Instant-runoff voting: Difference between revisions
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{{Wikipedia}}
When the [[single transferable vote]] (STV) [[voting system]] is applied to a single-winner election it is sometimes called '''instant-runoff voting''' (IRV), as it is much like holding a series of [[runoff voting|runoff]] elections in which the lowest polling candidate (based on 1st choice votes; see [[Ranked ballot|ranked ballot]]) is eliminated in each round until someone receives a [[simple majority|majority]]
Outside the US, IRV is known as the '''[[Alternative Vote]]''', '''[[preferential voting]]''', '''single-winner STV''', or the '''[[Thomas Hare|Hare]] System''', though there is room for confusion with some of these terms, since they can also refer to STV in general. In the US, IRV is also known as '''Ranked Choice Voting''' ('''RCV'''), a term preferred by election officials in San Francisco in 2004 because election results were not instant, and voters are responsible for ranking candidates.<ref name=":0">As described on a [https://web.archive.org/web/20040514072509/http://www.ci.sf.ca.us/site/election_page.asp?id=24269 City of San Francisco election page in 2004] "''Is 'ranked-choice voting' the same as 'instant runoff voting'? In San Francisco, ranked-choice voting is sometimes called 'instant run-off voting.' The Department of Elections generally uses the term ranked-choice voting, because it describes the voting method—voter are directed to rank their first, second and third choice candidates. The Department also uses the term ranked-choice voting because the word 'instant' might create an expectation that final results will be available immediately after the polls close on election night. But the term 'instant run-off' does not mean instantaneous reporting of results—the term means that there is no need for a separate run-off election.''"</ref>
== History ==
{{wikipedia|History and use of instant-runoff voting}}
Instant-Runoff Voting was invented around 1870 by American architect [[William Robert Ware]], who simply applied Hare's method to single-winner elections.<ref>{{Cite book|url=https://books.google.com/books?id=W7QRAAAAYAAJ&pg=PA192|title=Application of Mr. Hare's system of voting to the nomination of overseers of Harvard College.|last=Ware|first=William R.|date=1871|publisher=|year=|isbn=|location=|pages=|oclc=81791186|quote=It is equally efficient whether one candidate is to be chosen, or a dozen.}}</ref><ref>{{cite web|url=http://archive.fairvote.org/articles/reilly.pdf|title=The Global Spread of Preferential Voting: Australian Institutional Imperialism|author=Benjamin Reilly|publisher=FairVote.org|accessdate=17 April 2011}}</ref> Ware was not a mathematician, thus never subjected his election method to any rigorous analysis. He evidently based IRV on the single winner outcome of the [[Single Transferable Vote]] or STV developed in 1855 originally by [[Carl Andrae]] in [[Denmark]]. It was introduced into [[England]] in 1857 by the [[barrister]] [[Thomas Hare]], where it earned public praise from [[John Stuart Mill]], an English philosopher, member of parliament, and employee of the [[British East India Company|East India Company]].
IRV is used to elect the Australian House of Representatives, the lower houses of most of Australia's state parliaments, the President of Ireland, the Papua New Guinea National Parliament, and the Fijian House of Representatives. See below for a more detailed list.
:''See also: [[w:History and use of instant-runoff voting|History and use of instant-runoff voting]] on English Wikipedia''
== How IRV works ==
=== Voting ===
{{seealso|Truncation}}
Each voter ranks at least one candidate in [[Preferential voting|order of preference]]. In most Australian elections, voters are required to rank all candidates. In other elections, votes may be "[[truncation|truncated]]", for example if the voter only ranks his first five choices.
=== Counting the votes ===
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* '''Tie-breaking rules:'''
** LOGIC: If the tied candidates combined have fewer votes than the next
*** Logically deterministic, but may not apply
** LAST ROUND: Eliminate the candidate in the tie with the least votes from a previous round.
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*** Similar to random elimination, but with many nice properties not found with random elimination
Also consider batch elimination: if some batch of candidates can be eliminated that collectively have fewer votes than some other candidate. Example vote totals: 30 A 19 B 5 C 4 D 6 E. Because C, D, and E's collective 15 votes can't overtake B's 19 votes, all 3 can be eliminated at once without changing the result.
<br />
== Where IRV is used ==
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==== Failure to pick a good compromise ====
IRV exhibits [[center squeeze]]. That means that IRV can ignore a good compromise in favor of a polarized choice that enjoys smaller actual support.
