voting for a candidate they believe will receive overwhelming support, because their votes will then get reallocated to their next preference.

Though still theoretically possible, figuring out how to vote tactically in STV systems by exploiting the non-monotonicity of STV is extremely computationally difficult. It is NP-hard to determine whether there exists an insincere ballot preference that will elect a preferred candidate, even in an election for a single seat. This makes tactical voting in STV elections vastly more difficult than with other commonly-used election methods. Importantly, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions like the presumed difficulty of learning the preferences of other voters. Furthermore, it is NP-hard to determine when an STV election has violated the monotonicity criterion, greatly reducing the likelihood that the electorate will know if even accidental tactical voting has occurred. As a consequence, the difficulty of tactical voting in STV elections increases sharply as the number of voters, candidates, and winners increase.

Of special note is that voters have a real incentive to list their preferences honestly in STV, as it's the best strategy for securing representation if tactical voting is either impractical or impossible. This is frequently the case, as successful tactical voting (when possible) requires both nearly perfect information about how others are voting and the computation of a virtually unsolvable math problem. This contrasts heavily with non-proportional, plurality-based systems, where there is tremendous incentive and ability to vote tactically in order to avoid the spoiler effect.

However, in the older STV systems still used in many countries there is a loophole that can allow for easier tactical voting: candidates who have already been elected do not receive any more votes, so there is incentive to avoid voting for your top-ranked candidate until after he has already been elected. For example, a voter might make a tactical decision to rank her top-place candidate beneath a candidate she knows will lose. If the voter's true top-place candidate has not been elected by the time her fake top candidate loses, the voter's full vote will count for her true top-place candidate. Otherwise, the voter will have avoided either having had her ballot in the lottery to be "wasted" on their top-ranked candidate or with only a fraction transfered, and will continue on to lower-ranked candidates. Note that in modern STV systems using Meek's method, this loophole has been fixed: a vote receives the same fractional weighting regardless of when it arrives at the successful candidate.

Effect on factions and candidates

There are also tactical considerations for political parties standing more than one candidate in the 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. This effect is amplified when voters do not stick tightly to their preferred party's candidates; however, if voters vote for all candidates from a particular party before any other candidates and before stopping expressing preferences, then too many candidates is not an issue. In Malta, where voters tend to stick tightly to party preferences, parties frequently stand more candidates than there are seats to be elected. Similarly, in Australian Senate elections that require a voter to make a complete list of preferences, voters also tend to vote along party lines due to the relative ease of selecting a party's declared preferences rather than individually casting their own.

Voting system criteria

All voting systems can be evaluated academically based on the voting system criteria that they pass. No 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.

STV is also susceptible to the Alabama paradox: if a candidate is elected in an n seat constituency, she may not be elected in the same constituency with n + 1 seats even when voters express exactly the same preferences. This is due to the use of quotas: largest remainder list PR is similarly affected. Intuitively, a candidate who was elected largely because of transfers from two similar groups (neither obtaining a quota) may not be elected when the number of winning candidates increases, as both groups would instead get their preferred candidates elected (with the new, smaller quota) rather than automatically compromising on their mutual second choice as their votes transfer.



It is difficult to fill vacancies which occur under STV given the way that the results depend on transfers from multiple candidates. There are several possible ways of selecting a replacement:


The countback method is used in Tasmania, Malta, and Cambridge, Massachusetts. A new representative is selected by using the data from the previous election. The candidate who held the seat is eliminated, and a new election result is obtained by transfering votes from the now unrepresented voters. Importantly, a clone of the replaced representative would be guaranteed to win.

Although the countback method is designed to select a replacement representing the same group of voters who elected the original candidate, it remains possible that no similar candidates remain on the ballot. In 1985 the Tasmanian parliament amended the electoral act to allow true by-elections if no candidates of the same party as the outgoing representative remained on the ballot; in this circumstance the party may request that a by-election be held, however this has not yet happened.

An interesting consequence of the countback method for selecting replacements is that the results are often known before the vacancy actually occurs, potentially influencing the circumstances which create the vacancy in the first place.

Methods vary by whether or not wasted and exhausted ballots are additionally used during the countback - those of Delilah's supporters above. The effect this has on the result of the countback depends on the differences in the next preferences of voters; if there exists a true clone in the ballots, there should be no effect in this change. Moreover, in STV systems that use exhausted ballots during countbacks, it becomes theoretically possible that the order of multiple resignations will affect whom the ultimate replacements are - this is a consequence of the non-independence of irrelevant alternatives discussed above. Additionally, when exhausted ballots are used, it remains possible that the chosen replacement will only meet a fraction of a quota of voters; when this fraction is particularly small, a different method of filling the vacancy can be used.


The state legislatures appoint replacements members to the Australian senate. This is done at the suggestion of the party of the outgoing senator. Disputes over Senate vacancies contributed to the Australian constitutional crisis of 1975. In 1977 the people amended the Constitution of Australia to provide that the legislature must elect a member of the same party as the outgoing senator. Vacancies in the New South Wales Legislative Council are filled in a similar way by a joint sitting of both the legislative council and assembly.


Holding a single-winner by-election (instant-runoff), as happens in the Republic of Ireland; this allows the parties to choose new candidates and all voters to participate, but often leads to the most popular party picking up an extra seat. This is because the winner of a by-election typically represents a large group of voters, whereas the vacated member only represented one quota's worth.

Use of STV around the world


Australia uses two forms of STV, usually referred to within Australia as the "Hare-Clark System" and "STV".

The "Hare-Clark System" is used in Tasmania's House of Assembly and the Australian Capital Territory (ACT) Legislative Assembly. This is essentially the system described above using the Droop quota (not the Hare quota), but candidates' placements are randomised by Robson Rotation rather than grouped by party.

