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The '''single transferable vote''' ('''STV''') is a [[preferential voting|preferential voting system]] designed to minimize [[wasted votes]] in multi-candidate elections while ensuring that votes are explicitly for candidates rather than party lists. It works by assigning candidates votes based on the number of voters who ranked them 1st, electing candidates who reach a certain threshold of votes ("[[quota]]") and spending those votes to ensure as-of-yet unrepresented voters can get someone they like, and otherwise eliminating the candidate with the fewest 1st choices and then treating the uneliminated candidate their voters ranked next-highest as their "new" 1st choice.
 
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'''. When a similar method is applied to single-seat elections it is sometimes called ''[[instant-runoff voting]]'' or the ''alternative vote'', and has different proportionality implications for a similar ballot.
 
== History ==
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<blockquote>
<!--text below copied from https://en.wikipedia.org/w/index.php?title=History_and_use_of_the_single_transferable_vote&oldid=1045149797 -->
<!--a picture of an old STV voting machine would go very well here-->The concept of transferable voting was first proposed by [[Thomas Wright Hill]] in 1819.<ref>[[Nicolaus Tideman]], ''Collective Decisions and Voting: The Potential for Public Choice'', Ashgate Publishing Company, Burlington VT, 2006.</ref> The system remained unused in public elections until 1855, when [[Carl Andræ]] proposed a transferable vote system for elections in Denmark.<ref name=humphreys>{{cite book |last1=Humphreys |first1=John H |title=Proportional Representation, A Study in Methods of Election |date=1911 |publisher=Methuen & Co.Ltd |location=London |url=https://archive.org/details/proportionalrepr00humpuoft}}</ref> Andræ's system was used in 1856 to elect the Danish Rigsdag, and by 1866 it was also adapted for indirect elections to the second chamber, the Landsting, until 1915.
 
Although he was not the first to propose a system of transferable votes, the English barrister [[w:Thomas Hare (political scientist)|Thomas Hare]] is generally credited with the conception of Single Transferable Voting, and he may have independently developed the idea in 1857.<ref name=humphreys/> 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.<ref name="Lambert">{{cite book|title=Voting in democracies: a study of majority and proportional electoral systems|last1=Lakeman|first1=Enid|last2=Lambert|first2=James D.|year=1959|page=245|publisher=Faber & Faber|oclc=03088530}}
</ref>
 
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=== Counting The Votes ===
 
Process A: Top-preference votes are tallied. If one or more candidates have received at least as many votes as the quota, they are declared elected. After a candidate is elected, they may not receive any more votes (though see below for a modernization).
 
The excess votes for the winning candidate are reallocated to the next-highest ranked candidates on the ballots for the elected candidate. There are different methods for determining how to reallocate the votes. Some versions use random selection, others count each ballot fractionally.
 
Process A is repeated until there are no more candidates who have reached the quota.
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Process B: The candidate with the least support is eliminated, and
their votes are reallocated to the next-highest ranked candidates on
the eliminated ballots. After a candidate is eliminated, they may not receive any more votes.
receive any more votes.
 
After each iteration of Process B is completed, Process A starts
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The threshold is: <!-- <math>\left({30 \over (2+1)}\right) +1 = 11</math> --> floor(30 / (2 + 1)) + 1 = 11.
 
In the first round, Andrea receives 22 votes and Delilah 8. Andrea is
elected with 11 excess votes. Her 11 excess votes are reallocated to their second preferences (which votes are chosen may be decided by random selection). For example, 8 of the reallocated votes are for Carter, 3 for Brad. Note: this is not a realistic example - elections with a small number of votes often have special rules - for example, Irish Senate elections are conducted using thousands of votes.
 
As none of the candidates have reached their threshold, 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 11 votes and he is elected.
 
== Proportionality ==
== Is STV a proportional voting system? ==
STV is perhaps better described as quasi-proportional rather than truly proportional, as it is only proportional in some ways.
 
=== Overall proportionality ===
STV is not a proportional system in the strict sense. STV does not guarantee that a party will get the same percentage of seats as it gets as a percentage of votes. In fact the notion of a vote "for a party" is less meaningful for STV because votes are not necessarily for a single party. A vote can list candidates from an assortment of political parties, in any order. The candidates that are elected reflect the combined preferences of all votes cast.
A major complication with proportionality under STV is the requirement for constituencies, where a set of candidates is elected in each electoral district. Small constituencies are highly disproportional, but large constituencies make it difficult or impossible for voters to rank large numbers of candidates.
 
The proportionality of STV can be controversial, especially in close elections such aslike the 1981 election in Malta. In this election, the Maltese Labour Party won a majority of seats, despite the Nationalist Party winning a majority of ''first preference'' votes. This caused a constitutional crisis, leading to a provision forto theprovide possibilitybonus seats in case of bonusdisproportional seatsresults. These bonus seats were usedneeded in 1987, 1996, and again in 1996. Similarly2008, theshowing Northern IrelandSTV elections inare 1998often leddisproportional to the Ulster Unionists winning more seats than the Social Democratic and Labour Party, despite winningat a smaller share of thenational votelevel.▼
Another complication with proportionality under STV is the constituency system, where a set of candidates is elected in each electoral district. There is no explicit process in STV for balancing the votes between constituencies, so the overall electoral result is merely the sum of the constituency results.
 
