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Instant-runoff voting (IRV) (US: ranked-choice voting (RCV), AU: preferential voting, UK: alternative vote) is a single-winner, multi-round elimination rule that uses ranked voting to simulate a series of runoffs with only one vote. In each round, the candidate with the fewest votes counting towards them is eliminated, and the votes are transferred to their next available preference until one of the options reaches a majority of the remaining votes. Instant runoff falls under the plurality-with-elimination family of voting methods,^[1] and is thus closely related to rules like the exhaustive ballot and two-round runoff system.^[2]^[3]

IRV has found some use in national elections in several countries, predominantly in the Anglosphere. It is used to elect members of the Australian House of Representatives and the National Parliament of Papua New Guinea as well as the President of India, the President of Ireland, and the President of Sri Lanka.

The rule was first developed and studied by the Marquis de Condorcet, who came to reject it after discovering it could eliminate the majority-preferred candidate in a race (today often called a Condorcet winner).^[4]^[5]^[6] IRV is known to exhibit other mathematical pathologies, which include non-monotonicity^[7] and the no-show paradox.^[8]^[9] Like some other commonly-used systems, IRV also exhibits a kind of independence of irrelevant alternative violation called a center squeeze,^[10]^[11] which may sometimes prevent the election of a Condorcet winner. Whilst the Marquis de Condorcet early on showed that it did not satisfy his Condorcet winner criterion, which it may fail under certain scenarios, instant-runoff voting satisfies many other majoritarian criteria, such as the majority criterion, mutual majority criterion and the Condorcet loser criterion.

Advocates have argued these properties are positive, because voting rules should encourage candidates to focus on their core support or political base, rather than building a broad coalition.^[12] They also note that in countries like the United Kingdom without primaries or runoff elections, IRV can prevent spoiler effects by eliminating minor-party candidates in early rounds, and that unlike plurality, it is not affected by the presence of duplicate candidates (clones).

Election procedure

In instant-runoff voting, as with other ranked voting rules, each voter orders candidates from first to last. The counting procedure is then as follows:

If there is a candidate that has a majority of the top preferences of the valid, active ballots, then that candidate is elected and the count stops. If not, go to step 2.
If there is more than one candidate left, eliminate the one with the fewest top preferences.^[a]
Reassign votes held by the eliminated candidate(s) to the highest available preference indicated on each ballot paper (setting aside any with no remaining preferences). Return to Step 1.

It is possible for a candidate to win an instant-runoff race without any support from more than half of voters, even when there is an alternative majority-approved candidate; this occurs when some voters truncate their ballots to show they do not support any candidates in the final round.^[13] In practice, candidates who do not receive a majority of votes in the first round usually do not finish with a majority.^[14]

Properties

Wasted votes and Condorcet winners

Compared to a plurality voting system that rewards only the top vote-getter, instant-runoff voting mitigates the problem of wasted votes.^[15] However, it does not ensure the election of a Condorcet winner, which is the candidate who would win a direct election against any other candidate in the race.

Invalid, incomplete and exhausted ballots

All forms of ranked-choice voting reduce to plurality when all ballots rank only one candidate. By extension, ballots for which all candidates ranked are eliminated are equivalent to votes for any non-winner in plurality, and considered exhausted ballots.

Some political scientists have found the system contributes to higher rates of spoiled votes,^[16] partly because the ballot marking is more complex.^[16]^[14] Most jurisdictions with IRV do not require complete rankings and may use columns to indicate preference instead of numbers. In American elections with IRV, more than 99 percent of voters typically cast a valid ballot.^[17]

A 2015 study of four local US elections that used IRV found that inactive ballots occurred often enough in each of them that the winner of each election did not receive a majority of votes cast in the first round. The rate of inactive ballots in each election ranged from a low of 9.6 percent to a high of 27.1 percent.^[18]

Resistance to strategy

Instant-runoff voting has notably high resistance to tactical voting but less to strategic nomination.

Party strategizing and strategic nomination

In Australia, preference deals (where one party's voters agree to place another party's voters second, in return for their doing the same) between parties are common. Parties and candidates often encourage their supporters to participate in these preference deals using How-to-vote cards explaining how to use their lower rankings to maximize the chances of their ballot helping to elect someone in the preference deal before it may exhaust.^[19]

Instant runoff may be manipulable via strategic candidate entry and exit, reducing similar candidates' chances of winning. Such manipulation does not need to be intentional, instead acting to deter candidates from running in the first place.^[20] Spatial model simulations indicate that instant runoff rewards strategic withdrawal by candidates.^[21]^[b]

