Instant-runoff voting

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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 elections in which the lowest polling candidate (based on 1st choice votes; see ranked ballot) is eliminated in each round until someone receives a majority of votes. IRV is often considered independently of multi-winner STV because it is simpler and because it is the most widely advocated electoral reform in the United States.

Outside the US, IRV is known as the Alternative Vote, preferential voting, single-winner STV, or the 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.[1]


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Instant-Runoff Voting was invented around 1870 by American architect William Robert Ware, who simply applied Hare's method to single-winner elections.[2][3] 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 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: History and use of instant-runoff voting on English Wikipedia

How IRV works


See also

Each voter ranks at least one candidate in order of preference. In most Australian elections, voters are required to rank all candidates. In other elections, votes may be "truncated", for example if the voter only ranks his first five choices.

Counting the votes

First choices are tallied. If no candidate has the support of a majority of voters, the candidate with the least support is eliminated. A second round of counting takes place, with the votes of supporters of the eliminated candidate now counting for their second choice candidate. After a candidate is eliminated, he or she may not receive any more votes.

This process of counting and eliminating is repeated until one candidate has over half the votes. This is equivalent to continuing until there is only one candidate left. However it is possible, with voter truncation, for the process to continue until there is only one candidate left, who does not end up with more than half the votes.

An example

Tennessee's four cities are spread throughout the state
Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

  • Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
  • Nashville, with 26% of the voters, near the center of Tennessee
  • Knoxville, with 17% of the voters
  • Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis
City Round 1 Round 2 Round 3
Memphis 42 42 42
Nashville 26 26 26 0
Chattanooga 15 15 0 0
Knoxville 17 17 32 32 58

Chattanooga, having the smallest vote, is eliminated in the first round. All of the votes for Chattanooga have Knoxville as a second choice, so they are transferred to Knoxville. Nashville now has the smallest vote, so it is eliminated. The votes for Nashville have Chattanooga as a second choice, but as Chattanooga has been eliminated, they instead transfer to their third choice, Knoxville. Knoxville now has 58% of the vote, and it is the winner.

In a real election, of course, voters would show greater variation in the rankings they cast, which could influence the result.

Special cases of IRV eliminations

Instant Runoff Voting as an ideal does not explicitly define how to handle special cases such as ties and different rules can be considered. A good IRV election must define rules to handle these cases before the votes are cast. The reason why is that there are cases where one set of rules will select a winner different from another set of rules and the set of rules used may affect how the voters cast their ballots.

Especially when performing IRV counts on smaller elections, there can be frequent last-place ties that prevent clear bottom elimination.

Here are some approaches to consider, individually and combined. The first class of rules allows many candidates to be eliminated at the first count regardless of actual ties. These are practical rules before the first round that reward stronger candidates among the full set of competition. Such rules won't likely affect the winner but they will reduce the number of elimination rounds and thus the number of opportunities for ties to develop. A second class of rules consider actual ties that can't be avoided.

  • Consider multi-candidate elimination of weak candidates as the first step:
    • CANDIDATE COUNT: Define a maximum number of candidates that can survive the first round.
      • Example top-two
    • VOTE MINIMUM: Define a minimum vote threshold (5 vote for example) and eliminate all weaker candidates together.
      • Requires limitations for rule to apply
    • PERCENT MINIMUM: Define a minimum percent vote threshold (5% for example) and eliminate all weaker candidates together.
      • Again, requires limitations for application
    • PERCENT RETENTION: Define a minimum percent of votes by top candidates to be retained.
      • Example - retain the top set of candidates who combined control 50% of the vote
  • Tie-breaking rules:
    • LOGIC: If the tied candidates combined have fewer votes than the next higher candidate, the entire tied set can be eliminated at once.
      • Logically deterministic, but may not apply
    • LAST ROUND: Eliminate the candidate in the tie with the least votes from a previous round.
      • Traditional rule; violates purity of one-person, one vote ideal
    • ALL: Eliminate all tied candidates at once.
    • RANDOM: Eliminate one randomly to break the tie.
    • ORDER: If the order of the candidates on the ballot paper has been determined by lot, then ties can be eliminated by choosing say the top candidate.
    • Random Voter Hierarchy (RVH): Randomly determine a strict ordering of the candidates and when selecting a candidate to eliminate, pick one based on this strict ordering.
      • 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.