This failure mode occurs in a 3-choice election where parties A and B are bitterly opposed, and party C is first choice for a minority but tolerable for a large majority. For a real-life example, consider the 17th-century Europe struggle over "government-enforced [[Catholicism]]" versus "government-enforced [[Protestantism]]", with "freedom of private worship" as the compromise C.
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===Logistical issues===
Ballots in IRV cannot be easily summarized.<ref group="fn">IRV can be summarized in <math>\Theta(n2^n)</math> space by keeping a [[FPTP]] count for every possible selection of eliminated candidates, but this is not useful in practice.</ref> (Political scientists call this the [[Summability criterion]].) In most forms of voting, each district can examine the ballots locally and publish the total votes for each candidate. Anyone can add up the published totals to determine the winner, and if there are allegations of irregularities in one district only that district needs to be recounted.
With IRV, each time a candidate is dropped, the ballots assigned to them must be re-examined to determine which remaining candidate to assign them to. Repeated several times, this can be time-consuming. If there is a candidate X who got more votes than all of the candidates who got less than X put together, then all of these candidates who lost to X can be dropped simultaneously without affecting the final outcome, which can speed up counting.
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Federal elections are conducted by the Australian Electoral Commission, who employ all the workers at all the booths, to a common standard of neutrality and efficiency. Candidates may appoint scrutineers to watch (but not touch) what is going on.
== Criticisms ==
Many of the arguments against IRV can be summed up like this: if 1st choices alone don't show who the best candidate is (i.e. the [[FPTP]] winner), then they can't show who the worst candidate is either (the FPTP loser, the one that IRV eliminates in every round).
Though IRV is often praised for passing [[later-no-harm]], which is claimed to encourage voters to rank all of their preferences, it doesn't tend to use as much of the information provided by the voters as other ranked methods, such as [[Condorcet methods]]. This is a less extreme analog to how [[First Past the Post electoral system|first past the post]] technically passes [[later-no-harm]] by ignoring later preferences altogether. So IRV's [[later-no-harm]] compliance has to be evaluated in context of the other criteria it fails due to using less information than other methods - that is, there may be ambiguity to how much IRV is truly protecting a voter's interests by not using their later-preference information at all.
From this perspective, the main criticism of IRV is essentially that, while it does avoid treating the candidate FPTP considers best as being best, it determines who the worst candidate is using 1st choices. In so doing, it uses [[first past the post]] to determine who to eliminate, and ignores most of the voter's ballot each round. This ignoring of most of the ballot is what gives IRV its [[later-no-help]] and [[later-no-harm]] properties, but also leads to its vulnerability to [[center squeeze]] and [[Favorite Betrayal]] (since, if you make 1st choices matter much more than other choices, then this can require voters to lie about who their 1st choice is to get the best outcome).
In contrast, [[Nanson's method]] is a method that ''does'' examine the whole ballot for each voter for each round , and whose logic is otherwise the same as IRV. It passes [[Condorcet criterion|Condorcet]] but fails both [[later-no-help]] and [[later-no-harm]]. Both Nanson and IRV are nonmonotone, so the lack of monotonicity can't be attributed to IRV not looking at the whole ballot.
== Notes ==
IRV can rather simply be thought of as a modification to [[Choose-one FPTP voting|choose-one FPTP voting]] to pass the [[Mutual majority criterion|mutual majority criterion]] (and further, always elect from the [[Dominant mutual third set|dominant mutual third set]]). This is because when all but one of the candidates in the mutual majority-preferred set of candidates is eliminated, the remaining candidate will guaranteeably be the majority's 1st choice among the remaining candidates and thus win. Example:
18 A>B>C
17 B>C>A
16 C>A>B
25 D>E>B
24 E>D>B
In normal [[runoff voting]], D and E are the two candidates with the most votes, preventing the majority's preferred candidates from entering the runoff. In FPTP, D has the most votes. But with IRV, first C is eliminated, and then E, and then B, resulting in A having 51 votes and winning. Note that though the 49 voter-minority preferred B to A, B didn't win; this is an example of IRV ignoring voter preferences in a way that can lead to some majorities (when looking at [[Head-to-head matchup|head-to-head matchups]]) having less power. However, the majority still got a better result than it would've had in some other methods.
