Draft:Instant-runoff voting

Instant-runoff voting (IRV), also known as the alternative vote (AV) or plurality-with-elimination, is a rank-order voting system that repeatedly eliminates the last-place finisher until only one candidate is left. In the United States and Australia, IRV is often mistakenly conflated with ranked choice voting (RCV) or preferential voting, but such terms are often election scientists

IRV elections are a virtual (instant) variant on exhaustive elimination. In each round, voters choose a favorite candidate; the last-place finisher is eliminated and another round is held. IRV elections automate this process by having voters rank candidates from first to last in order of preference. Voting can then be completed "instantly" by automatically reassigning each voter's ballot to their alternate (i.e. second) choice. This process continues until every candidate except one has been eliminated, at which point they are declared the winner.

IRV is used in national elections in several countries, including to elect the (figurehead) presidents of India and Ireland, the National Parliament of Papua New Guinea, and the Australian House of Representatives.

In the United States
RCV is used for state primary, congressional, and presidential elections in Maine; and for state, congressional, and presidential general elections in Alaska. It is used for local elections in 47 US cities including Salt Lake City and Seattle. It is also used by the Virginia, Utah, and Indiana Republican parties in state conventions and primaries. It is also used by many universities and professional associations, such as the Academy of Motion Picture Arts and the American Philosophical Association. The Bay Area and Minnesota have a relatively large number of cities using the system.

After the 2000 election, is the second wave of reform efforts, after the earlier adoption of STV in the Progressive Era. Most cities that adopted STV repealed it in the 1940s over concerns regarding cost, complexity, and as has also occurred in some cities in the 21st century.

Ranked-choice voting was been seen by supporters as a much-needed boost to.

However, research by political scientists has found little effect of IRV on most outcomes of interest. demonstrated that RCV can disenfranchise poor, minority, and uneducated voters through improper ballot use. Because 94% of first-round RCV winners ultimately win the election, ignoring races with only one or two candidates, disenfranchisement may not allways be offset by greater fidelity to the popular opinion.

Process
In instant-runoff voting, as with other ranked election methods, each voter orders candidates from first to last. On their ballot, voters mark a '1' beside their first-round vote, a '2' beside their second (alternative) vote, who receives their vote if the first candidate is eliminated; and so on until every candidate has been ranked.

The instant-runoff procedure is as follows:


 * 1) Eliminate the candidate with the fewest votes.
 * 2) If only one candidate remains, elect this candidate and stop.
 * 3) Otherwise, re-assign ballots for eliminated candidate to the next choice, and go back to 1.

Ballots assigned to eliminated candidates are added to the totals of one of the remaining candidates based on the next preference ranked on each ballot. The process repeats until one candidate achieves a majority of the vote.

Terminology
Instant-runoff voting derives its name from the way the ballot count simulates a series of runoffs, much like an exhaustive ballot system, except that voters do not need to turn out several times to vote.

Britons and New Zealanders generally call IRV the alternative vote (AV). Australians, who use IRV for most single winner elections, call the method preferential voting.

In the United States, the misnomer ranked-choice voting (RCV) has spread as a result of various jurisdictions copying language directly from the San Francisco Department of Elections, which said the word "instant" might confuse voters into expecting results to be available soon after polls closed. State laws in South Carolina and Arkansas use "instant-runoff" to describe the method. IRV is referred to as RCV in Canada as well, as a result of American influence. However, the term is rarely used outside North America.

IRV is sometimes called the single transferable vote (STV),  also known as Hare's method, after Thomas Hare. 

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. 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. These issues are illustrated in the following election:


 * A wins plurality vote: second place preferences are ignored, so candidate A wins with 36 percent of the vote as against 34 percent for C and 30 percent (10 + 20) for B.
 * C wins IRV vote: candidate B gets the fewest first place votes and is therefor eliminated in the first round. Candidate C gets more of B's second choice preferences than candidate A, winning the second round by 54 percent (20 + 34) to 46 percent (36 + 10). This result is the same as would occur if there was a primary with 3 candidates and a general election with the two remaining candidates (assuming no voters changed their preferences before the general election). Every voter gets a say in the final runoff, so no votes are wasted.
 * B wins Condorcet methods, such as bottom-two runoff IRV: in the first round candidates B and C are in last place, so they go head to head. Candidate A's second place votes go to candidate B, so candidate B wins 66 percent (36 + 10 + 20) to 34 percent over candidate C. In the second runoff round candidate C has been eliminated so candidates A and B go head to head. Candidate C's second place votes go to candidate B, so candidate B wins 64 percent (10 + 20 + 34) to 36 percent over candidate A.

