# Instant-runoff voting

Instant-runoff voting (IRV; US: ranked-choice voting (RCV), AU: preferential voting, UK/NZ: alternative vote) is a single-winner ranked voting election system where multi-round eliminations is used to simulate a series of runoff elections. When no candidate has a majority of the votes in the first round of counting, in each following round, the candidate with the fewest first-preferences (among the remaining candidates) is eliminated, and their votes transferred if possible. This continues until one candidate accumulates a majority of the votes still in play.
Instant runoff voting falls under the plurality-based voting rule family, in that under certain conditions the candidate with the least votes (by plurality) is eliminated, making use of secondary rankings as contingency votes. Thus it is related to the two-round runoff system and the exhaustive ballot.
Unlike first-past-the-post voting, IRV is a sequential procedure. Unlike contingent voting (AKA supplementary voting), which has just two rounds of counting at most, IRV may entail numerous rounds of counting.
Instant-runoff voting (IRV) has been used 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, and to elect the head of state in India, Ireland, and Sri Lanka.
The rule was first studied by the Marquis de Condorcet, who observed it could eliminate the majority-preferred candidate (Condorcet winner). Since then, instant-runoff voting has been criticized for failing other criteria, including its ability to eliminate candidates for having too much support or too many votes. Instant-runoff voting may exhibit a kind of Independence of irrelevant alternatives violation called a center squeeze, which causes it to favor uncompromising alternatives over more-moderate ones, which may in turn hinder a recovery from increasing polarization between the candidates and limit free entry.
Some advocates of instant-runoff voting have argued these properties are positive, as voting rules should encourage candidates to appeal to their core support or political base rather than a broad coalition. They also note that in countries like the UK without primaries or runoffs, instant-runoff voting can prevent spoiler effects by eliminating minor-party candidates. Unlike a plurality vote system where votes are non-transferable, instant-runoff voting also avoids some kinds of vote-splitting by near-identical (clone) candidates. IRV has also been advocated for as a natural and practical generalization of the two-round system.

## 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.
* Eliminate the candidate with the fewest votes and transfer their votes to the next usable marked preference if any.
It is possible for a candidate to win an instant-runoff race with support from less than half of the voters who cast votes. This occurs when some voters do not rank all the candidates on their ballots.
In practice, the candidate who leads the first round usually finishes with a majority, or enough to win the seat: the IRV winner is usually the same as the first-past-the-post winner.

## Properties
### Wasted votes and Condorcet winners

Compared to a plurality voting system that rewards only the top vote-getter using non-transferable votes, instant-runoff voting mitigates the problem of wasted votes. 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.
Some advocates of instant-runoff voting argue that the failure to elect a Condorcet winner is positive, as it enables instant-runoff voting to pass later-no-help and later-no-harm, which together render the method immune to burying strategy. FairVote, in particular, has stated that they "believe [later-no-harm] is necessary in the context of high-stakes, competitive elections".

### 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 IRV system contributes to higher rates of spoiled votes, partly because the ballot marking is more complex. Most jurisdictions with instant-runoff voting do not require complete rankings and may use columns to indicate preference instead of numbers. In American elections with instant-runoff voting, more than 99 percent of voters typically cast a valid ballot.
A 2015 study of four local US elections that used instant-runoff voting 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.

### 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.
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. Spatial model simulations indicate that instant runoff rewards strategic withdrawal by candidates.

#### Tactical voting

Gibbard's theorem demonstrates that no (deterministic, non-dictatorial) voting method can be entirely immune from tactical voting. This implies that instant-runoff voting is susceptible to tactical voting in some circumstances. In particular, when there exists a Condorcet winner who instant-runoff voting fails to elect, voters who prefer the Condorcet winner to the instant-runoff voting winner have an incentive to use the compromising strategy.$^{:proposition17}$ instant-runoff voting is also sometimes vulnerable to a paradoxical strategy of ranking a candidate higher to make them lose, due to instant-runoff voting failing the monotonicity criterion.
Research suggests that instant-runoff voting is highly resistant to strategic 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. Instant-runoff voting is also completely immune to the burying strategy: ranking a strong opposition candidate lower can't get one's preferred candidate elected.$^{:proposition3}$
Tactical voting in instant-runoff voting 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 instant-runoff voting claim that instant-runoff voting eliminates the spoiler effect, since instant-runoff voting 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. Instant-runoff voting 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 instant-runoff voting, 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 second-favorite first and their favorite second, rather than first (favorite betrayal). 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. 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.

## Reception

The system has had a mixed reception among political scientists and social choice theorists. Some have suggested that the system does not do much to decrease the impact of wasted votes relative to plurality. Research has found instant-runoff voting causes lower confidence in elections and does not substantially affect minority representation, voter turnout, or long-run electoral competition. Opponents have also noted a high rate of repeals for the system.

### Voter confusion and legitimacy

Governor Paul LePage and Representative Bruce Poliquin claimed, ahead of the 2018 primary elections, that instant-runoff voting 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.

