Single transferable vote

{{bronze}}{{politics}}
The '''Single Transferable Vote''' (STV) is an electoral system that yields [[proportional representation]]. In a Single Transferable Vote election, voters rank candidates or parties in order of preference, and candidates are elected sequentially.<ref name=opa>[https://www.opavote.com/methods/single-transferable-vote OpaVote: Single Transferable Vote]</ref> Proportionality is maintained by associating a cost, or quota, with the election of each candidate, which a candidate's supporters must pay when that candidate is elected.<ref>[http://www.votingmatters.org.uk/ISSUE24/I24P2.pdf Notes on the Droop Quota], Lundell and Hill. ''Voting Matters'', Issue 24.</ref>

In a single winner election, it is [[Instant Runoff Voting]].<ref name=opa/>

==Procedure==
While there are several variants of STV,<ref name=opa/> most implementations of it more or less work as described below.

===Finding the quota===
First, the number of valid votes cast is used to compute the quota, that is, the number of votes that a candidate needs to be elected. The two major quotas are the Hare Quota, which is equal to Votes/Seats and the Droop Quota, which is equal to Votes/(Seats+1), rounded up.<ref group=note>This extends the concept of a majority as receiving 50%+1 of the votes in single-winner elections to elections with multiple winners.</ref> While the Hare Quota makes it possible for every vote to be assigned to a candidate, a candidate only needs to exceed the Droop Quota to guarantee that they will be elected. For this reason, using the Hare Quota can make a method more vulnerable to strategic voting, so the Droop Quota is more commonly used in practice.<ref>[https://www.prsa.org.au/quota_droop_vs_hare_voting_in_democracies_lakeman_&_lambert.pdf Droop vs Hare], Lakeman and Lambert. ''Voting In Democracies''.</ref>

===Counting the votes===
Initially, each vote starts out as having a weight of 1, and is assigned to the candidate that is ranked first on the ballot. A candidate's vote count is the sum of the weights of the votes assigned to them.

Any candidates with vote counts that are at least as large as the quota are declared elected. If an elected candidate has more votes than the quota, the amount by which their vote count exceeded the quota is called a surplus, and the ballots supporting the elected candidate have their weight multiplied by the ratio between the surplus and the total votes assigned to the elected candidate. (If there is no surplus, the weight is reduced to 0.)<ref group=note>This ensures that the votes assigned to the elected candidate spend exactly one quota of weight to elect that candidate, and that each vote pays in proportion to its weight.</ref> Then, the votes are transferred to the highest ranked candidate on the ballot who has not been elected or eliminated. If no such candidates are ranked on the ballot, the ballot is considered exhausted, and is ignored for the remainder of the election.

If no candidates exceed the quota, then the candidate with the smallest vote total is eliminated, and their votes are transferred in the same way as they would be for surplus transfers, except that the votes do not lose any weight.

The counting stops when all the seats are filled, or as many candidates as unfilled seats remain, in which case they are filled by the remaining candidates.

===Example===
Consider the following 3 winner election with the ballots
{|class="wikitable" style="text-align:center"
|-
!Vote
!Quantity
|-
|Alice>Aaron
|16
|-
|Alice>Aaron>Bob
|5
|-
|Bob>Brenda
|4
|-
|Brenda>Bob
|4
|-
|Charlie
|7
|}
There are 36 votes and 3 seats, so the Droop quota is 36/(3+1)=9 votes.

The first count is Alice: 21, Aaron: 0, Bob: 4, Brenda: 4, Charlie: 7. Only Alice exceeds the quota, so she is elected and each vote for Alice has its weight multiplied by (12/21). All of her votes transfer to Aaron.

The second count is Aaron: 12, Bob: 4, Brenda: 4, Charlie: 7. Only Aaron exceeds the quota, so he is elected, and each vote for him has its weight multiplied by (3/12). The Alice>Aaron votes are exhausted as all of the candidates they listed were elected. The Alice>Aaron>Bob votes transfer to Bob.

The third count is Bob: 4.952, Brenda: 4, Charlie: 7. No candidate exceeds the quota, so the one with the fewest votes, Brenda is eliminated. Her votes transfer to Bob.

The fourth count is Bob: 8.952, Charlie: 7, so Charlie is eliminated and Bob wins the third seat.