"STV" or "proportional voting" is the system used in the Australian Senate and the Legislative Councils of New South Wales, Victoria, Western Australia and South Australia. This system is counted in the same way as in Hare-Clark, but group voting tickets are used.

Each form has its pros and cons. The Hare-Clark system with Robson Rotation is advocated on the grounds that voters know who they are voting for as they must fill all their preferences, that each party's candidates compete with each other and the effect of 'donkey voting' is reduced because of the randomised ordering. The alternative system is advocated on the grounds that informal voting is reduced because only one number need be written; on the other hand, it greatly increases the potential for tactical voting by parties as they both have more information about the ballots and direct control of a larger percentage of the vote.


STV was used for the elections in the province of Alberta from 1926 to 1955. In a non-binding referendum question, British Columbians on May 17, 2005 did not give BC-STV the 60% province-wide support that is standard for referendum questions to pass, though the simple majorities in 72 ridings (of 79) far exceeded the 48 ridings that was also a requirement. Despite a recommendation of STV [1] ( by the Citizens' Assembly on Electoral Reform, the referendum garnered only 57.7% Yes support from voters as of May 18, 2005 while ballots were still being counted. Due to the evident support for electoral reform, the re-elected Liberal government is still considering implementing reforms during the next term in office. [2] (


Republic of Ireland, for all elections [3] ( (However, presidential elections and most by-elections elect only one candidate and so reduce to instant-runoff voting.) The Constitution specifies a minimum size of 3 seats for Dáil constituencies; the current maximum is 5. Senate panels have up to 11 seats.


STV applies for all elections in Malta [4] ( However, top-up seats (similar to the additional member system) may be added in the national parliament to ensure that a party with a majority of first-preference votes wins a majority of seats. This was a response to the controversial election in 1981 when the Nationalist Party won 51% of the first-preference vote but the Labour Party won a majority of the seats. Some accused Labour of having gerrymandered the 5-seat constituencies: 8 had narrowly split 3:2 in its favour, while 5 had more widely split 3:2 in favour of the Nationalists. The top-up rule has since been invoked in 1987 and 1996.

New Zealand

New Zealand used STV for the first time for district health board and some local authority elections in October 2004[5] ( New Zealand has chosen STV by Meek's method. Due to low voter turnout, the high number of invalid votes and the long time taken for the result to be declared, the Justice and Electoral Committee of the New Zealand Parliament has under taken an inquiry into the use of STV in New Zealand.

United Kingdom

Northern Ireland

STV is used in Northern Ireland, for local, Assembly and European elections, though not for elections to the House of Commons at Westminster.


All local governments in Scotland will be using STV to elect their councillors. The Local Governance (Scotland) Bill [6] ( passed on June 23, 2004.

United States

STV enjoyed some popularity in the United States in the first half of the 20th Century. Currently the only official governing bodies that use STV to elect representatives are the City Council and School Committee of Cambridge, Massachusetts. The community school boards of the City of New York used STV until they were abolished in 2002.


Many non-governmental organisations also use STV. Most Australian political parties, unions and peak business organisations use STV. All National Union of Students of the United Kingdom, Cambridge Union, and Oxford Union elections and those of their constituent members are under the system. It is used in several political parties for internal elections such as the British Liberal-Democrats and all the British Green Parties. It is also used to elect members of the General Synod of the Church of England. The UK Royal Statistical Society [7] ( uses STV with the Meek method to elect their council.

Ordering candidates for List PR

STV can be used used as a social preference function to produce an overall ranking of candidates. For example, closed party-list PR allots seats proportionally to lists and chooses candidates from that list in the order set down on the list. Some parties decide this centrally but others give the choice to the membership. STV has been used in such elections; in such an election the party members mark their ballots in just the same way as in a normal STV election.

When the votes come to be counted the same ballots are used first for an STV election to choose one winner, as an instant runoff election; then the same ballots are used to see which two would win when the votes are counted for a two winner election and so on. The head of the list is the party member who would be elected in the one winner count. The second place is taken by the next party member who succeeds in the two winner race (in the unusual event that the winner of the single winner count did not succeed in the two winner count, then the first to be elected in the two winner count), and so on.


Thomas Wright Hill first proposed transferable voting in 1821.

In 1855 Carl Andrae proposed a transferable vote system in Denmark. It was used in 1856 to elect the Rigsdag. In 1866 it was adapted for indirect elections to the second chamber, the Landsting, until 1915.

The English barrister Thomas Hare is generally credited with conceiving of Single Transferable Voting, and he may have independently developed the idea in the 1857. He proposed a single national constituency. His view was that it 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". He proposed that electors should have the opportunity of discovering which candidate their vote had counted for, to improve their personal connexion with voting.

John Stuart Mill, a friend of Hare, was an early proponent of STV and praised it in "On Representation." In the "English Constitution" Walter Bagehot praised the Hare system for allowing everyone, even ideological minorities, to elect an MP, but said that the Hare 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."

STV spread through the British Empire - leading it to be sometimes known as British Proportional Representation. Andrew Inglis Clark was successful in persuading the Tasmanian House of Assembly to be the first parliament in the world elected by Hare-Clark in 1896. Hare-Clark is named after Thomas Hare and Andrew Inglis Clark.

It was used in Canada in Calgary and Edmonton and optionally in the rest of the province from 1926 to 1955.

It is used for elections within the Church of England.

It has found use in America, and from 1936 to 1947 it was used in New York City municipal elections for a short while to break the Democrats' strangehold on the city. This reverted again to First Past The Post, after strenuous attempts by the Democrats to reverse the change, aided by scares over the election of Communist candidates.

Meek's version contained the innovation that electors could rank preferences equally, but this option has not been used.

See also


External links

de:single transferable vote


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