Single transferable vote: Difference between revisions
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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'''.
== 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>
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/>
</ref>
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=== Setting the quota===
When all the votes have been cast, a winning quota is set. In
=== Counting The Votes ===
Process A: Top-preference votes are tallied.
The excess votes for the winning candidate are reallocated to the next-highest ranked candidates on the ballots for the elected candidate.
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 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.
elected with 11 excess votes.
As none of the candidates have reached their threshold, Brad, the
candidate with the fewest votes, is eliminated.
Carter as the next-place choice, and are reallocated to Carter.
gives Carter 11 votes and he is elected.
== Proportionality ==
STV is perhaps better described as quasi-proportional rather than truly proportional, as it is only proportional in some ways.
=== Overall proportionality ===
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
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>
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
=== 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
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.
Within each constituency, STV passes
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.
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.▼
▲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.
[[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.
==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}}
=== 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-
* ER-
The nature of
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
33 D
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=== Ways of choosing a candidate to eliminate ===
* Standard STV: Eliminate the candidate with the fewest top-choice votes.
* [[BTR-STV]]: Eliminate the pairwise loser of the bottom two candidates.
* [[Benham's method|Benham]]: If the candidate with the fewest top-choice votes beats every other remaining candidate pairwise, eliminate the candidate with the next fewest top-choice votes. Meets the [[Condorcet criterion]] in single-winner elections.
* [[STV-CLE]]: Eliminate the loser of a [[Condorcet ranking]] or a [[Condorcet method]]'s ranking. Using a Condorcet method that passes [[local independence of irrelevant alternatives]] can lend additional stability to the STV method.
=== Methods of transferring votes from an eliminated candidate === <!-- Meek, Warren, Gregory, random transfer go here, or into "transferring excess votes", at some point -->
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