### 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.

### Participation

The effect of instant-runoff voting 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 eliminating the need for primaries. The overall impact on diversity of candidates is difficult to detect.

## Terminology

While instant run-off voting is distinguished from its multiple winner equivalent, the single transferable vote, most English-speaking discussion of electoral systems does not differentiate them. In Ireland, one of the few countries to use these systems in all elections, no distinction between the two is made, 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", 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. 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 single transferable vote.)
Britons and New Zealanders generally call instant-runoff voting the "alternative vote" (AV). Australians, who use instant-runoff voting for most single winner elections, call instant-runoff voting "preferential voting". 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 instant-runoff voting and single transferable vote), or would exclude instant-runoff voting (instant-runoff voting fails positive responsiveness because ballot markings are not interpreted as "preferences" in the traditional sense. Under instant-runoff voting (and single transferable vote), 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 instant-runoff voting 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. As a result of American influence, the term ranked-choice voting is often used in Canada as well. When discussing his promise of electoral reform, Canadian Prime Minister Justin Trudeau used the term "preferential ballot".
American NGO FairVote has promoted the terminology "ranked-choice voting" to refer to instant-runoff voting, a choice that has caused controversy and accusations that the organization is attempting to obscure the existence of other ranked-choice methods that are competing or could compete with instant-runoff voting.
Instant-runoff voting is occasionally referred to as Hare's method (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 instant-runoff voting; the government of Ireland has called instant-runoff voting "proportional representation" based on the fact that the same ballot form is used to elect its president by instant-runoff voting and parliamentary seats by proportional representation (single transferable vote), but instant-runoff voting is a non-proportional single-winner election method, while single transferable vote elects multiple winners and produces minority representation, as well as majority representation, in almost all cases.
State law in South Carolina and Arkansas 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 to any other candidate.
Instant-runoff voting 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, inventor of the Droop quota, then proposed applying the system to single-winner contests.
After conducting a demonstration STV election in 1881, William R. Ware, proposed that a single-winner versions (IRV) could be used to determine the winner in a byelection, thus helping push IRV as workable system. IRV was once known as "Ware's system" due to this advocacy.

### 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 | Instant-runoff voting | 151 |
| Ireland | President | Head of State | Instant-runoff voting | |
| Ireland | Dáil Éireann | Lower chamber of legislature | Single transferable vote (STV), by-elections using Instant-runoff voting | 174 |
| Papua New Guinea | National Parliament | Unicameral legislature | Instant-runoff voting | 109 |
| United States | President (via Electoral College) | Head of State and Government | Alaska and Maine use instant-runoff voting 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 receives all Electoral College electors of the state (as Alaska has only one at-large district, the effect is the same). | 7 EVs (out of 538) |
| United States | House of Representatives | Lower chamber of legislature | Instant-runoff voting in Maine Nonpartisan primary system with instant-runoff voting in the second round (among top four candidates) in Alaska. | 3 (out of 435) |
| United States | Senate | Upper chamber of legislature | Instant-runoff voting in Maine Nonpartisan primary system with instant-runoff voting in the second round (among top four candidates) in Alaska. | 4 (out of 100) |

### Robert's Rules of Order

In the United States, the sequential elimination method used by instant-runoff voting is described in Robert's Rules of Order Newly Revised as an example of ranked-choice voting that can be used to elect officers. Robert's Rules note that ranked-choice systems (including instant-runoff voting) 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 and Riddick's Rules of Procedure, 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 on the ballot - each voter marks only one preference. When no candidate receives a majority of voters in the first round, voters cast votes in two or more subsequent rounds of voting as the field of candidates is reduced. 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 instant-runoff voting.
The runoff method closest to instant-runoff voting is the exhaustive ballot. In this method—familiar to fans of the television show American Idol—one candidate is eliminated in each round, and many rounds of voting may be necessary. 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. If no candidate receives a majority of votes in the first round, all but the top-two candidates are excluded after the first round, and just one more round of voting determines the winner. Eliminations can occur with or without allowing and applying preference votes to choose the final two candidates. This method is used in Mali and France, and in Finnish and Slovenian presidential elections.

### Contingent vote

The contingent vote, also known as "top-two instant-runoff voting" ("top-two IRV"), is the same as instant-runoff voting, 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 instant-runoff voting, there is only one round of voting. Unlike instant-runoff voting, the vote count process entails only two rounds of counting, while instant-runoff voting can entail many rounds.
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 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" instant-runoff voting, 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 instant-runoff voting. 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

Instant-runoff voting may also be part of a larger runoff process:
* Some jurisdictions that hold runoff elections allow absentee (only) voters to submit ranked ballots, because the interval between rounds of balloting is too short for a second round of absentee voting. Ranked ballots enable absentee votes to count in the second (general) election round if their first choice does not make the second round runoff. Arkansas, South Carolina and Springfield, Illinois adopt this approach. Louisiana uses it only for members of the United States Service or who reside overseas.
* Under some exhaustive ballot runoff systems, instant-runoff voting may be used to quickly eliminate some weak candidates in early rounds, using rules to leave a desired number of candidates for further balloting.
* Instant-runoff voting elections that require a majority of cast ballots but not that voters rank all candidates may require more than a single instant-runoff voting contest due to exhausted ballots. (Most IRV systems require a winner to have only a majority of votes still in play, not a majority of votes cast.)
* Robert's Rules recommends preferential voting for elections by mail and requiring a majority of votes to elect a winner. For in-person elections, they recommend repeated balloting until one candidate receives a majority of votes; if candidates drop out when it becomes clear they will not 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.