Tactical voting

Gibbard's theorem demonstrates that no (deterministic, non-dictatorial) voting method can be entirely immune from tactical voting. This implies that IRV is susceptible to tactical voting in some circumstances. In particular, when there exists a Condorcet winner who IRV fails to elect, voters who prefer the Condorcet winner to the IRV winner have an incentive to use the compromising strategy.^[21]^{: proposition 17} IRV is also sometimes vulnerable to a paradoxical strategy of ranking a candidate higher to make them lose, due to IRV failing the monotonicity criterion.^[22]

Research suggests that IRV is very resistant to tactical voting. In a test of multiple methods, instant runoff was found to be the second-most-resistant to tactical voting, after a class of instant runoff-Condorcet hybrids.^[23] IRV is also completely immune to the burying strategy: ranking a strong opposition candidate lower can't get one's preferred candidate elected.^[21]^{: proposition 3}

Tactical voting in IRV seeks to alter the order of eliminations in early rounds, to ensure that the original winner is challenged by a stronger opponent in the final round. For example, in a three-party election where voters for both the left and right prefer the centrist candidate to stop the opposing candidate from winning, those voters who care more about defeating the opposition than electing their own candidate may cast a tactical first-preference vote for the centrist candidate.

Spoiler effect

Proponents of IRV claim that IRV eliminates the spoiler effect, since IRV makes it safe to vote honestly for marginal parties. Under a plurality method, voters who sympathize most strongly with a marginal candidate are strongly encouraged to instead vote for a more popular candidate who shares some of the same principles, since that candidate has a much greater chance of being elected and a vote for the marginal candidate will not result in the marginal candidate's election. An IRV method reduces this problem, since the voter can rank the marginal candidate first and the mainstream candidate second; in the likely event that the fringe candidate is eliminated, the vote is not wasted but is transferred to the second preference.

However, when the third-party candidate is more competitive, they can still act as a spoiler under IRV,^[24]^[25]^[26] by taking away first-choice votes from the more mainstream candidate until that candidate is eliminated, and then that candidate's second-choice votes helping a more-disliked candidate to win. In these scenarios, it would have been better for the third party voters if their candidate had not run at all (spoiler effect), or if they had voted dishonestly, ranking their favourite second rather than first (favorite betrayal).^[27]^{[better source needed]} This is the same bracketing effect exploited by Robinette and Tideman in their research on strategic campaigning, where a candidate alters their campaign to cause a change in voter honest choice, resulting in the elimination of a candidate who nevertheless remains more preferred by voters.

For example, in the 2009 Burlington, Vermont, mayoral election, if the Republican candidate who lost in the final instant runoff had not run, the Democratic candidate would have defeated the winning Progressive candidate. In that sense, the Republican candidate was a spoiler—albeit for an opposing Democrat, rather than some political ally—even though leading in first choice support.^[26] This also occurred in the 2022 Alaska's at-large congressional district special election. If Republican Sarah Palin, who lost in the final instant runoff, had not run, the more centrist Republican candidate, Nick Begich, would have defeated the winning Democratic candidate, Mary Peltola.^[28]

Reception

The system has had a mixed reception among political scientists and social choice theorists.^[29]^[30] Some have suggested that the system does not do much to decrease the impact of wasted votes relative to plurality.^[31]^[16]^[32] Research has found IRV causes lower confidence in elections^[33]^[34]^[35] and does not substantially affect minority representation,^[36] voter turnout,^[29]^[32] or long-run electoral competition.^[29]^[36] Opponents have also noted a high rate of repeals for the system.^[34]

Voter confusion and legitimacy

Governor Paul LePage^[37] and Representative Bruce Poliquin^[38] claimed, ahead of the 2018 primary elections, that IRV would result in "one person, five votes", as opposed to "one person, one vote". Federal judge Lance Walker rejected these claims, and the 1st circuit court denied Poliquin's emergency appeal.^[39]

Similarity to plurality

Often instant-runoff voting elections are won by the candidate who leads in first-count vote tallies so they choose the same winner as first-past-the-post voting would have. In Australia federal elections, the 1972 election had the largest number of winners who would not have won under first past the post but still only 14 out of 125 seats filled were not won by the first-count leader.^[40]

Participation

The effect of IRV on voter turnout is difficult to assess. In a 2021 report, researchers at New America, a think tank based in Washington, D. C., said it may increase turnout by attracting more and more diverse candidates, but the impact would be realized most significantly by getting rid of the need for primaries.^[41] The overall impact on diversity of candidates is difficult to detect.^[29]

Terminology

While instant run-off voting is distinguished from its multiple winner equivalent, the single transferable vote, in most English-speaking discussion of electoral systems, no distinction between the two is made in Ireland, one of the few countries to use these systems in all elections, either by the general population or in legal texts. The Constitution of Ireland describes the electoral system as "proportional representation by means of the single transferable vote"^[42], as do all other statutory authorities, when referring to either single-winner or multiple-winner elections. The acronym "PR-STV" is in general use to describe both types of elections. Examples of single-winner elections in Ireland which are described officially as "proportional representation by means of the single transferable vote" are the election of the President and the election of the Ceann Comhairle (chairperson of Dáil Éireann). The lack of distinction between the systems in Ireland reflects that there is no difference in the mechanics of the process from election to election, only the number of candidates to be elected by that process. This is not always the case when discussing the systems in the abstract, as there are many variations in how such elections could be run.