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.

Because the ballot marking is more complex than X voting, there can be an increase in spoiled ballots. In Australia, voters are required to write a number beside every candidate, and the rate of spoiled ballots is sometimes five times more common than plurality voting elections. Since Australia has compulsory voting, however, it is difficult to tell how many ballots are deliberately spoiled. Where complete rankings are not required, a ballot may become inactive (be declared exhausted) if it is up for transfer and none of the candidates marked as lower ranked choices on that ballot are still in the running. In both cases, even in the instances of high rates of spoiled or exhausted votes, their number is much less than the amount of wasted votes under single-member plurality, where as much as 82 percent of votes cast do not produce representation.

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.

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. As one point of comparison, the number of votes cast in the 190 regularly scheduled primary runoff elections for the US House and US Senate from 1994 to 2016 decreased from the initial primary on average by 39 percent, according to a 2016 study by FairVote.

Resistance to strategy
Instant-runoff voting has notably high resistance to tactical voting when it elects the Condorcet winner. IRV does not demonstrate resistance to tactical voting when it does not elect the Condorcet winner.

Party strategizing
The complexity of strategy under instant-runoff voting means parties and candidates must often explain to voters how they should assign their lower preferences or provide them with a prepared ballot. This is especially common in Australia, where voters must rank all candidates to cast a valid ballot; as a result, over 95 percent of Australians used a pre-filled ballot in 2016. Preference deals between parties (where one party's voters agree to place another party's voters second, in return for their doing the same) can lead to candidates winning seats off the back of far-downballot preferences voters were not even aware they had indicated. In one particularly notorious example, the Minor Party Alliance successfully manipulated this system to win several seats in 2016, despite receiving almost no first-preference votes.

Tactical voting
The Gibbard–Satterthwaite theorem demonstrates that no (deterministic, non-dictatorial) voting method using only the preference rankings of the voters can be entirely immune from tactical voting. This implies that IRV is susceptible to tactical voting in some circumstances.

Research concludes that IRV is one of the voting methods least vulnerable to tactical voting, with theorist Nicolaus Tideman noting that, "alternative voting is quite resistant to strategy", and Australian political analyst Antony Green dismissing suggestions of tactical voting.

By not meeting the monotonicity, Condorcet winner, and participation criteria, IRV may incentivize forms of tactical voting (such as compromising) when voters have sufficient information about other voters' preferences, such as from accurate pre-election polling. FairVote mentions that monotonicity failure can lead to situations where "having more voters rank [a] candidate first, can cause [the candidate] to switch from being a winner to being a loser". This occurs when a mutual majority exists which would elect a different candidate than the Condorcet candidate and a minority coalition running off to a single candidate exceeds one-half the size of this majority: the minority candidate cannot be eliminated until the mutual majority runs off to a majority winner. Moving the winner to the top of the minority ballots can shrink the minority sufficiently for their candidate to be eliminated, and their votes then cause the election of a different candidate.

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.

The 2009 mayoral election in Burlington, Vermont, provides an example in which strategy theoretically could have worked but would have been unlikely in practice. In that election, most supporters of the candidate who lost in the final round (a Republican who led in first choices) preferred the Condorcet winner, a Democrat, to the IRV winner, the Progressive Party nominee. If 371 (24.7%) out of the 1,510 backers of the Republican candidate (who also preferred the Democrat over the Progressive candidate for mayor) had insincerely raised the Democrat from their second choice to their first (not changing their rankings relative to their least favourite candidate, the Progressive), the Democrat would then have advanced to the final round (instead of their favourite), defeated any opponent, and proceeded to win the IRV election. This is an example of potential voter regret in that these voters who sincerely ranked their favourite candidate as first, find out after the fact that they caused the election of their least favourite candidate, which can lead to the voting tactic of compromising.

