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Instant-runoff voting (IRV) is a type of ranked preferential voting method. It uses a majority voting rule in single-winner elections where there are more than two candidates. It is commonly referred to as ranked-choice voting (RCV) in the United States (although there are other forms of
ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...
), preferential voting in
Australia Australia, officially the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands. With an area of , Australia is the largest country by ...
, where it has seen the widest adoption; in the
United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and ...
, it is generally called alternative vote (AV), whereas in some other countries it is referred to as the
single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
, which usually means only its multi-winner variant. All these names are often used inconsistently. Voters in IRV elections rank the candidates in order of preference. Ballots are initially counted for each voter's top choice. If a candidate has more than half of the first-choice votes, that candidate wins. If not, then the candidate with the fewest votes is eliminated, and the voters who selected the defeated candidate as a first choice then have their votes added to the totals of their next choice. This process continues until a candidate has more than half of the votes. When the field is reduced to two, it has become an "instant runoff" that allows a comparison of the top two candidates head-to-head. IRV is not a proportional voting system but rather a " winner takes all" method, as it elects only one winner in an election (in one district). IRV is used in national elections in several countries. It is used to elect members of the
Australian House of Representatives The House of Representatives is the lower house of the bicameral Parliament of Australia, the upper house being the Senate. Its composition and powers are established in Chapter I of the Constitution of Australia. The term of members of ...
, as well as most state lower houses and in some local government elections. It is the method used to elect the
President of India The president of India ( IAST: ) is the head of state of the Republic of India. The president is the nominal head of the executive, the first citizen of the country, as well as the commander-in-chief of the Indian Armed Forces. Droupadi Murm ...
, the
President of Ireland The president of Ireland ( ga, Uachtarán na hÉireann) is the head of state of Ireland and the supreme commander of the Irish Defence Forces. The president holds office for seven years, and can be elected for a maximum of two terms.Constitu ...
, and (in a modified form) the National Parliament of Papua New Guinea. It is used by many political parties for internal primaries/elections to elect party leaders and presidential/prime ministerial candidates, and by private associations for various voting purposes such as choosing the
Academy Award for Best Picture The Academy Award for Best Picture is one of the Academy Awards presented annually by the Academy of Motion Picture Arts and Sciences (AMPAS) since the awards debuted in 1929. This award goes to the producers of the film and is the only categ ...
.


Election procedure


Process

In instant-runoff voting, as with other ranked election methods, each voter ranks the list of candidates in order of preference. Under a common
ballot A ballot is a device used to cast votes in an election and may be found as a piece of paper or a small ball used in secret voting. It was originally a small ball (see blackballing) used to record decisions made by voters in Italy around the 16 ...
layout, the voter marks a '1' beside the most preferred candidate, a '2' beside the second-most preferred, and so forth, in
ascending order Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. # ordering: arranging items in a sequence ordered by some criterion; # categorizing: grouping items with similar pro ...
. The mechanics of the process are the same regardless of how many candidates the voter ranks, and how many are left unranked. In most implementations, the voter ranks as many or as few choices as they wish. The instant-runoff vote counting procedure is as follows: # Eliminate the candidate appearing as the first preference on the fewest ballots. # If only one candidate remains, elect this candidate and stop. # Otherwise go to 1. If there is an exact tie for last place in numbers of votes, various tie-breaking rules determine which candidate to eliminate. The set of all candidates with the fewest first-order votes whose votes together total less than any other candidate's can be eliminated without changing the outcome. This bulk elimination can bypass irrelevant ties, for example if one candidate receives 15 first-order votes and four others receive 5, 5, 3, and 1, and no other candidate receives fewer than 15, all four of the latter candidates will be eliminated during the next four rounds, and so can be eliminated immediately without considering the tie. 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 votes cast for continuing candidates. Ballots on which all of a voter's ranked candidates are eliminated become inactive.


Candidate order on the ballot paper

The common ways to list candidates on a ballot paper are alphabetically or by random lot. In some cases, candidates may also be grouped by political party. Alternatively, Robson Rotation involves randomly changing candidate order for each print run.


Party strategies

Where preferential voting is used for the election of an assembly or council, parties and candidates often advise their supporters on their lower preferences, especially in Australia where a voter must rank all candidates to cast a valid ballot. This can lead to "preference deals", a form of pre-election bargaining, in which smaller parties agree to direct their voters in return for support from the winning party on issues critical to the small party. It can also sometimes lead to joint campaigning between candidates with similar platforms. However, these strategies rely on the assumption that supporters of a party or candidate are receptive to advice on the other preferences on their ballot.


