Single Transferable Vote

This STV ballot for the Australian Senate illustrates group voting tickets.  Voters can either rank every candidate individually or use their preferred party's preferences by voting "above the line."
This STV ballot for the Australian Senate illustrates group voting tickets. Voters can either rank every candidate individually or use their preferred party's preferences by voting "above the line."

The Single Transferable Vote, or STV, is a preferential voting system designed to minimise wasted votes and provide proportional representation 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 unneeded or unused votes after candidates are either elected or eliminated according to the voter's stated preferences.

When promoted as a proportional representation method in multi-party multi-seat elections, STV methods are 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 used federally with parties able to indicate preferences is called simply STV. In the United States, STV is sometimes called choice voting. 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.

As of 2005 STV is used for major elections in Australia, the Republic of Ireland, Malta, New Zealand and Northern Ireland. – see History and usage of the Single Transferable Vote.

Voting

STV voting acknowledges that voters for each elected representative may prefer different unelected candidates. To ensure this, excess (unused) votes from winning and losing candidates are transferred 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.

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 transferred according to how their preferences are listed on their ballots. " Wasted votes", those that go to non-winning candidates or candidates that have already won, are therefore effectively minimized in STV systems, simultaneously minimizing the number of unrepresented voters and providing a degree of 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 portions 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, or portion of a vote, is unable to be transferred because there are no more candidates indicated on the exhausted 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, some STV systems may provide the voter with the option of using group voting tickets rather than having to manually identify a complete list of individual preferences.

Counting the ballots

\left({{\rm votes} \over {\rm seats}+1}\right)+1
The Droop Quota

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. To avoid unnecessary counting, candidates may instead be eliminated until the number of seats left to fill is the number of remaining candidates. This approach becomes necessary if ballots are allowed to be exhausted, as it then becomes possible for an insufficient number of candidates to reach the quota if the exhausted votes are numerous enough to fulfil a quota instead.

STV systems differ in how they transfer votes as well 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), transferring these votes would not alter the eventual outcome. For example, Meek's method, the method of transferring votes adopted in the New Zealand STV system, utilizes a computer to evenly transfer portions of excess votes from winning candidates until they barely satisfy the quota, thereby taking into account transfers to already elected candidates. Meek's method also dynamically adjusts the quota during the counting process of the election, lowering it slightly to take account newly exhausted votes. 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

# x x x x x x x x x x
x x x x
x x x x x x
1st Orange Tangerine Chocolate Chocolate Strawberry Candy
2nd Tangerine Orange Strawberry Candy

Suppose a food election is conducted to determine what to serve at a party. There are five candidates, three of which will be chosen: oranges, tangerines, chocolate, strawberries, and candy. The 20 guests at the party have the preferences marked on their ballots in the table at the right, with each ballot being represented by a colored x. Note that in this example it is not needed for some of the voters to indicate a complete preference list, however in a larger election with more candidates the value of ranking additional preferences to the voter increases.

Using the Droop quota, with 20 voters and 3 winners the number of votes required to win is therefore:
\left({20 \over {3+1}}\right)  +1 = 6

Note that if the quota were exactly 1 vote less, it would become possible for 4 candidates instead of 3 to fulfill it.

Candidate: Orange Tangerine Chocolate Strawberry Candy
Round 1 x x x x x x x x x x
x x x x

x x x x
x x Chocolate is 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 Chocolate's surplus votes transfer proportionately to strawberry and candy according to the chocolate voters' second choice preferences. Tangerine is eliminated since no new candidates meet the quota and tangerine has the least support.
Round 3 x x x x
x x
x x x x
x x
x x x x
x
x x x Tangerine's votes transfer to their second preference, orange, 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 Neither of the remaining candidates meets the quota, so candy is eliminated. Strawberry is the only remaining candidate and so wins the final seat.

In this sample election, the number of wasted votes is 4: the three unsuccessful votes for candy in the final round that did not elect a candidate, plus one less than the difference between strawberry and candy's votes in the final round (5 and 3, respectively). This is 4/20, or 20% of all the votes cast.

Vacancies

When compared with other voting methods, the question of how to fill vacancies which occur under STV can be difficult given the way that results depend upon transfers from multiple candidates. There are several possible ways of selecting a replacement:

Countback

The countback method is used in the Australian Capital Territory, 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 transferring votes from the now unrepresented voters. Importantly, a clone of the replaced representative would be guaranteed to win the vacated seat. An interesting consequence of the countback method's use of existing ballots 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.

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.

Appointment

Another option is to have a head official or remaining members of the elected body appoint a new member to fulfil the vacancy. In Australia, for example, the state legislatures appoint replacements members to the Australian Senate, now done at the suggestion of the party of the outgoing senator. Before this rule, disputes over Senate vacancies contributed to the Australian constitutional crisis of 1975, ultimately resulting in a 1977 amendment to 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.