Where IRV is used

The single-winner variant of STV is used in Australia for elections to the Federal House of Representatives, for the Legislative Assemblies ("lower houses") of all states and territories except Tasmania and the Australian Capital Territory, which use regional multi-member constituencies. It is also used for the Legislative Councils ("upper houses") of Tasmania and Victoria, although the latter will switch to the multi-member variant from 2006. The multi-member variant of STV is used to elect the Australian Senate and the Legislative Councils of New South Wales and South Australia in statewide constituencies, and of Western Australia in regional constituencies.

Ireland uses STV to elect its own parliament and its delegation to the European Parliament (by the multi-member variant), and its President (by the single-member variant). Northern Ireland also uses the multi-member variant for elections to its Assembly and for its European Parliamentary MPs. Malta uses the multi-member variant for its parliamentary elections.

In the Pacific, the single-member variant is used for the Fijian House of Representatives. Papua New Guinea has also decided to adopt it for future elections, starting in 2007. The Fijian system has been modified to allow for both "default preferences", specified by the political party or candidate, and "custom preferences", specified by the voter. Each political party or candidate ranks all other candidates according to its own preference; voters who are happy with that need only to vote for their own preferred candidate, whose preferences will automatically be transferred according to the ranking specified by the candidate. Voters who disagree with the ranking, however, may opt to rank the candidates according to their own preferences. In the 2001 election, about a third of all voters did so. The ballot paper is divided by a thick black line, with boxes above (for the default options) and below (for customized preferences).

The countries mentioned above all use STV for some or all of their municipal elections. Starting in 2004, some municipal areas in New Zealand also adopted STV to elect mayors (by the single-member variant) and councilors (by the multi-member variant). Political parties, cooperatives and other private groups also use STV and/or IRV.

The single winner version of IRV is also used to select the winning bid of both the Summer and Winter Olympics in the International Olympic Committee.

See Table of voting systems by nation

Adoption in the United States

Suggested by a recent version of Robert's Rules of Order, instant-runoff voting is increasingly used in the United States for non-governmental elections, including student elections at many major universities.

Notable supporters include Republican U.S. Senator John McCain and 2004 Democratic presidential primary election candidates Howard Dean and Dennis Kucinich. The system is favored by many third parties, most notably the Green Party and the United States Libertarian Party|Libertarian Party, as a solution to the "spoiler" effect third-party sympathizers suffer from under plurality voting (i.e., voters are forced to vote tactically to defeat the candidate they most dislike, rather than for their own preferred candidate). In order to increase awareness of the voting method and to demonstrate it in a real-world situation, the Independence Party of Minnesota tested IRV by using it in a straw poll during the 2004 Minnesota caucuses (results favored John Edwards).

This dilemma rose to attention in the United States in the U.S. 2000 presidential election. Supporters of Ralph Nader who nevertheless preferred Democrat Al Gore to Republican George W. Bush found themselves caught in a dilemma. They could vote for Nader, and risk Gore losing to Bush, or, they could vote for Gore, just to make sure that Bush is defeated. It has been argued that Bush won largely due to the "spoiler effect" of Nader supporters in Florida.

In March 2002, an initiative backed by the Center for Voting and Democracy passed by referendum making instant runoff voting the means of electing local candidates in San Francisco. It was first used in that city in Fall of 2004. (Note: The San Francisco Department of Elections prefers 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.") Although polls showed voters generally understood and liked the new voting system, certain software and logistical difficulties delayed the election results for several days (the 'first-round' results were available the next day).