Counting logistics

Most IRV elections historically have been tallied by hand, including in elections to Australia's House of Representatives and most state governments. In the modern era, voting equipment can be used to administer the count either partially or fully. In Australia, the
returning officer In various parliamentary systems, a returning officer is responsible for overseeing elections in one or more constituencies. Australia In Australia a returning officer is an employee of the Australian Electoral Commission or a state electoral ...
now usually declares the two candidates that are most likely to win each seat. The votes are always counted by hand at the polling station monitored by scrutineers from each candidate. The first part of the count is to record the first choice for all candidates. Votes for candidates other than the two likely winners are then allocated to them in a second pass. The whole process of counting the votes by hand and allocating preferences is typically completed within two hours on election night at a cost of $7.68 per elector in 2010 to run the entire election. Ireland in its presidential elections has several dozen counting centers around the nation. Each center reports its totals and receives instructions from the central office about which candidate or candidates to eliminate in the next round of counting based on which candidate is in last place. The count typically is completed the day after the election, as in 1997. In the United States, nearly all jurisdictions that use this format—like
Maine Maine () is a state in the New England and Northeastern regions of the United States. It borders New Hampshire to the west, the Gulf of Maine to the southeast, and the Canadian provinces of New Brunswick and Quebec to the northeast and nor ...
,
Oakland Oakland is the largest city and the county seat of Alameda County, California, United States. A major West Coast port, Oakland is the largest city in the East Bay region of the San Francisco Bay Area, the third largest city overall in the Bay ...
and
San Francisco San Francisco (; Spanish for " Saint Francis"), officially the City and County of San Francisco, is the commercial, financial, and cultural center of Northern California. The city proper is the fourth most populous in California and 17t ...
—administer IRV elections on voting machines, with optical scanning machines recording preferences and software tallying the IRV algorithm as soon as all ballots are recorded. In its first use of IRV in 2009,
Minneapolis Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origin ...
tallied first choices on optical scan equipment at the polls and then used a central hand-count for the IRV tally, but has since administered elections without hand tallies
Portland, Maine Portland is the largest city in the U.S. state of Maine and the seat of Cumberland County. Portland's population was 68,408 in April 2020. The Greater Portland metropolitan area is home to over half a million people, the 104th-largest metropo ...
in 2011 used its usual voting machines to tally first choice at the polls, then a central scan with different equipment if an IRV tally was necessary. The election results from IRV cannot be counted additively: all ballots must be present prior to the first elimination. Methods like plurality voting and pairwise voting can divide the work of counting and sum the results as more votes are reported. To produce pairwise results, each candidate ranked on a ballot receives one vote against each alternative ranked lower and each not ranked on that ballot; equal rankings, including non-ranked candidates, are ties and no vote is tallied. These tallies can be summed to produce a complete matrix of pairwise elections, which can then be used to compute the
Smith set In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats ever ...
or to calculate the outcomes of Schulze, Minimax, Ranked Pairs, and other methods. IRV is very unlikely to give rise to a tie when the number of voters is large. For this reason it is sometimes advocated as part of a tie break for methods (such as the Smith set) which do not have this property: see Smith/IRV and Tideman's Alternative.


Voter confusion

Research shows that voters in general can understand and use IRV. Various surveys in the U.S. found 80%–90% of voters reported understanding the ballot very well, and 90% reported it was easy to use. Voter comprehension increased with repeated use, eliminating demographic disparities over time. Older voters were more likely to say they found the system confusing, but in practice correctly completed IRV ballots at the same rate.


Invalid ballots and incomplete 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. Because the ballot marking is more complex, 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 can be five times higher 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 if none of the ranked choices on that ballot advance to the next round. 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% of voters typically cast a valid ballot. A 2015 study of four local U.S. 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% to a high of 27.1%. As one point of comparison, the number of votes cast in the 190 regularly scheduled primary runoff elections for the U.S House and U.S. Senate from 1994 to 2016 decreased from the initial primary on average by 39%, according to a 2016 study by FairVote.


Terminology

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 voter preferences do not change between rounds. It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting. Britons and New Zealanders generally call IRV the "alternative vote" (AV). while in Canada it is called "ranked choice voting". Australians, who use IRV for most single winner elections, call IRV "preferential voting". American NGO
FairVote FairVote, formerly the Center for Voting and Democracy, is a 501(c)(3) organization that advocates electoral reform in the United States. Founded in 1992 as Citizens for Proportional Representation to support the implementation of proportional r ...
uses the terminology "ranked choice voting" to refer to IRV in the case of single-winner offices and to refer to
single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
in the case of multi-winner offices. Jurisdictions using IRV such as
San Francisco San Francisco (; Spanish for " Saint Francis"), officially the City and County of San Francisco, is the commercial, financial, and cultural center of Northern California. The city proper is the fourth most populous in California and 17t ...
, California, Maine, Alaska, and Minneapolis, Minnesota have codified the term "ranked choice voting" in their laws. San Francisco has argued the word "instant" in term "instant runoff voting" could confuse voters into expecting results to be immediately available. IRV is occasionally referred to (rather confusingly) either as Hare's method (after Sir Thomas Hare) or as Ware's method after the American William Robert Ware. When the
single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
(STV) method is applied to a single-winner election, it becomes IRV; the government of Ireland has called IRV "proportional representation" based on the fact that the same ballot form is used to elect its president by IRV and parliamentary seats by STV, but IRV is a winner-take-all election method. State law in
South Carolina )''Animis opibusque parati'' ( for, , Latin, Prepared in mind and resources, links=no) , anthem = " Carolina";" South Carolina On My Mind" , Former = Province of South Carolina , seat = Columbia , LargestCity = Charleston , LargestMetro = ...
and
Arkansas Arkansas ( ) is a landlocked state in the South Central United States. It is bordered by Missouri to the north, Tennessee and Mississippi to the east, Louisiana to the south, and Texas and Oklahoma to the west. Its name is from the O ...
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.


Properties, advantages and disadvantages


Wasted votes and Condorcet winners

Unlike a plurality voting system that just compares the top two vote getters, instant-runoff voting minimizes the problem of wasted votes.J. R. Chamberlin and M. D. Cohen, ‘Toward Applicable Social Choice Theory...’, (1978). However, it does not ensure the election of a
Condorcet winner An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
, which is the candidate that 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% of the vote as against 34% for C and 30% (10+20) for B. * C wins IRV vote: candidate B gets the fewest first place votes so is eliminated in the first round. Candidate C gets more of B's second choice preferences than candidate A, winning the second round by 54% (20+34) to 46% (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. Every voter gets a say in the final runoff, so no votes are wasted. * B wins IRV / bottom two runoff: 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% (36+10+20) to 34% 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% (10+20+34) to 36% over candidate A. Bottom Two Runoff is an example of a
Condorcet method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...
of voting.