Instant-runoff voting derives its name from the way the ballot count simulates a series of runoffs, similar to an exhaustive ballot system, except that voters do not need to turn out several times to vote.^[43] It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting (but use of some of those terms may lead to misunderstanding as they also apply to STV.)^[44]

Britons and New Zealanders generally call IRV the "alternative vote" (AV).^[45]^[46] Australians, who use IRV for most single winner elections, call IRV "preferential voting".^[47] While this term is widely used by Australians, it is somewhat of a misnomer. Depending on how "preferential" is defined, the term would include all voting systems, apply to any system that uses ranked ballots (thus both IRV and STV), or would exclude IRV (IRV fails positive responsiveness because ballot markings are not interpreted as "preferences" in the traditional sense. Under IRV (and STV), secondary preferences are used as back-up preferences/contingency votes).

Jurisdictions in the United States such as San Francisco, Minneapolis, Maine, and Alaska have tended to use the term "ranked-choice voting" in their laws that apply to IRV contests. The San Francisco Department of Elections claimed the word "instant" in the term "instant-runoff voting" could confuse voters into expecting results to be immediately available.^[48]^[49] As a result of American influence, the term ranked-choice voting is often used in Canada as well.^[50] American NGO FairVote has promoted the terminology "ranked-choice voting" to refer to IRV,^[50]^[51] a choice that has caused controversy and accusations that the organization is attempting to obscure the existence of other ranked-choice methods that could compete with IRV.^{[citation needed]}

IRV is occasionally referred to as Hare's method^[52] (after Thomas Hare) to differentiate it from other ranked-choice voting methods such as majority-choice voting, Borda, and Bucklin, which use weighted preferences or methods that allow voter's lower preference to be used against voter's most-preferred choice.

When the single transferable vote (STV) method is applied to a single-winner election, it becomes IRV; the government of Ireland has called IRV "proportional representation" based on the fact that the same ballot form is used to elect its president by IRV and parliamentary seats by proportional representation (STV), but IRV is a non-proportional winner-take-all (single-winner) election method, while STV elects multiple winners.^[53]

State law in South Carolina^[54] and Arkansas^[55] use "instant runoff" to describe the practice of having certain categories of absentee voters cast ranked-choice ballots before the first round of an election and counting those ballots in any subsequent runoff elections.

History and use

History

This method was first discussed by the Marquis de Condorcet in 1788, who quickly rejected it after showing it would often eliminate a candidate preferred by a majority of voters.^[5]^[56]

IRV was later independently reinvented by Thomas Hare (of England) and Carl Andrae (of Denmark) in the form of the single transferable vote. Henry Richmond Droop then proposed applying the system to single-winner contests. (He also invented the Droop quota, which equates to a simple majority in a single-winner contest.)

Global use

National level elections

Country	Body or office	Type of body or office	Electoral system	Total seats
Australia	House of Representatives	Lower chamber of legislature	IRV	151
Ireland	President	Head of State	IRV
Ireland	Dáil Éireann	Lower chamber of legislature	Single transferable vote (STV), by-elections using IRV	158^[57]
Papua New Guinea	National Parliament	Unicameral legislature	IRV	109
United States	President (via Electoral College)	Head of State and Government	Alaska and Maine use IRV to select the state's electoral college seat winner or winners. In Maine, 2 electors are allocated to the winner of the state vote plurality and the others (currently 2) are allocated by plurality in each congressional district. In Alaska, the winner gets all Electoral College electors of the state (as Alaska has only one at-large district, the effect is the same).	7 EVs^[58] (out of 538)
	House of Representatives	Lower chamber of legislature	IRV in Maine Nonpartisan primary system with IRV in the second round (among top four candidates) in Alaska.^[59]^[60]^[61]^[62]	3 (out of 435)
	Senate	Upper chamber of legislature		4 (out of 100)

Robert's Rules of Order

In the United States, the sequential elimination method used by IRV is described in Robert's Rules of Order Newly Revised as an example of ranked-choice voting that can be used to elect officers.^[63] Robert's Rules note that ranked-choice systems (including IRV) are an improvement on simple plurality but recommend against runoff-based rules because they often prevent the emergence of a consensus candidate with broad support. The book instead recommends repeated balloting until some candidate manages to win a majority of votes. Two other books on American parliamentary procedure, The Standard Code of Parliamentary Procedure^[64] and Riddick's Rules of Procedure,^[65] take a similar stance.

