The Single Transferable Vote, or STV, is a preferential voting system designed to minimise wasted votes and provide proportional representation while ensuring that votes are explicitly for candidates rather than party lists. STV 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 2006, STV is used for elections in Australia, the Republic of Ireland, Northern Ireland (except elections to the British House of Commons) and Malta. It is also used for some local government elections in New Zealand — see History and use of the Single Transferable Vote.
When the rules of STV are used in a single winner election it is the same as instant-runoff voting, which is not a form of proportional representation. When used in multi-seat constituencies it is also sometimes known as Proportional Representation through the Single Transferable Vote or PR-STV. Because instant-runoff is not a form of proportional representation it is considered by some scholars to be a separate system from PR-STV. In any case, when the term STV is used it is usually PR-STV that is being referred to and that is the convention followed in this article. STV is also known by other names. In Australia it is sometimes known as the Hare-Clark Proportional method, while in the United States it is sometimes called choice voting.
When ballots are counted the election proceeds as follows:
| Candidate: | Orange | Tangerine | Chocolate | Strawberry | Candy |
| Round 1 | 4 | 2 | 12 | 1 | 1 |
| Round 2 | 4 | 2 | 6 | 5 | 3 |
| Round 3 | 6 | 6 | 5 | 3 | |
| Round 4 | 6 | 6 | 5 | 3 |
| Candidate: | |||||
|---|---|---|---|---|---|
| Round 1 | x x x x | x x | x x x x x x x x x x x x | x | x |
| Round 2 | x x x x | x x | x x x x x x | x x x x x | x x x |
| Round 3 | x x x x x x | x x x x x x | x x x x x | x x x | |
| Round 4 | x x x x x x | x x x x x x | x x x x x | x x x |
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-Brittan 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 Hill, I.D. (1987). "Algorithm 123 — Single Transferable Vote by Meek’s method".. 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 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's method (a single winner voting system) 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.
As seen above, voters in an STV election rank candidates on a preferential ballot. 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.
To prevent exhausted ballots, some STV systems instead oblige voters to give a complete ordering of all of the candidates in an election (if a voter does not rank all candidates her ballot may be considered spoilt). However, when there is a large set of candidates this requirement may prove burdensome and can lead to random voting, or "donkey voting" in which a voter who has no strong opinions about her lower preferences simply chooses them in the given order. Some jurisdictions compromise by setting a minimum number of preferences that must be filled for a ballot paper to be valid (for example Tasmania and Australian Capital Territory, which both require five preferences).
To facilitate a complete ballot, some STV systems provide the voter with the option of using group voting tickets rather than having to manually identify a complete list of individual preferences. For example, in elections to the Australian Senate a voter can either rank the candidates herself or place the number one in a box "above the line" to vote for a predetermined ordering of candidates drawn up by one of the political parties. This system diminishes the emphasis on individual candidates and increases the power of party leaders who submit the predetermined rankings; in practice it may even lead to a system resembling party-list proportional representation.
The simplest way to list candidates on a ballot paper is alphabetically, though they may also be grouped by party. However any fixed ordering will give some candidates an unfair advantage, because some voters, consciously or otherwise, are influence in their ordering of candidates by the order found on the ballot paper. For example, studies conducted in the Republic of Ireland, where candidates are listed alphabetically, have shown that candidates whose surnames begin with an early letter in the alphabet enjoy a small electoral advantage over candidates with later letters. To solve this problem some systems involve a random ordering of candidates, or an ordering that changes from one ballot paper to another (the latter is often called the Robson rotation, after Neil Robson, a Tasmanian MHA who championed such a system).
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.
Countback methods vary by whether or not wasted and exhausted ballots are additionally used during the countback. 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 who the ultimate replacements are - this is a consequence of the non-independence of irrelevant alternatives discussed above. Additionally, if ballots are allowed to be exhausted in the election, then by either method it remains possible that the chosen replacement will only meet a fraction of a quota of voters; when this fraction is particularly small, and therefore no similar candidates remain on the ballot, election rules may call for a different method of filling the vacancy to be used.