Resistance to strategy

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


Tactical voting

The
Gibbard–Satterthwaite theorem In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a si ...
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. James Green-Armytage tested four ranked-choice methods, and found the alternative vote to be the second-most-resistant to tactical voting, though it was beaten by a class of AV-
Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal p ...
hybrids, and did not resist strategic withdrawal by candidates well. These analyses only apply to tactical voting, but not to other forms of manipulation; for example, Tideman and Robinette demonstrate a method by which a candidate modifies their campaign to appeal to a slightly broader range of voters, including those of a popular opponent, so as to "bracket" that opponent out (cause them to be eliminated earlier). By not meeting the monotonicity,
Condorcet winner An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
, and participation criteria, IRV may incentivize forms of
tactical voting Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, ...
(such as compromising) when voters have sufficient information about other voters' preferences, such as from accurate pre-election polling.
FairVote FairVote, formerly the Center for Voting and Democracy, is a 501(c)(3) organization that advocates electoral reform in the United States. Founded in 1992 as Citizens for Proportional Representation to support the implementation of proportional r ...
mentions that monotonicity failure can lead to situations where "having more voters rank candidate first, can cause
he candidate He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' in ...
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. This situation occurred in the
2009 Burlington mayoral election The 2009 Burlington mayoral election was held in March 2009 for the city of Burlington, Vermont. A few years earlier, the city had switched to holding mayoral elections every three years (e.g. the 1997 election, the 2000 election, the 2003 el ...
: had several
Kurt Wright Kurt Wright (born February 7, 1956) is an American Republican politician who was elected and served in the Vermont House of Representatives The Vermont House of Representatives is the lower house of the Vermont General Assembly, the state legi ...
voters moved Bob Kiss to the top of their ballots, the winner would have changed from Bob Kiss to Andy Montroll. The change in lower candidates is important: whether votes are shifted to the leading candidate, shifted to a fringe candidate, or discarded altogether is of no importance. 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 Left may refer to: Music * ''Left'' (Hope of the States album), 2006 * ''Left'' (Monkey House album), 2016 * "Left", a song by Nickelback from the album '' Curb'', 1996 Direction * Left (direction), the relative direction opposite of right * ...
and
right Rights are legal, social, or ethical principles of freedom or entitlement; that is, rights are the fundamental normative rules about what is allowed of people or owed to people according to some legal system, social convention, or ethical ...
prefer the
centrist Centrism is a political outlook or position involving acceptance or support of a balance of social equality and a degree of social hierarchy while opposing political changes that would result in a significant shift of society strongly to the ...
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 File:2009 Events Collage V2.png, From top left, clockwise: The vertical stabilizer of Air France Flight 447 is pulled out from the Atlantic Ocean; Barack Obama becomes the first African American to become President of the United States; Protests ...
mayoral election in
Burlington, Vermont Burlington is the most populous city in the U.S. state of Vermont and the seat of Chittenden County. It is located south of the Canada–United States border and south of Montreal. As of the 2020 U.S. census, the population was 44,743. It ...
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 Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal p ...
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 favorite candidate, the Progressive), the Democrat would then have advanced to the final round (instead of their favorite), defeated any opponent, and proceeded to win the IRV election.Warren Smith (2009
"Burlington Vermont 2009 IRV mayor election; Thwarted-majority, non-monotonicity & other failures (oops)"
/ref> This is an example of potential voter regret in that these voters who sincerely ranked their favorite candidate as first, find out after the fact that they caused the election of their least favorite candidate, which can lead to the voting tactic of compromising. Yet because the Republican led in first choices and only narrowly lost the final instant runoff, his backers would have been highly unlikely to pursue such a strategy. This strategy still would not elect the Republican, due to a lack of preferences towards them.


Spoiler effect

The spoiler effect is when a difference is made to the anticipated outcome of an election due to the presence on the ballot paper of a candidate who (predictably) will lose. Most often this is when two or more politically similar candidates divide the vote for the more popular end of the political spectrum. That is, each receives fewer votes than a single opponent on the unpopular end of the spectrum who is disliked by the majority of voters but who wins from the advantage that, on that unpopular side, they are unopposed. Strategic nomination relies on triggering this situation, and requires understanding of both the electoral process and the demographics of the district. Proponents of IRV claim that IRV eliminates the spoiler effect, since IRV makes it safe to vote honestly for marginal parties: Under a plurality method, voters who sympathize most strongly with a marginal candidate are strongly encouraged to instead vote for a more popular candidate who shares some of the same principles, since that candidate has a much greater chance of being elected and a vote for the marginal candidate will not result in the marginal candidate's election. An IRV method reduces this problem, since the voter can rank the marginal candidate first and the mainstream candidate second; in the likely event that the fringe candidate is eliminated, the vote is not wasted but is transferred to the second preference. However, when the third-party candidate is more competitive, they can still act as a spoiler under IRV, 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 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. By contrast, in the seat of Prahran during the 2014 Victorian State Election, despite the Greens candidate outlasting the more centrist Labor candidate during counting, most of the Labor preferences ultimately helped elect the Greens rather than the further right Liberal candidate. In this case, the Greens candidate, despite only having the third most primary votes, ultimately was not a spoiler and was able to be elected. In practice, IRV does not seem to discourage candidacies. In Australia's House of Representatives elections in 2007, for example, the average number of candidates in a district was seven, and at least four candidates ran in every district; notwithstanding the fact that 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.


Proportionality

IRV is a single-winner application of a proportional voting method, technically single-winner STV with a
droop quota The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR ...
(50%+1). 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 The 2010 United Kingdom general election was held on Thursday 6 May 2010, with 45,597,461 registered voters entitled to vote to elect members to the House of Commons. The election took place in 650 constituencies across the United Kingdom unde ...
by the
Electoral Reform Society The Electoral Reform Society (ERS) is an independent campaigning organisation based in the United Kingdom which promotes electoral reform. It seeks to replace first-past-the-post voting with proportional representation, advocating the single t ...
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 The National Party of Australia, also known as The Nationals or The Nats, is an Australian political party. Traditionally representing graziers, farmers, and regional voters generally, it began as the Australian Country Party in 1920 at a fed ...
, can co-exist with
coalition A coalition is a group formed when two or more people or groups temporarily work together to achieve a common goal. The term is most frequently used to denote a formation of power in political or economical spaces. Formation According to ''A Gui ...
partners such as the
Liberal Party of Australia The Liberal Party of Australia is a centre-right political party in Australia, one of the two major parties in Australian politics, along with the centre-left Australian Labor Party. It was founded in 1944 as the successor to the United A ...
, 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 A hung parliament is a term used in legislatures primarily under the Westminster system to describe a situation in which no single political party or pre-existing coalition (also known as an alliance or bloc) has an absolute majority of legisla ...
), 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.