In September 2003, an amendment to the California State Constitution was proposed (SCA 14) with wide-ranging goals of election reform, including ranked-choice voting for statewide offices.

The voters in the city of Ferndale, Michigan, a Detroit suburb, amended their city charter in 2004 to allow for election of the mayor and city council by instant runoff voting.

Washington State has an initiative seeking ballot access in 2005 (I-318) that would change the state primary system to IRV.

Assessing IRV

Comparison of IRV to normal runoff voting

Advantages of instant runoff ballot (IRV) vs. normal runoff voting

  • FEWER GAMES: Voters and parties have less opportunity for playing games in early round(s) to influence the elimination order in favor of easier competition. (Runoffs allow more flexibility in tactical votes, influencing elimination, and still having a chance to move back to a favorite in the final round)
  • MORE POSITIVE: Candidates are discouraged from negative campaigning. (A winning candidate will usually need first, second and lower ranked preferences to win, and can't safely afford to make enemies with no second chance vote)

Advantages to normal runoff voting vs. IRV

  • EASIER TO VOTE: A runoff allows voters and factions to refocus their attention on remaining candidates in each round. (In IRV, voters must make careful choices among a large set of candidates in one ballot and may not have enough information to make informed rankings among the competitive candidates.)
  • CHANCE FOR APPEAL: Candidates that were eliminated are given another chance to endorse and remaining candidates have another chance to court voters supporting the eliminated candidates.

Effect on parties and candidates

Unlike runoff voting, however, there are no chances to deal in between rounds, change voters' minds, or gain support of the other candidates.

Giving them only one chance to do so, instant runoff preference voting encourages candidates to balance earning core support through winning first choice support and earning broad support through winning the second and third preferences of other candidates' core supporters. As with any winner-take-all voting system, however, any bloc of more than half the voters can elect a candidate regardless of the opinion of the rest of the voters.

This is considered a weakness by the advocates of a more deliberative democracy, who point to the French system of presidential election where such between-round dealings are heavily exploited and useful (they say) to draw together a very factionalized electorate. However, critics of the French runoff system point to the dreaded "votez escroc, pas facho" (vote for the crook, not the fascist) phenomenon, which awarded Chirac an undeserved landslide victory in 2002.

The Australian system also allows minority parties to have key planks of their platforms included in those of the major parties by means of so-called "preference deals". This is seen as legitimate political activity. If enough people care about (for instance) green party issues that that party's second preference can swing the vote, then it is fair enough that it have some limited say in policy.

Another advantage of runoff voting is that it allows a "protest vote" to be made without penalty. A person voting for a minority party doers not "throw their vote away", as with first-past-the-post systems, so allowing the electorate to send clear signals to the major parties.

Flaws of IRV

IRV meets few of the formal voting system criteria defined by political scientists for assessment of voting systems. Although the Gibbard-Satterthwaite theorem shows that all reasonable voting systems allow for some form of tactical voting, the scope and impact of tactical voting varies a great deal for different systems.

IRV is unusual in that it does not satisfy the monotonicity criterion —in some situations, if a voter or group of voters decides to rank a preferred candidate lower, it can result in that candidate winning the election, whereas if they had ranked the candidate higher, according to their sincere preference, that candidate would not have won.

These theoretical objections correspond with several serious practical 'failure modes' for IRV, discussed below. The first two, compromise and push-over, are common forms of tactical voting, where voters must change their preferred ranking of candidates to increase the likelihood of a favored outcome. Traditional plurality elections are also vulnerable to 'compromise' tactical voting. The other failure modes are more specific to IRV.

It should be noted that Condorcet methods can avoid the Return of the '3rd-party spoiler effect' and Failure to pick a good compromise problems.


Assume the earlier Tennessee example. If the voters from Memphis suspect that they do not comprise half of the voters and that Memphis is the last choice of all other voters, they can "compromise" by ranking Nashville over Memphis, and thus ensure that Nashville, their second choice, will win, rather than Knoxville, their last choice.