IRV passes [[clone independence]] while [[FPTP]] doesn't. This is because if a candidate would receive a majority of votes, then [[Clone|cloning]] them will not allow any other candidate to receive a majority, because when all but one of the clones is eliminated, the remaining clone will have the same number of votes as if all of the clones hadn't run in the first place. However, James Green-Armytage found that despite IRV passing clone independence, allied candidates still have an incentive to exit the race.<ref>{{Cite web|url=http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf|title=Four Condorcet-Hare Hybrid Methods for Single-Winner Elections|last=Green-Armytage|first=J.}}</ref>
IRV is equivalent to [[runoff voting]] (supposing no change in preferences) when there are 3 or fewer candidates. This is used to argue both for and against it; advocates claim it is cheaper and easier for the voters to vote once, while opponents argue that a delayed runoff actually gives voters a second look into the candidates in the runoff, potentially improving the quality of their decision-making, and that because ranking candidates is harder than picking one candidate, that runoff voting is actually easier for voters. Note that though IRV is called instant runoff, this is more because it elects a candidate who could win or tie a runoff ([[pairwise beat]] or tie) against at least one other candidate, rather than because it is equivalent to runoff voting in all cases.
IRV always elects a Condorcet winner who receives over [[Dominant mutual third|1/3rd]] of 1st choice votes. More generally, a candidate who at any point when they are uneliminated receives over 1/3rd of all active votes and [[Pairwise counting|pairwise beats]] (is preferred by more voters than) all other uneliminated candidates is guaranteed to win. This is because when all but two candidates are eliminated, the one preferred by more voters is guaranteed to win in IRV, and a candidate with over 1/3rd of active votes is guaranteed to be one of the final two remaining candidates, because at most only one other candidate can get more active votes than the over-1/3rd pairwise victor.
The number of votes a candidate has in any round of an IRV election is guaranteed to be
40 B
20 A=B </blockquote>If fractional equal-ranking is allowed, the number of votes each candidate has is 50, while if whole-votes equal-ranking is used instead, each candidate has 60 votes. However, they each have only 40 votes in their pairwise matchup.) In addition, an upper bound can be found for how many votes each candidate has in their pairwise matchups against other candidates by looking at how many active votes there are in a particular IRV round; for example, if Candidate A has 560 votes in an IRV round, Candidate B has 270, and all other candidates combined have 170 votes, then not only does Candidate A have a lower bound of getting 560 out of 1000 votes against B and all other candidates, guaranteeing A pairwise beats all of them, but the upper bound on the number of votes any of these candidates can get in a head-to-head matchup against A is 440, because that's how many active IRV votes there are that don't go to A in that round.
Example where IRV with whole votes equal ranking can give different results based on the winning rules used: <blockquote>45 A>B>C
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Votes in the 1st round are 45 A 35 B 65 C.
If you elect a candidate the moment they have a majority, C would win, making the strategy backfire. But if you keep eliminating until you have only two candidates, then B is eliminated first, and then A wins with 80 votes.<ref>https://www.reddit.com/r/EndFPTP/comments/f7daa0/key_details_emerge_for_how_rankedchoice_in_nyc/fib0pgd?utm_source=share&utm_medium=web2x</ref></blockquote>
Note that when the top candidate doesn't have a majority, but the top two candidates each have over 1/3rd of the active votes (i.e. they combinedly have over 2/3rds), they are guaranteed to be the two final remaining candidates in IRV, so all other candidates can be eliminated (or equivalently, the pairwise matchup between the two can be tallied) to find the result. This explains why some criticize IRV as mathematically inducing two-party domination, since often it does result in two mainstream factions vying to be pairwise preferred to each other.
Several [[:Category:Condorcet-IRV hybrid methods|variations of IRV]] have been proposed to meet the [[Condorcet]] and [[Smith criterion|Smith]] criteria. The simplest of these are to either (elect the [[Condorcet winner]] if one exists), or (eliminate all candidates not in the [[Smith//IRV|Smith set]]), and then run IRV.