Costs

The costs of printing and counting ballot papers for an IRV election are no different from those of any other method using the same technology. However, the more-complicated counting system may encourage officials to introduce more advanced technology, such as software counters or electronic voting machines. Pierce County, Washington, election officials outlined one-time costs of $857,000 to implement IRV for its elections in 2008, covering software and equipment, voter education and testing. Because it does not require two separate votes, IRV is assumed to cost less than two-round primary/general or general/runoff election methods. However, in 2009, the auditor of Pierce County reported that the ongoing costs of the system were not necessarily balanced by the costs of eliminating runoffs for most county offices, because those elections may be needed for other offices not elected by IRV. Other jurisdictions have reported immediate cost savings. Australian elections are counted by hand. The 2010 federal election cost a total of $7.68 per elector of which only a small proportion is the actual counting of votes. Counting is now normally performed in a single pass at the polling center as described above. The perceived costs or cost savings of adopting an IRV method are commonly used by both supporters and critics. In the 2011 referendum on the Alternative Vote in the UK, the NOtoAV campaign was launched with a claim that adopting the method would cost £250 million; commentators argued that this headline figure had been inflated by including £82 million for the cost of the referendum itself, and a further £130 million on the assumption that the UK would need to introduce electronic voting systems, when ministers had confirmed that there was no intention of implementing such technology, whatever the outcome of the election. Automated vote counting is seen by some to have a greater potential for election fraud; IRV supporters counter these claims with recommended audit procedures, or note that automated counting is not required for the method at all.


Negative campaigning

John Russo, Oakland City Attorney, argued in the ''
Oakland Tribune The ''Oakland Tribune'' is a weekly newspaper published in Oakland, California, by the Bay Area News Group (BANG), a subsidiary of MediaNews Group. Founded in 1874, the ''Tribune'' rose to become an influential daily newspaper. With the declin ...
'' on 24 July 2006 that "Instant runoff voting is an antidote to the disease of negative campaigning. IRV led to San Francisco candidates campaigning more cooperatively. Under the method, their candidates were less likely to engage in negative campaigning because such tactics would risk alienating the voters who support 'attacked' candidates", reducing the chance that they would support the attacker as a second or third choice. Campaign strategists in New York City reported that after IRV was introduced, they became more careful not to attack other candidates in ways that might offend voters that would otherwise give the campaign a second-choice ranking. In 2013–2014, the Rutgers-Eagleton Poll surveyed more than 4,800 likely voters in 21 cities after their local city elections—half in cities with IRV elections and 14 in control cities selected by project leaders Caroline Tolbert of the University of Iowa and Todd Donovan of Western Washington University. Among findings, respondents in IRV cities reported candidates spent less time criticizing opponents than in cities that did not use IRV. In the 2013 survey, for example, 5% of respondents said that candidates criticized each other "a great deal of the time" as opposed to 25% in non-IRV cities. An accompanying survey of candidates reported similar findings. Internationally, Benjamin Reilly suggests instant-runoff voting eases ethnic conflict in divided societies. This feature was a leading argument for why
Papua New Guinea Papua New Guinea (abbreviated PNG; , ; tpi, Papua Niugini; ho, Papua Niu Gini), officially the Independent State of Papua New Guinea ( tpi, Independen Stet bilong Papua Niugini; ho, Independen Stet bilong Papua Niu Gini), is a country i ...
adopted instant-runoff voting. However, Lord Alexander's objections to the conclusions of the British Independent Commission on the Voting System's report cites the example of Australia saying "their politicians tend to be, if anything, more blunt and outspoken than our own".


Plural voting

Some critics of IRV hold that voters supporting major candidates get their second and third place preferences ignored as those candidates are eliminated before their first choice is eliminated. Meanwhile, if you support a fringe candidate, it is more likely that your second and third place choices will be used. In
Ann Arbor, Michigan Ann Arbor is a city in the U.S. state of Michigan and the county seat of Washtenaw County. The 2020 census recorded its population to be 123,851. It is the principal city of the Ann Arbor Metropolitan Statistical Area, which encompasses all ...
, for example, 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 several legal challenges in the United States. In every instance, state and federal judges have rejected this argument. The argument was addressed and rejected by a Michigan court in 1975; in ''
Stephenson v. the Ann Arbor Board of City Canvassers Stephenson is a medieval patronymic surname meaning "son of Stephen". The earliest public record is found in the county of Huntingdonshire in 1279. There are variant spellings including Stevenson. People with the surname include: *Ashley Ste ...
'', the court held "majority preferential voting" (as IRV was then known) to be in compliance with the Michigan and United States constitutions, writing: 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.


Participation

Primary and runoff elections tend to have lower turnout than general elections. Consolidating these into a single election increases voter participation.