Similar methods

Runoff voting

The term instant-runoff voting is derived from the name of a class of voting methods called runoff voting. In runoff voting voters do not rank candidates in order of preference on a single ballot. Instead a similar effect is achieved by using multiple rounds of voting. All multi-round runoff voting methods allow voters to change their preferences in each round, incorporating the results of the prior round to influence their decision, which is not possible in IRV.

The runoff method closest to IRV is the exhaustive ballot. In this method—familiar to fans of the television show American Idol—one candidate is eliminated after each round, and many rounds of voting are used, rather than just two. Because holding many rounds of voting on separate days is generally expensive, the exhaustive ballot is not used for large-scale, public elections.

A more practical form of runoff voting is the two-round system, which excludes all but the top-two candidates after the first round, rather than gradually eliminating candidates over a series of rounds. Eliminations can occur with or without allowing and applying preference votes to choose the final two candidates. A second round of voting or counting is only necessary if no candidate receives an overall majority of votes. This method is used in Mali, France and the Finnish and Slovenian presidential election.

Contingent vote

The contingent vote, also known as "top-two IRV", is the same as IRV, except that if no candidate achieves a majority in the first round of counting, all but the two candidates with the most votes are eliminated, and the second preferences for those ballots are counted. As in IRV, there is only one round of voting.

Under a variant of contingent voting used in Sri Lanka, and formerly for the elections for Mayor of London in the United Kingdom, voters rank a specified maximum number of candidates. In London, the supplementary vote allowed^[c] voters to express first and second preferences only. Sri Lankan voters rank up to three candidates to elect the president of Sri Lanka.

While similar to "sequential-elimination" IRV, top-two can produce different results. Excluding more than one candidate after the first count might eliminate a candidate who would have won under sequential elimination IRV. Restricting voters to a maximum number of preferences is more likely to exhaust ballots if voters do not anticipate which candidates will finish in the top two. This can encourage voters to vote more tactically, by ranking at least one candidate they think is likely to win.

Conversely, a practical benefit of 'contingent voting' is expediency and confidence in the result with only two rounds.

Larger runoff process

IRV may also be part of a larger runoff process:

Some jurisdictions that hold runoff elections allow absentee (only) voters to submit IRV ballots, because the interval between votes is too short for a second round of absentee voting. IRV ballots enable absentee votes to count in the second (general) election round if their first choice does not make the runoff. Arkansas, South Carolina and Springfield, Illinois adopt this approach.^[66] Louisiana uses it only for members of the United States Service or who reside overseas.^[67]^{[better source needed]}^{[needs update]}
IRV can quickly eliminate weak candidates in early rounds of an exhaustive ballot runoff, using rules to leave the desired number of candidates for further balloting.
IRV elections that require a majority of cast ballots but not that voters rank all candidates may require more than a single IRV ballot due to exhausted ballots.
Robert's Rules recommends preferential voting for elections by mail and requiring a majority of cast votes to elect a winner. For in-person elections, they recommend repeated balloting until one candidate receives an absolute majority of all votes cast; if candidates drop out as soon as it becomes clear they cannot win, this procedure will always elect a Condorcet winner. The use of repeated balloting allows voters to resolve Condorcet cycles by discussion and compromise, or by electing a consensus candidate who might have polled poorly in the initial election.^[63]

Comparison to first-past-the-post

In the Australian federal election in September 2013, 135 out of the 150 House of Representatives seats (or 90 percent) were won by the candidate who led on first preferences. The other 15 seats (10 percent) were won by the candidate who placed second on first preferences.^[68]^{[better source needed]}

Variations

Example of a full preferential ballot paper from the Australian House of Representatives

A number of IRV methods, varying as to ballot design and as to whether or not voters are obliged to provide a full list of preferences, are in use in different countries and local governments.

In an optional preferential voting system, voters can give a preference to as many candidates as they wish. They may make only a single choice, known as "bullet voting", and some jurisdictions accept a single box marked with an "X" (as opposed to a numeral "1") as valid for the first preference. This may result in exhausted ballots, where all of a voter's preferences are eliminated before a candidate is elected, such that the "majority" in the final round may only constitute a minority fraction of all ballots cast. Optional preferential voting is used for elections for the President of Ireland as well as some elections in New South Wales and Queensland.^[69]^[70]

In a full-preferential voting method, voters are required to mark a preference for every candidate standing.^[71] Ballots that do not contain a complete ordering of all candidates are in some jurisdictions considered spoilt or invalid, even if there are only two candidates standing. This can become burdensome in elections with many candidates and can lead to "donkey voting", in which some voters simply choose candidates at random or in top-to-bottom order, or a voter may order his or her preferred candidates and then fill in the remainder on a donkey basis. Full preferential voting is used for elections to the Australian federal parliament and for most state parliaments.