== Presentation of procedure ==
There are two ways to make a diagram detailing an IRV result. The first is generally to create a [[W:Sankey diagram|Sankey diagram]] showing votes transferring, at least until some candidate has a majority of active votes. The other is to show a flow diagram where, for either of the two candidates with the most votes in a round, it is shown whether they have over 1/3rd of the active votes, and how many of the other uneliminated candidates they pairwise beat. Here is a visualization example of IRV (it should be read as "Voter 1 ranks Candidate A 1 i.e. 1st, etc.):
{| class="wikitable"
|+Rankings of the candidates
!Number of voters to the right
Candidates below
!2
!4
!5
!5
!6
|-
|A
|<small>5</small>
|'''<big>1</big>'''
|<small>3</small>
|<small>2</small>
|<small>3</small>
|-
|B
|<small>2</small>
|<small>5</small>
|<small>4</small>
|<small>5</small>
|'''<big>1</big>'''
|-
|C
|<small>4</small>
|<small>3</small>
|'''<big>1</big>'''
|<small>3</small>
|4
|-
|D
|<small>3</small>
|<small>2</small>
|<small>2</small>
|'''<big>1</big>'''
|<small>2</small>
|-
|E
|'''<big>1</big>'''
|<small>4</small>
|<small>5</small>
|<small>4</small>
|<small>5</small>
|}
This can be converted into:
{| class="wikitable"
|+Rankings of the candidates
!Number of votes for each candidate:
!2
!4
!5
!5
!6
|-
!Number of voters to the right
Rankings below
!2
!4
!5
!5
!6
|-
|1st
|'''<big>E</big>'''
|'''<big>A</big>'''
|'''<big>C</big>'''
|'''<big>D</big>'''
|'''<big>B</big>'''
|-
|2nd
|B
|D
|D
|A
|D
|-
|3rd
|D
|C
|A
|C
|A
|-
|4th
|C
|E
|B
|E
|C
|-
|5th
|A
|B
|E
|B
|E
|}
Because the smallest number in favor of any candidate is 2 for E, E is eliminated. This yields:
{| class="wikitable"
|+Rankings of the candidates
!Number of votes for each candidate:
! colspan="2" |<big>8</big>
!4
!5
!5
|-
!Number of voters to the right
Rankings below
!2
!6
!4
!5
!5
|-
|1st
|'''<big>B</big>'''
|'''<big>B</big>'''
|'''<big>A</big>'''
|'''<big>C</big>'''
|'''<big>D</big>'''
|-
|2nd
|D
|D
|D
|D
|A
|-
|3rd
|C
|A
|C
|A
|C
|-
|4th
|A
|C
|B
|B
|B
|}
Note that the last column has moved next to the 2nd column because both voters' 1st choices are now B, and so their combined support yields 8 votes for B, shown in the cell above them. Now A has the smallest coalition in favor of them (4 votes), so they are eliminated. Then:
{| class="wikitable"
|+Rankings of the candidates
!Number of votes for each candidate:
!8
!9
!5
!
!
|-
!Number of voters to the right
Rankings below
!8 (2 + 6)
!9 (4 + 5)
!5
!<small><s>0 (5 - 5)</s></small>
!<small><s>0 (6 - 6)</s></small>
|-
|1st
|'''<big>B</big>'''
|'''<big>D</big>'''
|'''<big>C</big>'''
|'''<small><s>D</s></small>'''
|'''<small><s>B</s></small>'''
|-
|2nd
|D
|C
|D
|<small><s>C</s></small>
|<small><s>D</s></small>
|-
|3rd
|C
|B
|B
|<small><s>B</s></small>
|<small><s>C</s></small>
|}
Two columns can be merged because, with all of the eliminated candidates, they now are identical in their rankings of the remaining candidates. Now C has the fewest votes (5), so they are eliminated. Since there are only two candidates remaining after this elimination, the result is guaranteed to be known, so this is the final round:
{| class="wikitable"
|+Rankings of the candidates
!Number of votes for each candidate:
!<small>8</small>
!<big>14</big>
!
!
!
|-
!Number of voters to the right
Rankings below
!8 (2 + 6)
!<big>14 (4 + 5 + 5)</big>
!<small><s>0 (5 - 5)</s></small>
!<small><s>0 (5 - 5)</s></small>
!<small><s>0 (6 - 6)</s></small>
|-
|1st
|'''<big>B</big>'''
|'''<big>D</big>'''
|'''<small><s>D</s></small>'''
|'''<small><s>D</s></small>'''
|'''<small><s>B</s></small>'''
|-
|2nd
|D
|<big>B</big>
|<small><s>B</s></small>
|<small><s>B</s></small>
|<small><s>D</s></small>
|}
D wins with 14 votes to B's 8.
Note that this form of visualization becomes harder when allowing for equal-ranking.