### 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.

### Variations

A number of instant-runoff voting methods, varying as to ballot design and as to whether or not voters are obliged to rank all the candidates, 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. Bullet voting 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 constitute only a minority 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.
In a full-preferential voting method, voters are required to mark a preference for every candidate standing. Ballots that do not contain a ranking of all candidates are in some jurisdictions considered spoilt or invalid, even if there are only two candidates standing. The full-preferential voting method 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. Such a system produces exhausted votes even when the voter would have been willing to rank more candidates.
A version of instant-runoff voting applying to the ranking of parties was first proposed for elections in Germany in 2013 as spare vote.

## 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. Instant-runoff voting is no exception: it passes some and fails others. The following criteria are satisfied and failed by instant-runoff voting:

### 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". Instant-runoff voting (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 instant-runoff voting meeting this criterion 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".

### 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 instant-runoff voting does not meet this criterion.
Instant-runoff voting 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 instant-runoff voting winner was the Condorcet winner, including a San Francisco election in which the instant-runoff voting 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.

#### 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$^{:Table6}$ to 8.5 percent in the case of a strict left–right spectrum.

#### 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. Instant-runoff voting fails this criterion. In his 1984 study, mathematician Depankar Ray found that in elections where instant-runoff voting elects a different candidate from plurality, that there was an estimated 50 percent probability that some voters would have received a more preferable outcome if they had not participated.

#### 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.
Instant-runoff voting 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 instant-runoff voting, are the same candidate.

### Comparison to other voting systems

Comparison of single-winner voting systems :
| Criterion Method | Majority winner | Majority loser | Mutual majority | Condorcet winner | Condorcet loser | Smith | Smith-IIA | IIA/LIIA | Clone­proof | Mono­tone | Participation | Later-no-harm | Later-no-help | No favorite betrayal | 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 | No | No | No | No | No | Yes | No | No | 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 | No | No | No | Ran­king |
| Schulze | Yes | Yes | Yes | Yes | Yes | Yes | Yes | No | Yes | Yes | No | 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 | Yes | Yes | Yes | No | Yes | Yes | Appr­ovals |
| Majority Judgement | No | No | No | No | No | No | No | Yes | Yes | Yes | No | No | Yes | Yes | Scores |
| Score | No | No | No | No | No | No | No | Yes | Yes | Yes | Yes | No | Yes | Yes | Scores |
| STAR | No | Yes | No | No | Yes | No | No | No | No | Yes | No | No | No | No | Scores |
| Quadratic | No | No | No | No | No | No | No | No | No | Yes | Yes | N/A | N/A | No | Credits |
| Random ballot | No | No | No | No | No | No | No | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Single mark |
| Sortition | No | No | No | No | No | No | No | Yes | No | Yes | Yes | Yes | Yes | Yes | None |
| Table Notes | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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. | 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. 1 2 3 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. 1 2 3 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

* v
* t
* e
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 receives 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 instant-runoff voting 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 instant-runoff voting 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. In the first round, Lenihan had the largest share of first-choice rankings but not a majority. Currie had the fewest votes and was eliminated. After this, Robinson received 82 percent of Currie's votes. This was enough for his vote tally to pass that of Lenihan, and thus form a majority of votes.
Irish presidential election, 1990 :
| Candidate | Round 1 | Round 1 | Round 2 | 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 | 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 instant-runoff voting 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. In the 7th and final round, Hibbins narrowly defeated Liberal candidate Clem Newton-Brown by a margin of 277 votes.
| Candidate | 1st | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 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 | 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 | Eliminated | Eliminated |
| Alan Walker (FFP) | 0.8% | 282 | 283 | 295N | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated |
| Jason Goldsmith (IND) | 0.7% | 247 | 263 | 316 | 349N | Eliminated | Eliminated | Eliminated | Eliminated |
| Steve Stefanopoulos (IND) | 0.6% | 227 | 241N | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated |
| Alan Menadue (IND) | 0.2% | 82N | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated | Eliminated |
| Total | 100% | 37,003 |

### 2009 Burlington mayoral election

Burlington mayoral election, 2009 (round-by-round analysis of votes) :
| Candidates | Candidates | 1st round | 1st round | 2nd round | 2nd round | 3rd 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 instant-runoff voting 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, claiming it helped the city save on costs of a traditional runoff and prevented a spoiler effect, although later analysis showed that without Wright in the election, Montroll would have defeated Kiss in a one-on-one race.
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).
Several electoral reform advocates branded the election a failure after Kiss was elected, despite 54 percent of voters voting for Montroll over Kiss, violating the principle of majority rule.