Alternatively, if the voters from Memphis are unlikely to vote tactically (because they think they have a chance of winning outright or for any other reasons), voters from Nashville can improve their result by "compromising" and ranking Chattanooga over Nashville. This would allow Chattanooga to defeat Knoxville in the first round and go on to become eventual winner, a better result for Nashville voters than a Knoxville win.


Tactical voters can intentionally promote "push-overs", candidates unlikely to win, past their real preference. This can sometimes benefit voters by bringing their preferred candidate to a more winnable final runoff round, basically using the push-overs as a shield for protection of their primary vote.

Return of the '3rd-party spoiler effect'

main article: Favorite betrayal criterion

IRV only stops the '3rd-party spoiler effect' as long as the 3rd party clearly does not have a chance to win. Just when the 3rd party grows to a competitive size, voters may start to find again that they benefit from tactically ranking a major party candidate over their favorite candidate.

This failure mode occurs if the voter fears that their 1st-choice candidate (the 3rd party) might first win from his best-liked major party, then not get enough of the redistributed votes, and finally almost certainly lose to the other major party. The voter would wind up with his least-favored outcome. The voter may seek to prevent this by ranking the best-liked major party over their actual first choice.

This problem is known as "favorite betrayal". A video which explains this problem more is "How our voting system (and IRV) betrays your favourite candidate" by Dr. Andy Jennings at Center for Election Science, and an overall summary of Favorite betrayal criterion can be found on this wiki.

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.

Voting turnout would resemble the following:

38% of voters 38% of voters 11% of voters 13% of voters
1. A 1. B 1. C 1. C
2. C 2. C 2. A 2. B
3. B 3. A 3. B 3. A

In IRV, the compromise (choice C) is eliminated immediately. Choice B is elected, giving severely lower total satisfaction among voters than choice C.

Failure to count the ballots in a way most favorable to the voters

26% of voters 25% of voters 49% of voters
1. A 1. C 1. D
2. B 2. B

Here, a majority is split between two candidates as their 1st choice, but can unanimously agree on a third candidate as their 2nd choice. IRV instantly eliminates the majority's 2nd choice for having no 1st choice votes, then eliminates C, and then elects D. Yet a majority of voters preferred a different outcome.

Logistical issues

Ballots in IRV cannot be easily summarized.[fn 1] (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.

If counting takes place in several places for a single IRV election (as in Australia), these counting centers must be connected by a securely authenticated channel (historically the telegraph was used) to inform them which candidate has come last and should be dropped. Centralizing the counting to avoid this problem can add opportunity for tampering.

Logistical issues in Australia

House of Representatives

Initially, in Australia, ballots are counted at the booth level, with first preference results reported to the Divisional Returning officer and then to the National Tally Room. If it is clear who the two leading candidates will be, a notional distribution of the preferences of the minor candidates may be made. Postal and absentee ballots are of course yet to be processed - that takes another week or two.

Over the next few weeks, ballots and matching documentation are concentrated in the offices of the Divisional Returning Officer, where an actual distribution of preferences is made. This may be done by physically moving the ballots around, or by entering ballot data into a suitable computer.

If a candidate wins 51% of first preferences, a distribution of minor party preferences is strictly speaking not necessary, however the law now allows that such preferences be distributed to see what the "two-party preferred vote" actually is.

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.


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 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 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.