Similarly, 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 the vote.
Within a constituency, however, STV can be said to be proportional for whatever characteristics the voters valued. For example, if 60% of voters put all the female candidates first, and 40% put all the male candidates first, 60% of the winners would be female and 40% would be male. (Assuming there are sufficient candidates of each gender to make up the numbers.)▼
 
In the 2020 Irish general elections, the Irish Labour party received 50% more votes than the Social Democrats, but both parties won 6 seats.<ref>{{Cite web|url=https://en.wikipedia.org/wiki/2020_Irish_general_election|title=2020 Irish general election|website=Wikipedia|url-status=live}}</ref>
STV provides this proportionality simply by wasting as few votes as possible. A vote is a "[[Wasted vote]]" if it does not elect anyone; it is partially wasted if it elects someone who gets more votes than is necessary to be elected. STV transfers votes that would otherwise be wasted, and it only transfers such votes.
 
The degree of proportionality nationwide is strongly related to the number of seats to be filled in each constituency. In a three-seat constituency, using the Droop quota, about a quarter of the vote is "wasted". These votes may be for minor candidates that were not eliminated, or elected candidates' surplus votes that did not get redistributed. In a nine-seat constituency, only a tenth of the vote is wasted, and a party needs only 10% of the vote in a constituency to win a seat. Consequently, the best proportionality is achieved when there are a large number of representatives per constituency.
 
=== Within-constituency ===
▲The proportionality of STV can be controversial, especially in close elections such as the 1981 election in Malta. In this election the Maltese Labour Party won a majority of seats despite the Nationalist Party winning a majority of first preference votes. This caused a constitutional crisis, leading to provision for the possibility of bonus seats. These bonus seats were used in 1987 and again in 1996. Similarly, 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 the vote.
▲Within a constituency, however, STV can be said to be proportional forif whateverthere characteristicsis thea single characteristic voters valuedvalue above any other. For example, in a five-seat election, if 6051% of voters put all the female candidates first, and 4049% put all the male candidates first, 60% of the winners (three out of five) would be female andwith 40%the wouldDroop bequota, male.whereas (Assumingsomewhere therebetween are40% sufficientand candidates60% ofwould eachbe genderfemale tounder makeHare up(depending on the numbers.precise allocation of votes).
 
STV provides this proportionality by reassigning votes to later preferences in a way that avoids waste. A vote is considered [[Wasted vote|wasted]] if it is not used to elect anyone, i.e. if it is not held by a winning candidate at the end of the count.
Advocates of STV argue that the apparent disproportionality in STV is indicative of poor support for the party's candidates in second and third preferences. They argue that the STV result is actually a more accurate estimate of the party's support than a simple tally of first-preference votes.
 
Within each constituency, STV passes the [[Droop proportionality criterion]]for whensolid using [[Hagenbach-Bischoff quota|Hagenbach-Bischoff quotascoalitions]]. (when doing so, it is suggested that a candidate win only if they exceed quota), because whenWhen all but k candidates of a solid coalition's supported candidates have been eliminated, one of the remaining candidates is now the 1st choice of over a quota of voters, and is thus elected, with. theirTheir surplus votes flowingflow towards some of the other k candidates, and this repeating,repeats until all k candidates are elected. This guarantees a majority will win at least half of the seats in each constituency.
 
STV violates most axioms of proportional representation other than [[Proportionality for Solid Coalitions|proportionality for solid coalitions]].
 
== Potential for tactical voting ==
 
The single transferable vote eliminates much of the reason for [[tactical voting]]. Voters are "safe" voting for a candidate they fear won't be elected, because their votes will be reallocated in Process B. They are "safe" voting for a candidate they believe will receive overwhelming support, because their votes will get reallocated in Process A.
because their votes will be reallocated in Process B. They are "safe" voting for a candidate they believe will receive overwhelming support, because their votes
will get reallocated in Process A.
 
However, in older STV systems there is a loophole: 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 they have already been elected. For example, a voter might make a tactical decision to rank their top-place candidate beneath a candidate they know will lose (perhaps a fictional candidate). If the voter's true top-place candidate has not been elected by the time their fake top candidate loses, the voter's full vote will count for their true top-place candidate. Otherwise, the voter will have avoided having had their ballot in the lottery to be "[[wasted vote]]s" on their top-ranked candidate, and will continue on to lower-ranked candidates.▼
However, in older STV systems there is a loophole:
▲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 they have already been elected. For example, a voter might make a tactical decision to rank their top-place candidate beneath a candidate they know will lose (perhaps a fictional candidate). If the voter's true top-place candidate has not been elected by the time their fake top candidate loses, the voter's full vote will count for their true top-place candidate. Otherwise, the voter will have avoided having had their ballot in the lottery to be "[[wasted vote]]s" on their top-ranked candidate, and will continue on to lower-ranked candidates.
 