Spoiler effect
A common misconception claims that IRV eliminates the spoiler effect. However, this is not correct: Arrow's impossibility theorem famously demonstrated that no

A well-known example of an election 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 by splitting the first-round vote, knocking out. 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.

However, when the third-party candidate is more competitive, they can still act as a spoiler under IRV,    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 (favourite 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.

Australia only has two major political parties. Every seat was won with a majority of the vote, including several where results would have been different under plurality voting. A study of ballot image data found that all of the 138 RCV elections held in four Bay Area cities in California elected the Condorcet winner, including many with large fields of candidates and 46 where multiple rounds of counting were required to determine a winner.

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.

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.

Proportionality
IRV is a single-winner application of the proportional voting system known as STV, with a Droop quota (50%). Like all winner-take-all voting methods, IRV tends to exaggerate the number of seats won by the largest parties; small parties without majority support in any given constituency are unlikely to earn seats in a legislature, although their supporters will be more likely to be part of the final choice between the two strongest candidates. A simulation of IRV in the 2010 UK general election by the Electoral Reform Society concluded that the election would have altered the balance of seats among the three main parties, but the number of seats won by minor parties would have remained unchanged.

Australia
Australia, a nation with a long record of using IRV for the election of legislative bodies, has had representation in its parliament broadly similar to that expected by plurality methods.

Medium-sized parties, such as the National Party of Australia, can co-exist with coalition partners such as the Liberal Party of Australia, and can compete against it without fear of losing seats to other parties due to vote splitting, although generally in practice these two parties only compete against each other when a sitting member of the coalition leaves Parliament. IRV is more likely to result in legislatures where no single party has an absolute majority of seats (a hung parliament), but does not generally produce as fragmented a legislature as a fully proportional method, such as is used for the House of Representatives of the Netherlands, where coalitions of numerous small parties are needed for a majority.

Criticism from political scientists
Ranked-choice voting has received supported from political advocacy groups like FairVote, who have previously argued the method provides a much-needed boost to American democracy.

However, empirical research comparing IRV to choose-one voting has had mixed results according to political scientists. Although IRV reduces (but does not eliminate) vote-splitting, most research on the topic has found that instant-runoff makes little-to-no difference in the vast majority of elections, affecting the outcome in only 3.8% of cases, and generally only in situations where. it is worth noting that are rare and generally limited to races with narrow margins.

An MIT study concluded the

Researchers have found little-to-no effect of IRV on political competition, diversity, or political polarization; and a mild negative effect on racial equality, with poor, minority, and uneducated communities being most affected by the higher rate of spoiled ballots; substantial increases in.

Social choice theorists have generally taken a more negative view of IRV, contrasting it with rated voting and Condorcet methods. Social choice theorists have noted a wide variety of pathologies that are mostly-unique to IRV, and has a relatively high rate of spoiled elections

Voter confusion and legitimacy of elections
Some critics of IRV have noted that because of its greater complexity, IRV can create distrust among voters who misunderstand it. Often such criticism is related to allegations that IRV is a kind of plural voting. In Ann Arbor, arguments over IRV in letters to newspapers included the belief that IRV "gives minority candidate voters two votes", because some voters' ballots may count for their first choice in the first round and a lesser choice in a later round. The argument that IRV represents plural voting is sometimes used in arguments over the "fairness" of the method, and has led to repeated legal challenges in the United States.

The same argument was advanced in opposition to IRV in Maine. Governor Paul LePage claimed, ahead of the 2018 primary elections, that IRV would result in "one person, five votes", as opposed to "one person, one vote". In litigation following the results of the 2018 election for Maine's 2nd congressional district, Representative Bruce Poliquin claimed that IRV allowed his opponents to "cast ballots for three different candidates in the same election". Federal judge Lance Walker rejected this claim, and the 1st circuit court denied Poliquin's emergency appeal, leading to Poliquin dropping his claim.

The findings of the experiment were stark. I found that RCV produced significantly lower levels of voter confidence, voter satisfaction, and ease of use. It also increased the perception that the voting process was slanted against the respondent’s party."

Similarity to plurality
Because it is effectively a "repeated plurality" vote, results with instant-runoff voting are typically very similar to those under plurality, and instant-runoff behaves similarly to plurality. This has led many commentators and voting reform advocates to question whether IRV is worth the substantial additional costs and complexity needed to ultimately elect the same winner. For example, instant-runoff voting fails the Condorcet criterion, meaning it fails to elect consensus winners.