Other methods only allow marking preferences for a maximum of the voter's top three favourites, a form of partial preferential voting.^[72]

A version of instant-runoff voting applying to the ranking of parties was first proposed for elections in Germany in 2013^[73] as spare vote.^{[citation needed]}

Voting method criteria

As shown by Arrow, Gibbard, and others, it's usually impossible for a method to pass all of a number of seemingly reasonable properties, or criteria, at once. IRV is no exception: it passes some and fails others. The following criteria are satisfied and failed by IRV:

Satisfied criteria

Condorcet loser Criterion

The Condorcet loser criterion states that "if a candidate would lose a head-to-head competition against every other candidate, then that candidate must not win the overall election". IRV (like all voting methods with a final runoff round) meets this criterion, since the Condorcet loser cannot win a runoff.

Independence of clones criterion

The independence of clones criterion states that "the election outcome remains the same even if an identical candidate who is equally preferred decides to run". Advocates have noted that IRV meeting this criterion^[74]^[75] greatly reduces the impact of clones compared to FPTP.

Later-no-harm criterion

The later-no-harm criterion states that "if a voter alters the order of candidates lower in his/her preference (e.g. swapping the second and third preferences), then that does not affect the chances of the most preferred candidate being elected". Instant runoff satisfies this criterion.

Majority criterion

The majority criterion states that "if one candidate is preferred by an absolute majority of voters, then that candidate must win". Instant runoff also satisfies this criterion.

Mutual majority criterion

The mutual majority criterion states that "if an absolute majority of voters prefer every member of a group of candidates to every candidate not in that group, then one of the preferred group must win". Note that this is satisfied because when all but one candidate that a mutual majority prefer is eliminated, the votes of the majority all flow to the remaining candidate, in contrast to FPTP, where the majority would be treated as separate small groups. Instant runoff satisfies this criterion as well.

Resolvability criterion

The resolvability criterion states that "the probability of an exact tie must diminish as more votes are cast".^{[citation needed]}

Failed criteria

Condorcet winner criterion

The Condorcet winner criterion states that "if a candidate would win a head-to-head competition against every other candidate, then that candidate must win the overall election". It is incompatible with the later-no-harm criterion, so IRV does not meet this criterion.

IRV is more likely to elect the Condorcet winner than plurality voting and traditional runoff elections. The California cities of Oakland, San Francisco and San Leandro in 2010 provide an example; there were a total of four elections in which the plurality-voting leader in first-choice rankings was defeated, and in each case the IRV winner was the Condorcet winner, including a San Francisco election in which the IRV winner was in third place in first choice rankings.

A particularly notable Condorcet failure occurred in the 2009 Burlington mayoral election.

Independence of irrelevant alternatives

The independence of irrelevant alternatives criterion states that "the election outcome remains the same even if a candidate who cannot win decides to run." Instant-runoff voting violates this. In the general case, instant-runoff voting can be susceptible to strategic nomination: whether or not a candidate decides to run at all can affect the result even if the new candidate cannot themselves win. This is less likely to happen than under plurality, but much more likely than under the Minimax Condorcet method.^[21]

Monotonicity criterion

The monotonicity criterion says that a voter ranking a candidate higher on their ballot should not cause that candidate to lose and conversely, that a voter ranking a candidate lower on their ballot should not help that candidate win. The exact probability of a monotonicity failure depends on the circumstances, but with 3 major candidates, the probabilities range from 15 percent under the impartial culture model^[76]^{: Table 6} to 8.5 percent in the case of a strict left–right spectrum.^[77]

Participation criterion

The participation criterion says that candidates should not lose as a result of having "too many voters"—a set of ballots that all rank A>B should not switch the election winner from B to A. IRV fails this criterion. In his 1984 study, mathematician Depankar Ray found that in elections where IRV elects a different candidate from plurality, that there was an estimated 50 percent probability that some voters would have gotten a more preferable outcome if they had not participated.^[9]

Reversal symmetry criterion

The reversal symmetry criterion states that the first- and last-place candidates should switch places if every ballot is reversed. In other words, it should not matter whether voters rank candidates from best-to-worst and select the best candidate, or whether they rank them worst-to-best and then select the least-bad candidate.