History and use


History

This method was considered by
Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal p ...
as early as 1788, though only to condemn it, for its ability to eliminate a candidate preferred by a majority of voters. IRV can be seen as a special case of the
single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
method, which began use in the 1850s. It is historically known as Ware's method, due to the implementation of STV in 1871 at
Harvard College Harvard College is the undergraduate college of Harvard University, an Ivy League research university in Cambridge, Massachusetts. Founded in 1636, Harvard College is the original school of Harvard University, the oldest institution of higher ...
by American
architect An architect is a person who plans, designs and oversees the construction of buildings. To practice architecture means to provide services in connection with the design of buildings and the space within the site surrounding the buildings that h ...
William Robert Ware, who suggested it could also be used for single-winner elections. Unlike the single transferable vote in multi-seat elections, however, the only ballot transfers are from backers of candidates who have been eliminated. The first known use of an IRV-like method in a governmental election was in the 1893 general election in the
Colony of Queensland The Colony of Queensland was a colony of the British Empire from 1859 to 1901, when it became a State in the federal Commonwealth of Australia on 1 January 1901. At its greatest extent, the colony included the present-day State of Queensland, ...
(in present-day Australia). The variant used for this election was a " contingent vote", where all candidates but two are eliminated in the first round. IRV in its true form was first used in
Western Australia Western Australia (commonly abbreviated as WA) is a state of Australia occupying the western percent of the land area of Australia excluding external territories. It is bounded by the Indian Ocean to the north and west, the Southern Ocean to t ...
, in the 1908 state election. The Hare-Clark system was introduced for the
Tasmanian House of Assembly The House of Assembly, or Lower House, is one of the two chambers of the Parliament of Tasmania in Australia. The other is the Legislative Council or Upper House. It sits in Parliament House in the state capital, Hobart. The Assembly has 25 m ...
at the 1909 state election. IRV was introduced for federal (nationwide) elections in Australia after the Swan by-election in October 1918, in response to the rise of the conservative Country Party, representing small farmers. The Country Party split the non-
Labor Labour or labor may refer to: * Childbirth, the delivery of a baby * Labour (human activity), or work ** Manual labour, physical work ** Wage labour, a socioeconomic relationship between a worker and an employer ** Organized labour and the la ...
vote in conservative country areas, allowing Labor candidates to win without a majority of the vote. The conservative government of
Billy Hughes William Morris Hughes (25 September 1862 – 28 October 1952) was an Australian politician who served as the seventh prime minister of Australia, in office from 1915 to 1923. He is best known for leading the country during World War I, but ...
introduced IRV (in Australia called "preferential voting") as a means of allowing competition between the
Coalition A coalition is a group formed when two or more people or groups temporarily work together to achieve a common goal. The term is most frequently used to denote a formation of power in political or economical spaces. Formation According to ''A Gui ...
parties without putting seats at risk. It was first used at the Corangamite by-election on 14 December 1918, and at a national level at the 1919 election. IRV continued to benefit the Coalition until the 1990 election, when for the first time Labor obtained a net benefit from IRV.


Global use


National level elections


''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 preferential voting:
The term preferential voting refers to any of a number of voting methods by which, on a single ballot when there are more than two possible choices, the second or less-preferred choices of voters can be taken into account if no candidate or proposition attains a majority. While it is more complicated than other methods of voting in common use, and is not a substitute for the normal procedure of repeated balloting until a majority is obtained, preferential voting is especially useful and fair in an election by mail if it is impractical to take more than one ballot. In such cases, it makes possible a more representative result than under a rule that a plurality shall elect ... Preferential voting has many variations. One method is described here by way of illustration.
The instant-runoff voting method is then detailed. ''Robert's Rules'' continues:
The system of preferential voting just described should not be used in cases where it is possible to follow the normal procedure of repeated balloting until one candidate or proposition attains a majority. Although this type of preferential ballot is preferable to an election by plurality, it affords less freedom of choice than repeated balloting, because it denies voters the opportunity of basing their second or lesser choices on the results of earlier ballots, and because the candidate or proposition in last place is automatically eliminated and may thus be prevented from becoming a compromise choice.
Two other books on American parliamentary procedure take a similar stance, disapproving of plurality voting and describing preferential voting as an option, if authorized in the bylaws, when repeated balloting is impractical: ''
The Standard Code of Parliamentary Procedure ''The Standard Code of Parliamentary Procedure'' (formerly the ''Sturgis Standard Code of Parliamentary Procedure'' by Alice Sturgis) is a book of rules of order. It is the second most popular parliamentary authority in the United States after ...
'' and ''
Riddick's Rules of Procedure ''Riddick's Rules of Procedure'' is a parliamentary authority - a book explaining the parliamentary procedure, including the rules, ethics, and customs governing meetings and other operations of the United States Senate. It was written by Floyd ...
''.


Similar methods


Runoff voting

The term ''instant runoff voting'' is derived from the name of a class of voting methods called runoff voting. In runoff voting voters do not rank candidates in order of preference on a single ballot. Instead a similar effect is achieved by using multiple rounds of voting. All multi-round runoff voting methods allow voters to change their preferences in each round, incorporating the results of the prior round to influence their decision. This is not possible in IRV, as participants vote only once, and this prohibits certain forms of
tactical voting Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, ...
that can be prevalent in "standard" runoff voting.


Exhaustive ballot

A method closer to IRV is the exhaustive ballot. In this method—one familiar to fans of the television show ''
American Idol ''American Idol'' is an American singing competition television series created by Simon Fuller, produced by Fremantle North America and 19 Entertainment, and distributed by Fremantle North America. It aired on Fox from June 11, 2002, to ...
''—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.


Two-round methods

The simplest form of runoff voting is the
two-round system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
, which typically excludes all but 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 ''batch-style'', 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 Sri Lanka (, ; si, ශ්‍රී ලංකා, Śrī Laṅkā, translit-std=ISO (); ta, இலங்கை, Ilaṅkai, translit-std=ISO ()), formerly known as Ceylon and officially the Democratic Socialist Republic of Sri Lanka, is an ...
, and the elections for
Mayor of London The mayor of London is the chief executive of the Greater London Authority. The role was created in 2000 after the Greater London devolution referendum in 1998, and was the first directly elected mayor in the United Kingdom. The current m ...
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 for the
President of Sri Lanka The President of Sri Lanka ( si, ශ්‍රී ලංකා ජනාධිපති ''Śrī Laṃkā Janādhipathi''; ta, இலங்கை சனாதிபதி ''Ilankai janātipati'') is the head of state and head of government of t ...
. 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. Particularly in elections with few (e.g., fewer than 100) voters, numerous ties can destroy confidence. Heavy use of tie-breaking rules leaves uncomfortable doubts over whether the winner might have changed if a recount had been performed.