=== "Condorcet winner with over 1/3rd of votes" presentation ===
The "A Condorcet winner with over 1/3rd of 1st choice votes is guaranteed to win" [[Dominant mutual third|factoid]] can be used to speed up the counting; in the above example, when the votes were 8 B 9 D 5 C, D was a Condorcet winner:
{| class="wikitable"
|+Pairwise counting matrix
!
!A
!B
!C
!D
!E
|-
|A
| ---
|20 (+18 Win)
|15 (+8 Win)
|4 (-14 Loss)
|20 (+18 Win)
|-
|B
|2 (-18 Loss)
| ---
|8 (-6 Loss)
|8 (-6 Loss)
|11 (Tie)
|-
|C
|7 (-8 Loss)
|14 (+6 Win)
| ---
|5 (-12 Loss)
|20 (+18 Win)
|-
|'''D'''
|'''18 (+14 Win)'''
|'''14 (+6 Win)'''
|'''17 (+12 Win)'''
|'''---'''
|'''20 (+18 Win)'''
|-
|E
|2 (-18 Loss)
|11 (Tie)
|2 (-18 Loss)
|2 (-18 Loss)
| ---
|}
When looking at only B, C, and D's matchups, this becomes:
{| class="wikitable"
|+Pairwise counting matrix
!
!B
!C
!D
|-
|B
| ---
|8 (-6 Loss)
|8 (-6 Loss)
|-
|C
|14 (+6 Win)
| ---
|5 (-12 Loss)
|-
|'''D'''
|'''14 (+6 Win)'''
|'''17 (+12 Win)'''
|'''---'''
|}
D [[Pairwise beat|pairwise wins]] against all others, and had 9 out of the 22 active votes = 40.9%, greater than 1/3rd, at that time. So there was no need to eliminate C at that point to find the winner.
== Variants ==
See the [[Equal-ranking methods in IRV]] article. IRV can be done with equal ranking allowed. The two main ways of doing this are either fractional (split the voter's ballot equally between all of their highest-ranked candidates that are ranked equally (3 candidates ranked 1st each get 1/3rd of a vote)), or whole votes (give each highest-equally-ranked candidate one vote (3 candidates get 1 vote each and 3 votes total)).
With whole votes equal-ranking, there are two ways to find a winner (which give the same result in standard IRV but differ for whole votes): either eliminate candidates until only two remain, and declare the one with more votes the winner, or eliminate candidates until one or more candidates are supported by a majority of active ballots, and then elect the candidate with the largest majority. Some have argued<ref>[https://www.reddit.com/r/EndFPTP/comments/e6bt6s/proportionality_failure_in_stv_with_equalranks/f9s5yno/?context=3]</ref> that in order to limit opportunities for pushover strategy with whole votes, a ballot that equally ranks candidates should be allowed to help those candidates win, but not prevent those candidates from getting eliminated.
One simple way to modify IRV to address many of the issues IRV opponents have without changing IRV fundamentally is to allow voters to approve candidates (using an [[approval threshold]]). If there are any majority-approved candidates, elect the most-approved of them, otherwise run IRV. Even if voters [[Favorite Betrayal|Favorite Betray]], they can still approve their honest favorite, giving that candidate a chance to still win. In addition, this allows voters to better avert the [[center squeeze effect]]. The standard argument made by IRV advocates against [[Approval voting]], that it fails [[later-no-harm]], has little to no relevance to this modification, since voters seeking to avoid hurting their favorite candidates' chances of winning in the approval round can simply refrain from approving anyone, forcing the election to run under IRV rules.
== Naming ==
:''see also: [[FairVote#IRV]]''
Prior to FairVote's work, the single-winner version of [[single transferable vote]] was primarily used outside of the United States (e.g. in Australia), and was known in Australia as "preferential voting".