IRV fails this criterion: it is possible to construct an election where reversing the order of every ballot does not alter the final winner; that is, the first- and last-place finishers, according to IRV, are the same candidate.^[78]

Comparison to other voting systems

Comparison of single-winner voting systems
Criterion Method	Majority winner	Majority loser	Mutual majority	Condorcet winner^{[Tn 1]}	Condorcet loser	Smith^{[Tn 1]}	Smith-IIA^{[Tn 1]}	IIA/LIIA^{[Tn 1]}	Cloneproof	Monotone	Participation	Later-no-harm^{[Tn 1]}	Later-no-help^{[Tn 1]}	No favorite betrayal^{[Tn 1]}	Ballot type
First-past-the-post voting	Yes	No	No	No	No	No	No	No	No	Yes	Yes	Yes	Yes	No	Single mark
Anti-plurality	No	Yes	No	No	No	No	No	No	No	Yes	Yes	No	No	Yes	Single mark
Two round system	Yes	Yes	No	No	Yes	No	No	No	No	No	No	Yes	Yes	No	Single mark
Instant-runoff	Yes	Yes	Yes	No	Yes	No	No	No	Yes	No	No	Yes	Yes	No	Ranking
Coombs	Yes	Yes	Yes	No	Yes	No	No	No	No	No	No	No	No	Yes	Ranking
Nanson	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	Ranking
Baldwin	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	Ranking
Tideman alternative	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	No	No	No	No	No	Ranking
Minimax	Yes	No	No	Yes^{[Tn 2]}	No	No	No	No	No	Yes	No	No^{[Tn 2]}	No	No	Ranking
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	No	No	No	Ranking
Black	Yes	Yes	No	Yes	Yes	No	No	No	No	Yes	No	No	No	No	Ranking
Kemeny–Young	Yes	Yes	Yes	Yes	Yes	Yes	Yes	LIIA Only	No	Yes	No	No	No	No	Ranking
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	LIIA Only	Yes	Yes	No^{[Tn 3]}	No	No	No	Ranking
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No^{[Tn 3]}	No	No	No	Ranking
Borda	No	Yes	No	No	Yes	No	No	No	No	Yes	Yes	No	Yes	No	Ranking
Bucklin	Yes	Yes	Yes	No	No	No	No	No	No	Yes	No	No	Yes	No	Ranking
Approval	Yes	No	No	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	Yes	No	Yes	Yes	Approvals
Majority Judgement	No	No^{[Tn 5]}	No^{[Tn 6]}	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	No^{[Tn 3]}	No	Yes	Yes	Scores
Score	No	No	No	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	Yes	No	Yes	Yes	Scores
STAR	No	Yes	No	No	Yes	No	No	No	No	Yes	No	No	No	No	Scores
Random ballot^{[Tn 7]}	No	No	No	No	No	No	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Single mark
Sortition^{[Tn 8]}	No	No	No	No	No	No	No	Yes	No	Yes	Yes	Yes	Yes	Yes	None
Table Notes	^ ^a ^b ^c ^d ^e ^f ^g Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. ^ ^a ^b A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. ^ ^a ^b ^c In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. ^ ^a ^b ^c Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. ^ Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters. ^ Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade. ^ A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria. ^ Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

Examples

The first example is a fictional one for the purpose of demonstrating the principle of instant runoff. The other examples are drawn from the results of real-life elections.

Tennessee capital example

Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:

Memphis, the largest city, but far from the others (42% of voters)
Nashville, near the center of the state (26% of voters)
Chattanooga, somewhat east (15% of voters)
Knoxville, far to the northeast (17% of voters)

The preferences of each region's voters are:

42% of voters Far-West	26% of voters Center	15% of voters Center-East	17% of voters Far-East
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

It takes three rounds to determine a winner in this election.

Round 1 – In the first round no city gets a majority:

Votes in round/ City Choice	1st
Memphis	42%
Nashville	26%
Knoxville	17%
Chattanooga	15%

If one of the cities had achieved a majority vote (more than half), the election would end there. If this were a first-past-the-post election, Memphis would win because it received the most votes. But IRV does not allow a candidate to win on the first round without having an absolute majority of the active votes. Since no city has won yet, the city with the least first-place support (Chattanooga) is eliminated from consideration. The ballots that listed Chattanooga as first choice are added to the totals of the second-choice selection on each ballot.

Round 2 – In the second round of tabulation, Chattanooga's 15% of the total votes have been added to the second choices selected by the voters for whom that city was first-choice (in this example Knoxville):

Votes in round/ City Choice	1st	2nd
Memphis	42%	42%
Nashville	26%	26%
Knoxville	17%	32%
Chattanooga	15%

In the first round, Memphis was first, Nashville was second and Knoxville was third. With Chattanooga eliminated and its votes redistributed, the second round finds Memphis still in first place, followed by Knoxville in second and Nashville has moved down to third place. No city yet has secured a majority of votes, so the now last placed Nashville is eliminated and the ballots currently counting for Nashville are added to the totals of Memphis or Knoxville based on which city is ranked next on that ballot.