In the Republic of Ireland, vacancies on local authorities are filled by co-option of a candidate nominated by the departed councillor's party colleagues.Membership of local authorities in Ireland Accessed 7 Oct, 2005. In the Republic of Ireland, vacancies from amongst the Taoiseach's nominees to the Seanad are filled by appointment.
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 Andrae proposed a transferable vote system for elections in Denmark. Andrae'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 Single Transferable Voting, 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.Lambert & Lakeman (1955). "Voting in democracies". London : Faber, pg. 245. 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 "On Representation." 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: "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."Bagehot, Walter. "English Constitution".
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.
However, as with all voting systems, once STV is understood there remain a number of areas of controversy surrounding its use. In particular, arguments for and against proportional representation in general are frequently referenced in debates among electorates considering STV, however the specific implications of a particular STV system can be examined as well.
Similarly to differences in voter turnout, instances of malapportionment across districts can also cause disproportionate results for the legislature as a whole. 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. By contrast, the New South Wales Legislative Council avoids the use of districts entirely, electing all 21 members using a single, statewide constituency and guarenteeing results that are proportional to the final allocation of preferences.
STV differs from other PR systems in that it allows the voter to decide the issues that should matter for the proportionality. In most PR systems the voter can only influence a single aspect - party representation. STV allows the voter to choose other criteria that can be used to create the proportionality: gender, ethnicity, age, or character as examples. The problem with this is that the voter and the political elite are often not in accord with what sort of proportionality should be achieved. Increased voter choice and control reduces the power of the political elites to determine the political debate.
STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented voters. In this way STV provides Droop proportionality - an example STV election using the Droop quota method for 9 seats and with no exhausted preferences would guarantee representation to every distinct group of 10% of the voters, with at most only 10% of the vote being wasted as unneeded excess. Unlike other proportional representation methods employing party lists, voters in STV do not explicitly state their preferred political party; this in turn can create some difficulty when attempting to analyze how an STV election's results compare with the nationwide partisan makeup. 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, however this method of estimation is made more complicated by the possibility of independent candidates and of cross-party voting.
Tactical voting is chiefly accomplished in STV by making assumptions about the other voters. A preferred popular candidate can be assumed to win and thus ranked lower on a tactical voter's ballot, allowing the voter to give more weight in transfers to his second-choice candidates (and, implicitly, giving fellow supporters of the popular candidate less weight.) This is particularly effective in the older STV systems still used in many countries that prevent elected candidates from receiving additional votes, as in that case none of the tactical vote is diluted on the already winning candidate. Under such old systems, a voter may even rank a non-preferred candidate that is assumed to lose first in order to increase the chances of his vote arriving late. This method of tactical voting is much less effective in the New Zealand STV system using Meek's method, however, as votes receive the same fractional weighting regardless of when they arrive at the successful candidate.
Though still theoretically possible, figuring out how to successfully vote tactically in modern STV systems by exploiting the non-monotonicity in this way can be 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.Bartholdi, John J. III and Orlin, James B (2003). "Single Transferable Vote Resists Strategic Voting". 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, such as the presumed difficulty of learning the preferences of other voters. Furthermore, it is also 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. This gives an incentive for larger electoral districts other than their increased proportionality, since particularly small electoral districts may have few enough candidates to make tactical voting feasible.
Of special note is that voters have a real incentive to list their preferences honestly in STV, as it is the best strategy for securing representation if tactical voting is either impractical or impossible. This is frequently the case in large electoral districts, 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. Since tactical voting in STV works by effectively substituting one's own alternate preferences for transfers with other supporters of the same candidate, the effectiveness of tactical voting is greatly reduced when other supporters of preferred candidates have similar second-choice preferences. Although there is no way to completely prevent tactical voting by hiding support for preferred candidates, the tactical voter carries the significant danger of his assumptions about the popularity of his preferred candidate being wrong, risking his most preferred candidate losing because of his miscast tactical vote. This contrasts heavily with non-proportional, plurality-based systems, where there is both tremendous incentive and ability to vote tactically in order to avoid the spoiler effect.