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..

By-election

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. This often leads to a different party winning the seat (usually one of the largest parties, since the quota is large). In the Republic of Ireland, by-elections are used for the Dáil; also for the Seanad, though there the by-election franchise is more restricted than in ordinary elections, and might equally be categorised under appointment.

Replacement list

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 member is replaced with the top eligible name from a replacement list submitted by the candidate at the time of the original election.


History and usage of STV

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. 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: "[the Hare system] is inconsistent with the extrinsic independence as well as the inherent moderation of a Parliament - two of the conditions we have seen, are essential to the bare possibility of parliamentary government."

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

Meek also considered a variant on his system which would have allowed for equal preferences to be expressed.

This image, created for a campaign to promote STV in Scotland, characterizes votes under Scotland's plurality system as being tied up in bondage.
This image, created for a campaign to promote STV in Scotland, characterizes votes under Scotland's plurality system as being tied up in bondage.

Issues

A frequent concern with STV among electorates considering its adoption is its relative complexity compared with plurality voting methods. For example, when the Canadian province of British Columbia held a referendum on adopting the BC-STV Single Transferable Vote in 2005, according to polls a majority of "no" voters gave their reason as "wasn't knowledgeable" when they were asked why, specifically, they voted against STV.

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.

Proportionality

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. Differential turnout across districts, for example, may alter the impact of individual votes in different constituencies, and when combined with rounding error associated with a finite number of winners in each constituency the election as a whole may throw up anomalous results. For example, the 1981 election in Malta resulted in the Labour Party winning a majority of seats despite the Nationalist Party winning 51% of the first-preference vote. Controversy over the election ultimately resulted in a constitutional crisis, leading to an amendment adjusting the voting system to allow for the possibility of bonus seats and making the Maltese voting system more similar to an open-list PR system. This kind of difference due to rounding error can occur with any PR system used at a district level, although greater rounding error occurs with smaller districts and there is a tendency for STV elections to use smaller districts when compared with PR elections employing party lists.

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 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

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 transferred 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 with less than the value of a full vote. However, the Gibbard-Satterthwaite theorem states that tactical voting is possible in any deterministic voting system where any candidate can win, and that STV is no exception.

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. 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.

Effects on factions and candidates

This campaign poster highlights STVs tendency to provide descriptive representation according to each voter's individual preferences by making a comparison with diverse flavors of candy.
This campaign poster highlights STVs tendency to provide descriptive representation according to each voter's individual preferences by making a comparison with diverse flavors of candy.

The use of STV may reduce the role of political parties in the electoral process and corresponding partisanship in the resulting government. Unlike proportional representation systems employing party lists, voters in STV are not explicitly constrained by parties even when they do exist; voters may ignore candidate party labels and mix their preferred candidate rankings between parties. Similarly, candidates may achieve electoral success by obtaining a quota of voters not generally within their own party, perhaps by winning transfers from moderates or by championing a specific issue contrary to party doctrine. Unlike List PR, STV can be used in elections in organizations without any political parties at all, such as in trade unions, clubs, and schools.

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.

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.

Voting system criteria

Academic analysis of voting systems such as STV generally centers 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. Failure to satisfy independence of irrelevant alternatives makes STV slightly prone to strategic nomination, albeit less so than with plurality methods where the spoiler effect is more pronounced and predictable. Non-monotonicity, in turn, makes it possible under some circumstances to elect a preferred candidate by reducing his position on some of the ballots; by helping elect a candidate who displaces the preferred candidate's main rival, a voter may cause the preferred candidate to profit from transfers resulting from the rival's defeat. STV fails the participation criterion which can result in a more favorable outcome to an STV voter by not voting at all. However, STV satisfies the Non-compulsory support criterion. A voter who truncates a candidate off the ballot does not harm a ranked candidate, nor is another truncated candidate helped on the ballot.

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.

District size

Another issue commonly considered with STV elections is the size of the voting districts in terms of the number of candidates elected and, to a lesser extent, the total size of the body being elected. In STV and other proportional representation systems, a larger number of candidates elected results in a smaller number of wasted votes and subsequent rounding error, leading to a more proportionally representative outcome based on the preferences of the voters. For this reason, larger electoral districts can also significantly reduce the effects of gerrymandering; because gerrymandering relies on wasted votes to award the "last seat" in each district, proportional representation systems such as STV with larger multimember districts are intrinsically more difficult to gerrymander. Larger districts can also make for significantly harder tactical voting: since the problem of making correct assumptions about other voter's behaviour and rearranging one's tactical ballot is NP-hard, the difficulty of tactical voting increases sharply as the number of candidates grows. Some STV elections make use of districts with the number of seats available as small as three, however there is no theoretical upper limit to the size of districts in STV, and they may not even be needed at all: Thomas Hare's original proposal was for a single, nationwide district.

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.