Round 3

As Memphis and Knoxville are the only two cities remaining in the contest, this round will be the final round. In this example the second-choice of the Nashville voters is Chattanooga, which is already eliminated. Therefore, the votes are added to their third-choice: Knoxville. The third round of tabulation yields the following result:

Votes in round/ City Choice	1st	2nd	3rd
Memphis	42%	42%	42%
Nashville	26%	26%
Knoxville	17%	32%	58%
Chattanooga	15%

Result: Knoxville, which was running third in the first tabulation, has moved up from behind to take first place in the third and final round. The winner of the election is Knoxville. However, if 6% of voters in Memphis were to put Nashville first, the winner would be Nashville, a preferable outcome for voters in Memphis. This is an example of potential tactical voting, though one that would be difficult for voters to carry out in practice. Also, if 17% of voters in Memphis were to stay away from voting, the winner would be Nashville. This is an example of IRV failing the participation criterion.

For comparison, note that traditional first-past-the-post voting would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city. As Nashville is a Condorcet winner, Condorcet methods would elect Nashville. A two-round method would have a runoff between Memphis and Nashville where Nashville would win, too.

1990 Irish presidential election

The 1990 Irish presidential election provides a simple example of how instant-runoff voting can produce a different result from first-past-the-post voting and prevent some spoiler effects associated with plurality voting. The three major candidates were Brian Lenihan of Fianna Fáil, Austin Currie of Fine Gael, and Mary Robinson of the Labour Party. After the first count, Lenihan had the largest share of first-choice rankings. Currie had the fewest votes and was eliminated. After this, Robinson received 82 percent of Currie's votes, thereby overtaking Lenihan.

Irish presidential election, 1990^[79]
Candidate	Round 1		Round 2
Mary Robinson	612,265	38.9%	817,830	51.6%
Brian Lenihan	694,484	43.8%	731,273	46.2%
Austin Currie	267,902	16.9%N	Eliminated
Exhausted ballots	9,444	0.6%	34,992	2.2%
Total	1,584,095	100%	1,584,095	100%

2014 Prahran election (Victoria)

Another real-life example of IRV producing results different from first-past-the-post can be seen in the 2014 Victorian general election in Prahran. In this rare instance, the candidate who initially placed third, (Greens candidate Sam Hibbins), won the seat.^[80] In the 7th and final round, Hibbins narrowly defeated Liberal candidate Clem Newton-Brown by a margin of 277 votes.

Candidate	1st		2nd	3rd	4th	5th	6th	7th
Clem Newton-Brown (LIB)	44.8%	16,582	16,592	16,644	16,726	16,843	17,076	18,363	49.6%
Neil Pharaoh (ALP)	25.9%	9,586	9,593	9,639	9,690	9,758	9,948N	Eliminated
Sam Hibbins (GRN)	24.8%	9,160	9,171	9,218	9,310	9,403	9,979	18,640	50.4%
Eleonora Gullone (AJP)	2.3%	837	860	891	928	999N	Eliminated
Alan Walker (FFP)	0.8%	282	283	295N	Eliminated
Jason Goldsmith (IND)	0.7%	247	263	316	349N	Eliminated
Steve Stefanopoulos (IND)	0.6%	227	241N	Eliminated
Alan Menadue (IND)	0.2%	82N	Eliminated
Total	100%	37,003

2009 Burlington mayoral election

Burlington mayoral election, 2009 (round-by-round analysis of votes)
Candidates		1st round		2nd round		3rd round
Candidate	Party	Votes	±	Votes	±	Votes	±
Bob Kiss	Progressive	2585	+2585	2981	+396	4313	+1332
Kurt Wright	Republican	2951	+2951	3294	+343	4061	+767
Andy Montroll	Democrat	2063	+2063	2554	+491	0	−2554
Dan Smith	Independent	1306	+1306	0	−1306
Others		71	+71	0	−71
Exhausted		4	+4	151	+147	606	+455

Under Burlington, Vermont's second-ever IRV mayoral election in 2009, the winner, Bob Kiss, was elected over the more popular Andy Montroll as a result of a first-round spoiler effect.