==Use in government elections==
===Use in national elections===
STV is used to elect the [[Australian]] Senate, [[Republic of Ireland|Irish]] Dáil Éireann, and [[Malta|Maltese]] House of Representatives. Ireland and Malta also use it for all local and regional elections as well.<ref group=note>Additionally, Australian elections always use either STV or its single-winner analogue, Instant Runoff Voting, but legislatures in Australia sometimes use single-winner districts.</ref><ref name=ni>[https://web.archive.org/web/20181007064514/http://www.ark.ac.uk/elections/gstv.htm The Single Transferable Vote], Northern Ireland Elections.</ref>

===Use in local elections===
Some Australian state and territorial houses are elected with STV.<ref name=pw>[https://www.theage.com.au/politics/victoria/hire-me-and-get-into-parliament-the-preference-whisperer-s-message-20181214-p50mdh.html 'Hire me and get into parliament': the preference whisperer's message], Millar, Preiss, and Schneiders, 2018. ''The Age''.</ref>

STV is used in local and regional elections in [[Northern Ireland]] except for MPs of the [[UK]] [[House of Commons]].<ref name=ni/> It is used for local elections in [[Scotland]].<ref>[https://web.archive.org/web/20060104050011/http://www.scottish.parliament.uk/business/bills/billsnotInProgress-s2/14LocalGovernance.htm Local Governance (Scotland) Bill], Scottish Parliament, 2004.</ref>

It was used in municipal elections in the [[Canadian]] provinces of Alberta and Manitoba between the mid-1920s to mid-1950s.<ref>[https://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/tape15/PQDD_0004/NQ29051.pdf The Single Transferable Vote in Alberta and Manitoba], Harold John Jansen, 1998.</ref>

In the [[US]], it is currently used in Cambridge, Massachusetts.<ref name=us>[https://www.electoral-reform.org.uk/latest-news-and-research/publications/a-short-history-of-stv-in-the-us/ A short history of STV in the US], Douglas J. Amy, 1996. Electoral Reform Society.</ref>, and Minneapolis, Minnesota.<ref>[https://vote.minneapolismn.gov/ranked-choice-voting/history/ Ranked choice voting history], Minneapolis Elections Office.</ref> It was used in several major American cities such as New York during the first half of the 20th century, but during the 1950s it was largely [[Racism|abandoned]] [[McCarthyism|because]] it allowed racial minorities and [[Communists]] to be elected.<ref name=us/>

==Benefits==
{{main|Proportional representation}}
STV can provide proportional representation while still allowing voters to vote for individual candidates instead of political parties, unlike party list systems, where voting for a party means supporting the entire list.<ref>[https://www.electoral-reform.org.uk/voting-systems/types-of-voting-system/party-list-pr/ Party List PR], Electoral Reform Society.</ref> It also makes it easier for independent candidates to get elected compared to other proportional representation systems.

Transferring votes helps mitigate wasted votes, in contrast with list PR systems, especially those with thresholds, which effectively discard votes for parties below the threshold.

==Problems==
===Difficulty of judging individual candidates===
Even when voters can vote for individual candidates (and not just parties), it is more difficult than party voting, so voters will often prefer to vote for parties if given the option. For example, in Australian Senate elections, very few voters vote "below the line".<ref>[https://www.theage.com.au/politics/victoria/why-you-should-vote-below-the-line-today-20181123-p50i0a.html Why you should vote below the line today], 2018. ''The Age''.</ref>

Furthermore, some regional elections in Australia allow minor parties to direct the preferences of above-the-line voters when they are eliminated if the voter ranks only one party;<ref>[https://web.archive.org/web/20151017092630/http://blogs.abc.net.au/antonygreen/2015/09/the-orogins-of-senate-group-ticket-voting-and-it-wasnt-the-major-parties.html The Origins of Senate Group Ticket Voting], Antony Green, 2015. ABC Elections.</ref> this rule allows minor parties to make deals that can allow obscure candidates to be elected with the votes of voters who may not have even heard of the candidate whom their votes elected.<ref name=pw/><ref>[https://www.smh.com.au/politics/federal/preference-deals-rarely-end-well-20190503-p51js6.html Preference Deals Rarely End Well], Tony Walker, 2019. ''The Sydney Morning Herald''.</ref>

===Free riding===
Free riding occurs in STV elections when a voter attempts to avoid contributing to the election of a candidate whom they are sure will be elected, in order to avoid paying the cost of electing that candidate. There are two major ways of doing this.