Some STV variations, however, may encourage the role of political parties and actually strengthen them. In Australian Senate elections, where a combination of large districts, mandatory complete ballots, and compulsory voting results in the near 95% usage of partisan group voting tickets, political parties gain significant power in determining election results by adjusting the relative ordering of their tickets, both in terms of their own candidates and of transfers to other parties.
Successful campaign strategy in STV elections may differ significantly from other voting systems. In particular, individual candidates in STV have little incentive for negative campaign advertising, as reducing a particular opponent's ranking among voters does not necessarily elevate one's own; if negative campaigning is seen as distasteful by the voters, the practice may even prove harmful to the attacking candidate. Conversely, in order to avoid elimination in early counting rounds by having too few first place votes, candidates have a significant incentive to convince voters to rank them explicitly first as their top preference, rather than merely higher. This incentive to attain top preferences, in turn, may lead to a strategy of candidates placing greater importance on a core group of supporters. Avoiding early elimination, however, is usually not enough to win election, as a candidate must still subsequently win enough votes on transfers to meet the quota; consequently, strategies which sacrifice wide secondary support in favor of primary support amidst a core group may ultimately fail unless the group is particularly large.
There are also tactical considerations for political parties in the number of candidates they stand in an election where full ballots are not required. 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, 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 complete list.
STV is also susceptible to the Alabama paradox: a candidate elected in an n seat constituency may or 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; list PR by a largest remainder method is similarly affected, though a highest averages method is not. 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.
Some modifications to STV have been proposed in order to pass monotonicity and other criteria. The most common method of proposed modification to STV is to alter the order in which candidates are eliminated: theoretically, a candidate who ranked second on every ballot could be the first candidate eliminated even if he is a Condorcet winner. Meek noted this problem in proposing his variation of transferring votes to nearly eliminate tactical voting in STV, however Meek himself did not propose a method for satisfying the Condorcet criterion. Other theorists have proposed further refinements of STV, such as using a Condorcet method to rank candidates for elimination order. Some of these modifications alter STV in a way such that it no longer reduces to instant-runoff voting when applied to a single seat but instead reduces to some other single winner system, such as a Condorcet method.
See also: CPO-STV, Quota Borda system
However, because STV is proportional, larger elections also reduce the support a candidate requires to become elected as a percentage of the district. With 9 candidates, for example, any with 10% electoral support may win a seat, whereas with 19 candidates only 5% popular support is required to be in the government. Because of this, proportional representation methods such as STV can implicitly allow for the election of particularly small minorities provided they secure a quota's worth of votes. The potential admission of small voting minorities into the government, perhaps including political extremists, can be quite controversial even though they would occupy only an equivalently small proportion of the government once elected. Other proportional representation methods attempt to avoid the election of small political minorities by imposing partisan threshold requirements, such as the "5% rule" in Germany's Mixed Member Proportional system. While impossible at the national level, such a threshold requirement could be approximated in STV on a per-district basis by limiting the number of seats to 19 (and therefore making the quota one more than 5% of the vote). Larger districts and the implicit larger number of candidates also increase the difficulty of giving meaningful rankings to all candidates from the perspective of the individual voter, and may result in increased numbers of exhausted ballots and reliance on party labels or group voting tickets.
Single Transferable Vote | PR electoral systems | non-monotonic electoral systems | preferential electoral systems
Übertragbare Einzelstimmgebung | Système de Hare | 단기이양식 선거제도 | Enkelvoudige overdraagbare stem | Pojedynczy głos przechodni | Siirtoäänivaalitapa | Enkel överförbar röst
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