IRV can rather simply be thought of as a modification to choose-one FPTP voting to pass the mutual majority criterion (and further, always elect from the 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 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 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.[4]

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 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 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 a lower bound on the number of votes they receive in a pairwise matchup against all other candidates who are uneliminated during that round. This is because it is guaranteed that the candidate who a voter's vote is supporting in any round was ranked higher than any of the other uneliminated candidates by that voter, since at every point in IRV a voter's ballot is transferred to their highest-ranked candidate among the uneliminated candidates, thus that candidate receives that voter's vote in all pairwise matchups against those lower-ranked candidates. This means that when the IRV winner receives a majority of active votes, they guaranteeably pairwise beat all other uneliminated candidates, and that when there are only two candidates remaining, the number of votes each candidate has is exactly the number of votes they each receive in their pairwise matchup (if equal ranking is allowed, the exact number of votes may differ; for example:

40 A

40 B

20 A=B

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:

45 A>B>C

35 B>A>C

20 C>B>A

B is a Condorcet winner with over 1/3rd of 1st choice votes, so they're guaranteed to win in IRV. But if the sneaky A-top voters vote:

45 A=C>B

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.[5]

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 variations of IRV have been proposed to meet the Condorcet and Smith criteria. The simplest of these are to either (elect the Condorcet winner if one exists), or (eliminate all candidates not in the 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 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.):

Rankings of the candidates
Number of voters to the right

Candidates below

2 4 5 5 6
A 5 1 3 2 3
B 2 5 4 5 1
C 4 3 1 3 4
D 3 2 2 1 2
E 1 4 5 4 5

This can be converted into:

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 E A C D B
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:

Rankings of the candidates
Number of votes for each candidate: 8 4 5 5
Number of voters to the right

Rankings below

2 6 4 5 5
1st B B A C D
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:

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 0 (5 - 5) 0 (6 - 6)
1st B D C D B
2nd D C D C D
3rd C B B B C

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:

Rankings of the candidates
Number of votes for each candidate: 8 14
Number of voters to the right

Rankings below

8 (2 + 6) 14 (4 + 5 + 5) 0 (5 - 5) 0 (5 - 5) 0 (6 - 6)
1st B D D D B
2nd D B B B D

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" 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:

Pairwise counting matrix
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:

Pairwise counting matrix
B --- 8 (-6 Loss) 8 (-6 Loss)
C 14 (+6 Win) --- 5 (-12 Loss)
D 14 (+6 Win) 17 (+12 Win) ---

D 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.


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[6] 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 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.


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".[7]

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",[8] which included the following caveat:

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.

In 1997, FairVote began referring to preferential voting as "Instant Runoff voting".[9][10] However, the city of San Francisco preferred the term "ranked-choice voting", which was used as early as 1999.[11][12] By 2004, San Francisco was careful to explain that the method codified as "ranked choice voting" was the same as "instant runoff voting.[1] Because organizations in Arizona borrowed San Francisco's language, many used "ranked choice" as the preferred wording, which FairVote accommodated as early as 2006.[13] FairVote didn't appear to publicly deprecate the term "instant runoff voting" until 2013,[14] 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


  1. IRV can be summarized in space by keeping a FPTP count for every possible selection of eliminated candidates, but this is not useful in practice.


  1. a b As described on a 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."
  2. Ware, William R. (1871). Application of Mr. Hare's system of voting to the nomination of overseers of Harvard College. OCLC 81791186. It is equally efficient whether one candidate is to be chosen, or a dozen.
  3. Benjamin Reilly. "The Global Spread of Preferential Voting: Australian Institutional Imperialism" (PDF). Retrieved 17 April 2011.
  4. Green-Armytage, J. "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF).
  6. [1]
  7. Anderson, John B. (1992-07-24). "Opinion | Break the Political Stranglehold". The New York Times. ISSN 0362-4331. Retrieved 2020-04-30.
  9. "Fuller, Fairer Elections? How?". Christian Science Monitor. 1997-07-21. ISSN 0882-7729. Retrieved 2019-12-14.
  10. From 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")."
  11. San Francisco Charter Amendment, introduced October 1999 "SEC. 13.102. RANKED-CHOICE BALLOTS"
  12. 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."
  13. "FairVote and the LWV-Arizona Support Ranked Choice Voting" Dr. Barbara Klein and Rob Richie
  14. The July 2013 homepage of was the first to refer to "ranked choice voting" as a preferred term to "instant-runoff"

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