Most instant-runoff voting elections are won by the candidate who leads in first-choice rankings, choosing the same winner as plurality voting. In Australia, the 1972 federal election had the highest proportion of winners who would not have won under first past the post—with only 14 out of 125 seats not won by the plurality candidate.

The effect of IRV on voter turnout is difficult to assess. In a lengthy 2021 review of the literature on Ranked-Choice Voting, researchers at New America, a liberal think tank based in Washington, D.C., wrote: "And to the extent that RCV combines the primary and the general election into one, it increases turnout. However, many of the other hoped-for benefits, such as more diverse candidates (by gender, race, and ideology), higher turnout, and more viable parties, are harder to detect. Nor is there any evidence that RCV changes policy outcomes[...] In most elections, the candidate who would have won under plurality voting is also the candidate who won under ranked-choice voting."Social choice theorists, by contrast, have noted that instant-runoff can

History
This method was first discussed by the Marquis de Condorcet in 1788, who though only to condemn it for its ability to eliminate a candidate preferred by a majority of voters.

IRV was later independently reinvented by Thomas Hare, in the form of the single transferable vote. Henry Richmond Droop then proposed applying the system to the single-winner case.

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. 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 and Riddick's Rules of Procedure, take a similar stance.

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" or the "supplementary vote", 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 the elections for Mayor of London in the United Kingdom, voters rank a specified maximum number of candidates. In London, the supplementary vote allows 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. Louisiana uses it only for members of the United States Service or who reside overseas.
 * 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.

Variations
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.

In a full-preferential voting method, voters are required to mark a preference for every candidate standing. 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.

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
Scholars rate voting methods using mathematically derived voting method criteria, which describe desirable features of a method. No ranked-preference method can meet all of the criteria, because some of them are mutually exclusive, as shown by statements such as Arrow's impossibility theorem and the Gibbard–Satterthwaite theorem.

Many of the mathematical criteria by which voting methods are compared were formulated for voters with ordinal preferences. If voters vote according to the same ordinal preferences in both rounds, criteria can be applied to two-round systems of runoffs, and in that case, each of the criteria failed by IRV is also failed by the two-round system as they relate to automatic elimination of trailing candidates. Partial results exist for other models of voter behavior in the two-round method: see the two-round system article's criterion compliance section for more information.

Satisfied criteria
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. However, IRV can still elect the "second-worst" candidate when the two worst candidates are the only ones remaining in the final round.

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". IRV meets this 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".

The majority criterion states that "if one candidate is preferred by an absolute majority of voters, then that candidate must win". 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. The resolvability criterion states that "the probability of an exact tie must diminish as more votes are cast".

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.

Systems which fail Condorcet but pass mutual majority can exclude voters outside the mutual majority from the vote, essentially becoming an election between the mutual majority. IRV demonstrates this exclusion of up to 50 percent of voters, notably in the 2009 Burlington mayoral election where the later rounds became a runoff between the mutual majority of voters favouring Andy Montroll and Bob Kiss. This can recurse: if a mutual majority exists within the mutual majority, then the majority becomes a collegiate over the minority, and the inner mutual majority solely decides the votes of this collegiate.

Spoiler effects
Instant-runoff voting is vulnerable to spoiler effects, as it violates independence of irrelevant alternatives (see below). 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 ranked pairs or score voting.

Monotonicity criterion
The monotonicity criterion says that ranking a candidate higher on your ballot should not cause them to lose. The exact probability of a monotonicity failure depends on the circumstances, but with 3 major candidates, the probabilities range from 14.5 percent under the impartial culture model to 8.5 percent in the case of a strict left–right spectrum, quickly approaching 100 percent for more than a handful of candidates.

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: about 50 percent of elections where IRV elects a different candidate from plurality involve participation failures.

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.

Tennessee capital election
It takes three rounds to determine a winner in this election: Round 1 – In the first round, Chattanooga is eliminated.

Round 2 – Chattanooga's votes go to Knoxville (the closest city to Chattanooga). Nashville is in last place and is therefore eliminated.