In commentary published in the New York Times in 1992, John Anderson referred to the single-winner system as "majority preferential voting".<ref>{{Cite news|last=Anderson|first=John B.|url=https://www.nytimes.com/1992/07/24/opinion/break-the-political-stranglehold.html|title=Opinion {{!}} Break the Political Stranglehold|date=1992-07-24|work=The New York Times|access-date=2020-04-30|language=en-US|issn=0362-4331}}</ref>
In 1993, the Center for Voting and Democracy (now known as "[[FairVote]]") published their first annual report. In that report, they referred to the system as "preference voting",<ref>https://web.archive.org/web/19990507180316/http://www.fairvote.org/cvd_reports/1993/introduction.html</ref> which included the following caveat:<blockquote>''A Note on Terminology: Reflecting the range of contributors, this report has some inconsistencies in terminology to describe different voting systems. In addition, what many call the "single transferable vote" here is termed "preference voting" in order to focus on the voting process rather than the ballot count.''</blockquote>In 1997, FairVote began referring to preferential voting as "Instant Runoff voting".<ref>[https://www.csmonitor.com/1997/0721/072197.opin.opin.1.html "Fuller, Fairer Elections? How?"]. ''Christian Science Monitor''. 1997-07-21. [https://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN] [https://www.worldcat.org/issn/0882-7729 0882-7729]<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-12-14</span></span>.</ref><ref>From [https://web.archive.org/web/19990427031915/http://www.fairvote.org/email_archives/070298.htm the 1998 newsletter]: "Note that the transferable ballot can be used as a proportional representation system in multi-seat districts (what we call "choice voting") and in one-winner elections (what we call "instant runoff voting")."</ref> However, the city of San Francisco preferred the term "ranked-choice voting", which was used as early as 1999.<ref>http://archive.fairvote.org/library/statutes/irv_stat_lang.htm San Francisco Charter Amendment, introduced October 1999 "SEC. 13.102. RANKED-CHOICE BALLOTS"</ref><ref>Instant Runoff Voting Charter Amendment for San Francisco passed on March 5, 2002, "''to provide for the election of the Mayor, Sheriff, District Attorney, City Attorney, Treasurer, Assessor-Recorder, Public Defender, and members of the Board of Supervisors using a ranked-choice, or “instant run-off,” ballot, to require that City voting systems be compatible with a ranked-choice ballot system, and setting a date and conditions for implementation.''"</ref> By 2004, San Francisco was careful to explain that the method codified as "ranked choice voting" was the same as "instant runoff voting.<ref name=":0" /> Because organizations in Arizona borrowed San Francisco's language, many used "ranked choice" as the preferred wording, which [[FairVote]] accommodated as early as 2006.<ref>"[https://web.archive.org/web/20060927205517/http://www.fairvote.org/rcv/ FairVote and the LWV-Arizona Support Ranked Choice Voting]" Dr. Barbara Klein and Rob Richie</ref> [[FairVote]] didn't appear to publicly deprecate the term "instant runoff voting" until 2013,<ref>The [https://web.archive.org/web/20130729141521/http://www.fairvote.org/ July 2013 homepage of fairvote.org] was the first to refer to "ranked choice voting" as a preferred term to "instant-runoff"</ref> but now appears to prefer "ranked choice voting" to describe the method.
When equal-ranking is disallowed, as is most often the case, IRV is sometimes called '''nER-IRV''' (for "no Equal Ranking").
==See also==
*[[Australian electoral system]]
*[[Electoral systems of the Australian states and territories]]
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*[[Table of voting systems by nation]]
*[[Bottom-Two-Runoff IRV]] - a variant that meets the Condorcet criterion
== Footnotes ==
<references group="fn"/>
== References ==
Line 273 ⟶ 622:
==External links==
* Pro/advocacy positions
** [
** [https://rankthevote.us RankTheVote]
** [http://instantrunoff.com instant runoff]
** [http://www.firv.org Ferndale for Instant Runoff Voting]
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* Examples
** [http://www.mnip.org/caucusresults.htm Minnesota Independence Party 2004, IRV poll for U.S. President.]
** [http://www.aec.gov.au/ Australian Electoral Commission]
* Software
** [http://www.OpenSTV.org/ OpenSTV]—Software for computing IRV and STV
** [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp Software that computes IRV and STV methods with shared rankings counted ]
*Further Explanation
** [http://anewprogressiveamerica.blogspot.com/2004/11/what-is-instant-runoff-voting.html What is Instant Runoff Voting?]
** [https://www.newamerica.org/political-reform/reports/what-we-know-about-ranked-choice-voting/ "What We Know About Ranked Choice Voting"] from the New America Foundation
{{fromwikipedia}}
[[Category:Single-winner voting methods]]
[[Category:
[[Category:Plurality-runoff voting methods]]
[[Category:Sequential loser-elimination methods]]
[[Category:Clone-independent electoral systems]]
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