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 Arkansas ( ) is a landlocked state in the South Central United States. It is bordered by Missouri to the north, Tennessee and Mississippi to the east, Louisiana to the south, and Texas and Oklahoma to the west. Its name is from the O ...
,
South Carolina )''Animis opibusque parati'' ( for, , Latin, Prepared in mind and resources, links=no) , anthem = " Carolina";" South Carolina On My Mind" , Former = Province of South Carolina , seat = Columbia , LargestCity = Charleston , LargestMetro = ...
and
Springfield, Illinois Springfield is the capital of the U.S. state of Illinois and the county seat and largest city of Sangamon County. The city's population was 114,394 at the 2020 census, which makes it the state's seventh most-populous city, the second largest ...
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 allows an arbitrary victory threshold in a single round of voting, e.g., 60%. In such cases a second vote may be held to confirm the winner. * 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, giving IRV as their example. For in-person elections, they recommend repeated balloting until one candidate receives an absolute majority of all votes cast. Repeated voting allows voters to turn to a candidate as a compromise who polled poorly in the initial election. The common feature of these IRV variations is that one vote is counted per ballot per round, with rules that eliminate the weakest candidate(s) in successive rounds. Most IRV implementations drop the requirement for a
majority A majority, also called a simple majority or absolute majority to distinguish it from related terms, is more than half of the total.Dictionary definitions of ''majority'' aMerriam-Websterepistemic properties of democracy. Under theories of
public reason Public reason requires that the moral or political rules that regulate our common life be, in some sense, justifiable or acceptable to all those persons over whom the rules purport to have authority. It is an idea with roots in the work of Thomas Ho ...
, a democratic decision uses the knowledge of the whole voting body. When a voter has no preference, or decides themselves that their ability to form a correct preference is insufficient, the correct vote is no vote. This is expressed by equal rankings, and when all rankings are equal it is expressed by no vote.


Comparison to first-past-the-post

At 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 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 The president of Ireland ( ga, Uachtarán na hÉireann) is the head of state of Ireland and the supreme commander of the Irish Defence Forces. The president holds office for seven years, and can be elected for a maximum of two terms.Constitu ...
and the
New South Wales Legislative Assembly The New South Wales Legislative Assembly is the lower of the two houses of the Parliament of New South Wales, an Australian state. The upper house is the New South Wales Legislative Council. Both the Assembly and Council sit at Parliament Ho ...
. Optional preferential voting is used for some elections in
Queensland ) , nickname = Sunshine State , image_map = Queensland in Australia.svg , map_caption = Location of Queensland in Australia , subdivision_type = Country , subdivision_name = Australia , established_title = Before federation , establishe ...
. 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 The domestic donkey is a hoofed mammal in the family Equidae, the same family as the horse. It derives from the African wild ass, ''Equus africanus'', and may be classified either as a subspecies thereof, ''Equus africanus asinus'', or as a ...
", 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 The Parliament of Australia (officially the Federal Parliament, also called the Commonwealth Parliament) is the legislative branch of the government of Australia. It consists of three elements: the monarch (represented by the governor-gen ...
and for most State parliaments. Other methods only allow marking preferences for a maximum of the voter's top three favorites, 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 Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...
and the
Gibbard–Satterthwaite theorem In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a si ...
. 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 system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
s of runoffs, and in that case, each of the criteria failed by IRV is also failed by the
two-round system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
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. A table summarising satisfaction of the criteria by IRV and other methods is shown in an
appendix Appendix, or its plural form appendices, may refer to: __NOTOC__ In documents * Addendum, an addition made to a document by its author after its initial printing or publication * Bibliography, a systematic list of books and other works * Index (pu ...


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."


Non-satisfied criteria


Condorcet winner criterion

The
Condorcet winner An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
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 Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per ...
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% of voters, notably in the 2009 Burlington, Vermont mayoral election where the later rounds became a runoff between the mutual majority of voters favoring 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.


Consistency criterion

The
consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
criterion states that if dividing the electorate into two groups and running the same election separately with each group returns the same result for both groups, then the election over the whole electorate should return this result. IRV, like all preferential voting methods which are not positional, does not meet this criterion.


Independence of irrelevant alternatives criterion

The
independence of irrelevant alternatives The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it ...
criterion states that "the election outcome remains the same even if a candidate who cannot win decides to run." 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 much less likely to happen than under plurality.


Monotonicity criterion

The monotonicity criterion states that "a voter can't harm a candidate's chances of winning by voting that candidate higher, or help a candidate by voting that candidate lower, while keeping the relative order of all the other candidates equal." Allard claims failure is unlikely, at a less than 0.03% chance per election. Some critics argue in turn that Allard's calculations are wrong and the probability of monotonicity failure is much greater, at 14.5% under the
impartial culture Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules. The model is understood to be unrealistic, and not a good representation of real-world voting beha ...
election model in the three-candidate case, or 7–10% in the case of a left-right spectrum. Lepelley ''et al.'' find a 2–5% probability of monotonicity failure under the same election model as Allard. The diagram shows the non-monotonicity of IRV, where moving the center of opinion away from a candidate can help that candidate win, and moving the center of opinion towards a candidate can cause that candidate to lose.


Participation criterion

The participation criterion states that "the best way to help a candidate win must not be to abstain". IRV does not meet this criterion: in some cases, the voter's preferred candidate can be best helped if the voter does not vote at all. Depankar Ray finds a 50% probability that, when IRV elects a different candidate than Plurality, some voters would have been better off not showing up.


Reversal symmetry criterion

The reversal symmetry criterion states that "if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected". IRV does not meet this criterion: it is possible to construct an election where reversing the order of every ballot paper does not alter the final winner.


Examples

Some examples of IRV elections are given below. The first two (fictional elections) demonstrate the principle of IRV. The others offer examples of the results of real elections.