====Woodall Free Riding====
Woodall Free Riding occurs when a voter intentionally gives their first preference to a candidate they expect to lose quickly at the top of the ballot.<ref name="schulze">[https://web.archive.org/web/20200201102638/http://9mail-de.spdns.de/m-schulze/schulze2.pdf Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote], Markus Schulze.</ref> This ensures that they will not have to pay for the election of a candidate until after the first eliminations, since that candidate will have to be eliminated in order for their vote to be transferred. In particular they will not have to pay for the election of a candidate who exceeds the quota on the first count.

Meek STV, used in RationalWiki moderator elections, allows votes to be transferred to already-elected candidates in order to prevent Woodall Free Riding.<ref>[https://www.votingmatters.org.uk/ISSUE18/I18P2.PDF Free Riding], Markus Schulze.</ref><ref>[https://blog.opavote.com/2017/04/meek-stv-explained.html Meek STV Explained], OpaVote.</ref> So don't get any big ideas!

====Hylland Free Riding====
Hylland Free Riding occurs when a voter does not rank any candidates whom they are sure will be elected.<ref name="schulze"/> When it is practiced ''en masse'', it leads to several candidates being elected with less than a full quota,<ref name="schulze"/> magnifying the power of the votes for that candidate.

===Vote management===
Vote management involves coordinated campaigns of Hylland Free Riding, typically by a political party.<ref name="schulze"/> The strategy is for the party to estimate the number of seats that they believe they will be able to compete for, dividing their voters into groups of roughly equal size, and assigning each group to one of that party's candidates, whom they are instructed to give their first choice to. The advantage of this tactic is demonstrated in the following example.

{|class="wikitable" style="text-align:center"
|-
!Vote
!Quantity
|-
|A1>A2>A3
|16
|-
|A2>A3>A1
|16
|-
|A3>A1>A2
|16
|-
|B1>B2>B3
|51
|-
|C
|9
|}
As there are 108 votes, the Droop quota is 108/6=18.

Candidate B1 will be elected first, followed by B2. This will cost the B voters 36 votes, leaving them with 15 votes worth of weight.

After that, no candidate will have exceeded the quota, so C will be eliminated, followed by B3, leaving A1, A2, and A3 as the winners of the remaining seats. This allows party A to win a 3-2 majority of the seats despite being outnumbered 51-48 by party B voters.

It is commonly practiced in Irish elections.<ref name=schulze/><ref>[https://www.irishtimes.com/culture/vote-management-was-key-to-fianna-fail-s-extra-23-seats-1.196336 Vote Management was key to Fianna Fail's extra 23 seats], 1999. ''The Irish Times''.</ref> A consequence of vote management in the 2020 Irish election was that Sinn Féin won slightly fewer seats than their proportional share of the vote, since they received a late increase in support too late to run more candidates and thus underestimated the number of seats they could win in some constituencies.<ref>[https://www.irishtimes.com/news/politics/election-2020-sinn-f%C3%A9in-surpluses-added-extra-dimension-to-transfer-battle-1.4169192 Sinn Féin surpluses added extra dimension to transfer battle], 
Marie O'Halloran, 2020. ''The Irish Times''.</ref><ref>[https://www.irishexaminer.com/news/spotlight/arid-40222064.html Special report: Sinn Féin was the big winner in election 2020 and surge can continue], Daniel McConnell, 2021. ''Irish Examiner''.</ref>

===Monotonicity and spoilers===
{{main|Instant Runoff Voting}}
As a multiwinner analogue of Instant Runoff Voting, STV inherits some of its flaws as well, such as [[Instant Runoff Voting#Non-monotonicity|nonmonotonicity]]<ref group=note>This is when it is possible that raising a candidate's ranking on a ballot can cause them to lose.</ref> and participation failure.<ref group=note>This is when it is possible that casting a ballot can cause a lower-ranked candidate to be elected instead of a higher-ranked one.</ref><ref>[https://www.votingmatters.org.uk/ISSUE3/P5.HTM Properties of Preferential Election Rules], Douglas R. Woodall, 1994. ''Voting Matters'', Issue 3.</ref>

==See also==
*[[Proportional representation]]
*[[Instant Runoff Voting]]

==External links==
*[https://www.youtube.com/watch?v=P38Y4VG1Ibo Video Explaining STV]

==Notes==
{{reflist| group=note|2}}

==References==
{{reflist|2|80%}}

[[Category:Voting systems]]

Categories: Voting systems