Note that in more modern STV systems, this loophole has been fixed. A vote receives the same fractional weighting regardless of when it arrives at the successful candidate. This modernisation has not been adopted in all STV systems.
 
There are also tactical considerations for parties standing more than one candidate in the election. Standing too few may result in all the candidates 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 amongst them, and several being eliminated before any are elected and their second-preference votes distributed, if 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 strictly express party preference, parties frequently stand more candidates than there are seats to be elected.
 
[[Vote management]] is a potential strategy in STV that involves [[Bullet voting|bullet voting]] in a way that approximates [[D'Hondt]] to maximize a party's seat share. 5-winner example:
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British Columbia will decide in 2005 by referendum whether to adopt STV to replace its current [[First Past the Post]] electoral system, after a recommendation of STV [http://www.citizensassembly.bc.ca/public/news/2004/10/dmaclachlan-3_0410241345-701] by the Citizens' Assembly on Electoral Reform.
 
Some non-governmental organisations also use STV. For instance, all National Union of Students of the United Kingdom elections and those of their constituent members are under the system.
 
==Historical assessments==
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=== Quotas ===
* [[Hare quota]] (most proportional)
* [[Droop quota]] (most common)
* [[Ross quota]]{{Cn}}{{Clarify|reason=WTF is a Ross quota|date=April 2024}}
* [[Imperiali quota]]
* [[Hagenbach-Bischoff quota]] (sometimes also called a Droop quota)
* [[Ross quota]]
 
=== Ways of dealing with equal rankings ===
* Disallowing them, requiring full rankings.
* Counting a ballot with N top-ranked candidates as a single vote for one of them chosen at random. This approach could be used for a manual count with a large number of ballots to make the counting process easier. There's no reason to use it with computer counting, and it shouldn't be used if there are only a few ballots to count.
* ER-IRVSTV (fractional): Counting a ballot with N top-ranked candidates as 1/N of a vote for each candidate.
* ER-IRVSTV (whole votes) or Approval-IRVSTV: Giving one vote to each equally-top-ranked candidate. Can optionally be combined with a suggestion that ballots that equally rank candidates shouldn't be able to prevent the elimination of those candidates.<ref name="reddit 2011">{{cite web | title=Proportionality failure in STV with equal-ranks with whole votes : EndFPTP | website=reddit | date=2019-12-05 | url=https://www.reddit.com/r/EndFPTP/comments/e6bt6s/proportionality_failure_in_stv_with_equalranks/f9thuy4/?context=8&depth=9 | access-date=2020-02-10}}</ref>
 
The nature of IRVSTV is such that many of its derived properties depend on each voter exerting influence such that their support for all candidates adds up to at most "one vote" (see [[:Category:FPTP-based voting methods|Category:FPTP-based voting methods]]). Thus, fractional equal-ranking preserves most of IRV's criterion compliances and properties, but not Approval-IRV. In addition, fractional equal-ranking creates less ambiguity around how to configure the IRV rules, whereas with Approval-IRV, different variations of the rules which would give the same results with other forms of IRV can give different results:
 
Note that in the single-winner case, giving a vote to each equally-top ranked candidate can lead to different results when using either the "if in any round any candidate gets a quota (if using a Droop quota, a majority, in the single-winner case) they win" rule or the "all but ((number of winners) + 1) candidates must be eliminated, with the (number of winners) candidate(s) with the most votes then winning" rule (which can also be thought of as "all but (number of winners) candidates must be eliminated, with the remaining candidate(s) winning"). Single-winner example: <blockquote>45 A=C>B
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35 B>A>C
 
20 C>B>A </blockquote>If the first rule is used (modified to also say "if multiple candidates have Droop quotas in the same round, the candidate(s) with the largest Droop quotas win"), then C wins with 65 votes to start off with, whereas under the second rule, B is eliminated, and then A wins. The second rule can actually create greater possibility for [[Tactical voting#Types of tactical voting|pushover]] strategy, since it could have been the case the A=C>B voters' honest preferences were A>B>C, and if they had voted their honest preference, C would've been eliminated and then B would've won, a worse result from their point of view. Also, this can lead to different results when using either the "all candidates who reach quota are elected" rule or the "the candidate who most exceeds the quota is elected, then spend their ballots, and repeat" rule. 3-winner example with Droop quotas: <blockquote>34 A=B=C
 
Also, this can lead to different results when using either the "all candidates who reach quota are elected" rule or the "the candidate who most exceeds the quota is elected, then spend their ballots, and repeat" rule. 3-winner example with Droop quotas: <blockquote>34 A=B=C
 
33 D
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