Five voters, three candidates

A simple example is provided in the accompanying table. Three candidates are running for election, Bob, Bill and Sue. There are five voters, "a" through "e". The voters each have one vote. They rank the candidates first, second and third in the order they prefer them. To win, a candidate must have a majority of vote; that is, three or more. In Round 1, the first-choice rankings are tallied, with the results that Bob and Sue both have two votes and Bill has one. No candidate has a majority, so a second "instant runoff" round is required. Since Bill is in bottom place, he is eliminated. The ballot from any voter who ranked Bill first (in this example solely voter "c" ) gets modified as follows: the original 2nd choice candidate for that voter becomes their new 1st choice, and their original 3rd choice becomes their new 2nd choice. This results in the Round 2 votes as seen below. This gives Sue 3 votes, which is a majority.


Tennessee capital election

Most instant-runoff voting elections are won by the candidate who leads in first-choice rankings, choosing the same winner as
first-past-the-post voting In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...
. As an example 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. Some IRV elections are won by a candidate who finishes second after the first-round count. In this case, IRV chooses the same winner as a
two-round system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
if all voters were to vote again and maintain their same preferences. A candidate may also win who is in third place or lower after the first count, but gains majority support (among the non-eliminated candidates) in the final round. In such cases, IRV would choose the same winner as a multi-round method that eliminated the last-place candidate before each new vote, assuming all voters kept voting and maintained their same preferences. Here is an example of this last case. It takes three rounds to determine a winner in this election.Round 1 – In the first round no city gets a majority: If one of the cities had achieved a majority vote (more than half), the election would end there. If this were a first-past-the-post election, Memphis would win because it received the most votes. But IRV does not allow a candidate to win on the first round without having an absolute majority of the vote. While 42% of the electorate voted ''for'' Memphis, 58% of the electorate voted ''against'' Memphis in this first round. Round 2 – In the second round of tabulation, we remove the city with the least first-place support from consideration. Chattanooga received the lowest number of votes in the first round, so it is eliminated. The ballots that listed Chattanooga as first choice are added to the totals of the second-choice selection on each ballot. Everything else stays the same. Chattanooga's 15% of the total votes are added to the second choices selected by the voters for whom that city was first-choice (in this example Knoxville): 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. Round 3 – No city yet has secured a majority of votes, so we move to the third round with the elimination of Nashville, and it becomes a contest between Memphis and Knoxville. As in the second round with Chattanooga, all of 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. 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: Result: Knoxville, which was running third in the first tabulation, has moved up from behind to take first place in the third and final round. The winner of the election is Knoxville. However, if 6% of voters in Memphis were to put Nashville first, the winner would be Nashville, a preferable outcome for voters in Memphis. This is an example of potential tactical voting, though one that would be difficult for voters to carry out in practice. Also, if 17% of voters in Memphis were to stay away from voting, the winner would be Nashville. This is an example of IRV failing the participation criterion. For comparison, note that traditional
first-past-the-post voting In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...
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 A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...
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 result of the
1990 Irish presidential election The 1990 Irish presidential election was the tenth presidential election to be held in Ireland, the fifth to be contested by more than one candidate, and the first to have a female candidate and winner. It was held on Wednesday, 7 November 1990 ...
provides an example of how instant-runoff voting can produce a different result from
first-past-the-post voting In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...
. The three candidates were Brian Lenihan of the traditionally dominant
Fianna Fáil Fianna Fáil (, ; meaning 'Soldiers of Destiny' or 'Warriors of Fál'), officially Fianna Fáil – The Republican Party ( ga, audio=ga-Fianna Fáil.ogg, Fianna Fáil – An Páirtí Poblachtánach), is a conservative and Christia ...
party, Austin Currie of
Fine Gael Fine Gael (, ; English: "Family (or Tribe) of the Irish") is a liberal-conservative and Christian-democratic political party in Ireland. Fine Gael is currently the third-largest party in the Republic of Ireland in terms of members of Dáil É ...
, and
Mary Robinson Mary Therese Winifred Robinson ( ga, Máire Mhic Róibín; ; born 21 May 1944) is an Irish politician who was the 7th president of Ireland, serving from December 1990 to September 1997, the first woman to hold this office. Prior to her electi ...
, nominated by the Labour Party and the Workers' Party. After the first round, Lenihan had the largest share of the first-choice rankings (and hence would have won a first-past-the-post vote), but no candidate attained the necessary majority. Currie was eliminated and his votes reassigned to the next choice ranked on each ballot; in this process, Robinson received 82% of Currie's votes, thereby overtaking Lenihan.


2014 Prahran election (Victoria)

A real-life example of IRV producing a result which differs from what would be expected under a
first-past-the-post In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...
or the two-round voting system is the result for the seat of Prahran in the
2014 Victorian state election The 2014 Victorian state election, held on Saturday, 29 November 2014, was for the 58th Parliament of Victoria. All 88 seats in the Victorian Legislative Assembly and 40 seats in the Victorian Legislative Council were up for election. The incum ...
. In this instance, it was the candidate who initially finished ''third'' ( Greens candidate
Sam Hibbins Samuel Peter Hibbins (born 18 February 1982) is an Australian politician. He has been a Australian Greens Victoria, Greens member of the Victorian Legislative Assembly since November 2014, representing the electoral district of Prahran. Along wi ...
) in the primary vote went on to win the seat on the back of favourable preferences from the other two minor parties and independents, narrowly beating the second-ranked candidate (
Labor Labour or labor may refer to: * Childbirth, the delivery of a baby * Labour (human activity), or work ** Manual labour, physical work ** Wage labour, a socioeconomic relationship between a worker and an employer ** Organized labour and the la ...
candidate Neil Pharaoh) by 31 votes, and the first-ranked candidate ( Liberal candidate
Clem Newton-Brown Clement Arundel Newton-Brown (born 3 September 1967) is an Australian former politician who served as the member for Prahran in the Victorian Legislative Assembly. Political career Prior to his election, he worked as a barrister, specialis ...
) by 277 votes. It was not until the final round of counting that one of the two remaining candidates (Hibbins) had more than 50% of the total vote. In theory, the elimination of the center-left Labor candidate before the left-wing Green candidate could have transferred enough votes to the center-right Liberal candidate for him to win, but instead roughly 8:1 Labor voters chose the Green ahead of the Liberal.