FairVote touted the 2009 election as one of its major success stories,^[81] claiming it helped the city save on costs of a traditional runoff^[81]^[82] and prevented a spoiler effect,^[83] although later analysis showed that without Wright in the election, Montroll would have defeated Kiss in a one-on-one race.^[84]

Mathematicians and voting theorists criticized the election results as revealing several pathologies associated with instant-runoff voting, noting that Kiss was elected as a result of 750 votes cast against him (ranking Kiss in last place).^[85]^[86]

Several electoral reform advocates branded the election a failure after Kiss was elected, despite 54 percent of voters voting for Montroll over Kiss,^[87] violating the principle of majority rule.^[84]^[88]^[89]^[90]

Notes

^ This procedure can be sped-up by eliminating more than one candidate if their combined top preferences are less than the next-lowest remaining candidate; this process is sometimes called batch elimination. When batch elimination is used, the procedure can terminate if some candidate has a majority.
^ Figure 4 on page 137 shows instant-runoff voting having exit incentive despite being clone independent.
^ Following the Elections Act 2022, voting in mayoral elections now takes place under the first-past-the-post system.

References

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^ Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.
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^ Ellenberg, Jordan (29 May 2014). How Not to Be Wrong: The Power of Mathematical Thinking. Penguin. p. 385. ISBN 9780698163843. a majority of voters liked the centrist candidate Montroll better than Kiss, and a majority of voters liked Montroll better than Wright ... yet Montroll was tossed in the first round.
^ Stensholt, Eivind (7 October 2015). "What Happened in Burlington?". SSRN 2670462. K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner.
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External links

"Explainer: Instant runoff voting" by MIT Election Science Lab

[condorcet-iia-incompatibility-82] ^ ^a ^b ^c ^d ^e ^f ^g Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria.

[MinimaxVarient-83] A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.

[semipc-84] In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one.

[IIA_rating_methods-85] Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.

[86] Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters.

[mjmmc-87] Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade.

[88] A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria.

[89] Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

[13] This procedure can be sped-up by eliminating more than one candidate if their combined top preferences are less than the next-lowest remaining candidate; this process is sometimes called batch elimination. When batch elimination is used, the procedure can terminate if some candidate has a majority.

[ExitIncentive-23] Figure 4 on page 137 shows instant-runoff voting having exit incentive despite being clone independent.

[68] Following the Elections Act 2022, voting in mayoral elections now takes place under the first-past-the-post system.

[1] Nurmi, Hannu (June 2005). "Aggregation problems in policy evaluation: an overview". European Journal of Political Economy. 21 (2): 287–300. doi:10.1016/j.ejpoleco.2004.08.001. ISSN 0176-2680.

[2] Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.

[3] Hyman, Ross; Otis, Deb; Allen, Seamus; Dennis, Greg (1 September 2024). "A majority rule philosophy for instant runoff voting". Constitutional Political Economy. 35 (3): 425–436. doi:10.1007/s10602-024-09442-3. ISSN 1572-9966.

[:034-4] Condorcet, Jean-Antoine-Nicolas de Caritat (1788). "On the Constitution and the Functions of Provincial Assemblies". Complete Works of Condorcet (in French). Vol. 13 (published 1804). p. 243. En effet, lorsqu'il y a plus de trois concurrents, le véritable vœu de la pluralité peut être pour un candidat qui n'ait eu aucune des voix dans le premier scrutin.

[:032-5] Nanson, E. J. (1882). "Methods of election: Ware's Method". Transactions and Proceedings of the Royal Society of Victoria. 17: 206. The method was, however, mentioned by Condorcet, but only to be condemned.

[:22322323-6] Campbell, D.E.; Kelly, J.S. (2000). "A simple characterization of majority rule". Economic Theory. 15 (3): 689–700. doi:10.1007/s001990050318. JSTOR 25055296. S2CID 122290254.

[7] Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN 0092-5853. JSTOR 2110496.

[:05-8] Stensholt, Eivind (2018). "What is Wrong with IRV?". SSRN 3272186.

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[:5-93] Totten, Shay. "Burlington Residents Seek Repeal of Instant Runoff Voting". Seven Days. Retrieved 17 March 2018. We waited to bring in the signatures because we didn't want this to be about Kurt Wright losing after being ahead, or Andy Montroll who had more first and second place votes and didn't win. We wanted this to be about IRV.

[:02-94] Bouricius, Terry (17 March 2009). "Response to Faulty Analysis of Burlington IRV Election". FairVote.org. Retrieved 1 October 2017. successfully prevented the election of the candidate who would likely have won under plurality rules, but would have lost to either of the other top finishers in a runoff

[:10-95] Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". Phoenix L. Rev. 6: 117. SSRN 2276015. election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive'

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[99] Ellenberg, Jordan (29 May 2014). How Not to Be Wrong: The Power of Mathematical Thinking. Penguin. p. 385. ISBN 9780698163843. a majority of voters liked the centrist candidate Montroll better than Kiss, and a majority of voters liked Montroll better than Wright ... yet Montroll was tossed in the first round.

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