Note that Nashville was both the Condorcet winner and the "most central" city (supported by the median voter). This elimination is an example of a centre squeeze, where a popular consensus candidate is eliminated thanks to a spoiler effect.

Round 3 – In the final round, Nashville's votes are redistributed to Knoxville, giving Knoxville a majority.

For comparison, note that a plurality vote would elect Memphis, even though most citizens consider it the worst choice, because 42 percent is larger than any other single city. As Nashville is a Condorcet winner, Condorcet methods would elect Nashville.

This election is an example of a participation failure because Memphis eliminated Nashville in round 3. If Memphis lost half its population, Nashville (the Memphis voters' second choice) would have won the election instead of Knoxville (the Memphis voters' last choice).

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.

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 case, it was the candidate who initially placed third (Green candidate Sam Hibbins). Hibbins would ultimately go on to defeat center-left Australian Labor candidate Neil Pharaoh with the help of 31 voters who placed him in 6th place (third-to-last), despite losing the first five rounds of voting. In the 7th round, Hibbins narrowly defeated Coalition candidate Clem Newton-Brown by a margin of 277 votes.

In this race, Newton-Brown spoiled the election for Labor candidate and Condorcet winner Neil Pharaoh, who likely would have defeated Sam Hibbins by a 3:1 ratio if Newton-Brown had not run.

2009 Burlington mayoral election
Under Burlington'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, claiming it helped the city save on costs of a traditional runoff and prevented a spoiler effect, although later analysis showed this not to be the case: without Wright in the election, Montroll would have defeated Kiss in a one-on-one race.

FairVote also claimed the election was a success because most voters were able to complete at least one preference on their ranked-choice ballot. However, 16% of voters cast incomplete ballots, and 6% of ballots were thrown out before the final round, leading some observers to question that interpretation.

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.

Locals argued the system was convoluted, turned the election into a "gambling game" by disqualifying Montroll for having won too many votes, and "eliminated the most popular moderate candidate and elected an extremist".

Practice

 * Advantages and disadvantages of AV from the ACE Project Electoral Design Reference Materials
 * A Handbook of Electoral System Design from International IDEA
 * Australian Electoral Commission Web Site
 * Australian Senate:
 * Australian House of Representatives:
 * Preferential Voting in Australia from Australian Politics.com
 * San Francisco Department of Elections, California
 * Alameda County Registrar of Voters, California
 * City of Minneapolis, Minnesota
 * Ranked Choice Voting Resource Center

Demonstrations and simulations

 * The Star Tribune: How ranked-choice voting works – an interactive graphic
 * RankedVote — Online ranked-choice voting platform for voter education with detailed results animations and explanations.
 * RCV123.org - Free, non-profit site with on-line and paper ballot ranked-choice voting systems for any group vote.
 * AmericanQuorum.com A ranked-choice ballot tool from the Indaba Application Network, including the animated display of an instant runoff.
 * BBC: Would the alternative vote have changed history?, illustration of how the results of the last six general elections might have looked had the 'alternative vote' system been in place.
 * Voting System Visualizations – 2-dimensional plots of results of various methods, with assumptions of sincere voting behavior.
 * Simulation Of Various Voting Models for Close Elections Opposition article by Brian Olson.

Advocacy groups and positions

 * Yes to Fairer Votes campaign site for the Yes side of the 2011 United Kingdom Alternative Vote referendum
 * Washington Post
 * Ranked Choice Voting at [Represent.Us]
 * InstantRunoff.com
 * Ranked Ballot Initiative of Toronto, rabit.ca
 * Roosevelt Institution
 * Citizens for Voter Choice :: Massachusetts
 * FairVote Minnesota
 * Common Cause Massachusetts
 * Brookings Institution's "Empowering Moderate Voters" paper
 * Does the Alternative Vote Bring Tyranny to Australia? – Antony Green ABC
 * Brookings Institution's "Empowering Moderate Voters" paper
 * Does the Alternative Vote Bring Tyranny to Australia? – Antony Green ABC

Opposition groups and positions

 * Center for Election Science compares Instant runoff to Approval voting
 * Fair Vote Canada paper on the Alternative Vote
 * Instant Runoff Voting Report Values and Risks Report by the N.C. Coalition for Verified Voting