2009 Burlington mayoral election

Unlike Burlington's first IRV mayoral election in 2006, the IRV winner in 2009 (Bob Kiss) was neither the same as the plurality winner (Kurt Wright) nor the
Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal p ...
winner (Andy Montroll). Burlington voters repealed IRV in 2010 by a vote of 52% to 48% and in 2021 voted to use RCV for city council elections by a vote of 64% to 36%. The organization
FairVote FairVote, formerly the Center for Voting and Democracy, is a 501(c)(3) organization that advocates electoral reform in the United States. Founded in 1992 as Citizens for Proportional Representation to support the implementation of proportional r ...
, which advocates for IRV, claimed the election as a success, citing three reasons (1) it prevented the election of the presumed winner under a plurality system by avoiding the effect of vote-splitting between the other candidates, (2) 99.99% of the ballots were valid suggesting that voters handled the system without difficulty, and (3) "contributed to producing a campaign among four serious candidates that was widely praised for its substantive nature." However, the election was considered a failure by advocates of the
Condorcet winner An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
, who point out that "in a head-to-head election, Andy Montroll should have beaten Bob Kiss by a 7.8% margin". In this case, a mutual majority causes a lock-out of a sufficiently large (e.g. plurality) minority. In examples where a smaller minority would break the lock-out ''and'' would change the winner in their favor, the participation criterion is violated. Wright voters were 40%, versus voters who placed Montroll and Kiss above Wright at 51.5%. That means a lot of Wright voters would have had to stay home for their demographic to matter at all, causing a participation criterion failure. If Wright voters preferred Montroll over Kiss, it would have been more advantageous to abstain or not give Wright their first preference; this would then result in Montroll reaching the final runoff and beating Kiss (54% to 46%), as opposed to the actual final runoff between Wright and Kiss. This would elect the candidate who started with only the third most primary votes, Montroll, and still would not be able to elect Wright without more of Montroll voters’ preferences or a higher primary vote (possibly to the point of having an outright majority)


Comparison of Schulze to preferential voting systems


See also

* Alternative vote plus (AV+), or alternative vote top-up, proposed by the Jenkins Commission in the UK *
Comparison of electoral systems Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner (or several winners) from the ballots cast. This article discusses methods and results of comparing different electora ...
*
First-past-the-post voting In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast the ...
*
None of the above "None of the above" (NOTA), or none for short, also known as "against all" or a "scratch" vote, is a ballot option in some jurisdictions or organizations, designed to allow the voter to indicate disapproval of the candidates in a voting syste ...
(NOTA) or Re-open Nominations (RON) * Outline of democracy *
Ranked-choice voting in the United States Ranked-choice voting (RCV) is a ranked voting system used in some states and cities in the United States in which voters may prioritize (rank) their choice of candidates among many, and a procedure exists to count lower ranked candidates if and af ...
*
Ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...
*
Single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
, AV method for elections with multiple positions to be filled (for example the
Australian Senate The Senate is the upper house of the bicameral Parliament of Australia, the lower house being the House of Representatives. The composition and powers of the Senate are established in Chapter I of the Constitution of Australia. There are a t ...
)


References


External links


Preferential Voting
at Australian Eelectoral Commission * 2010 articles from th
Constitution Society
an
Electoral Reform Society
summarizing the proposed change in the United Kingdom to IRV/Alternative Vote


Practice


Advantages and disadvantages of AV
from th
ACE Project
Electoral Design Reference Materials
A Handbook of Electoral System Design
fro
International IDEA

Australian Electoral Commission Web Site
**
Australian Senate The Senate is the upper house of the bicameral Parliament of Australia, the lower house being the House of Representatives. The composition and powers of the Senate are established in Chapter I of the Constitution of Australia. There are a t ...
: **
Australian House of Representatives The House of Representatives is the lower house of the bicameral Parliament of Australia, the upper house being the Senate. Its composition and powers are established in Chapter I of the Constitution of Australia. The term of members of ...
:
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.

OpenSTV – Open source software for computing IRV and STV

''Favourite Futurama Character Poll''

Voting System Visualizations
– 2-dimensional plots of results of various methods, with assumptions of sincere voting behavior.

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
FairVote FairVote, formerly the Center for Voting and Democracy, is a 501(c)(3) organization that advocates electoral reform in the United States. Founded in 1992 as Citizens for Proportional Representation to support the implementation of proportional r ...

League of Women Voters of Vermont

Ranked Choice Voting
at epresent.Us
InstantRunoff.com
*
Ranked Ballot Initiative of Toronto ''Ranked Ballot Initiative of Toronto'' (RaBIT) is a Canadian, grassroots, public policy and advocacy group that supports reforming the municipal electoral voting system in the city of Toronto from a first-past-the-post voting system to instant ...

rabit.ca

Roosevelt Institution

Citizens for Voter Choice :: Massachusetts

FairVote Minnesota

Common Cause Massachusetts

Brookings Institution's "Empowering Moderate Voters" paper



Opposition groups and positions


Center for Election Science
compares Instant runoff to
Approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...

Fair Vote Canada paper
on the Alternative Vote

at the
Center for Range Voting Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added (or averaged), and the candidate with the highest total is elected. It has been described by various ...

Instant Runoff Voting Report
Values and Risks Report by the N.C. Coalition for Verified Voting {{DEFAULTSORT:Instant-Runoff Voting Non-monotonic electoral systems Preferential electoral systems Single-winner electoral systems