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Instant-runoff voting

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For the proportional electoral system applying ranked ballots to multi-member constituencies, see Single transferable vote.

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Paradoxes and pathologies
Spoiler effects

Pathological response

Strategic voting

Paradoxes of majority rule

Social and collective choice
Impossibility theorems

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Instant-runoff voting (IRV), also known as plurality with elimination or sequential loser plurality,[1] is a ranked-choice voting system that modifies plurality by repeatedly eliminating the last-place winner until only one candidate is left.[2][3] In the United Kingdom, it is generally called the alternative vote (AV).[4] In the United States, IRV is often referred to as ranked-choice voting (RCV), by way of conflation with ranked voting systems in general;[5] however, this use is not widespread outside of North America.

IRV elections are a virtual (instant) variation on exhaustive elimination. In each round, voters choose a favourite 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. In Australia, it is used to elect members of the federal House of Representatives,[6] as well as the lower houses in most states, and in some local government elections. It is used to elect the president of India, the president of Ireland,[7] and the National Parliament of Papua New Guinea.[8] It is also used in choosing the Academy Award for Best Picture,[citation needed] and a non-instant variant is used for the TV show American Idol.[citation needed]

Election procedure

Process

Flowchart of instant-runoff voting

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.[9]

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, 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, similar to an exhaustive ballot system, except that voter preferences do not change between rounds.[10] It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting.[11]

Britons and New Zealanders generally call IRV the "alternative vote" (AV).[12][13] Australians, who use IRV for most single winner elections, call IRV "preferential voting".[14] While this term is widely used by Australians, it is somewhat of a misnomer: Depending on how "preferential" is defined, the term would either include all voting systems or else would exclude IRV (as it fails positive responsiveness, implying ballot markings cannot be reinterpreted as "preferences" in the traditional sense).

Jurisdictions in the United States such as San Francisco, Minneapolis, Maine, and Alaska have tended to use the term "ranked choice voting" in their laws. The San Francisco Department of Elections claimed the word "instant" in the term "instant-runoff voting" could confuse voters into expecting results to be immediately available.[15][16] As a result of American influence, the term ranked-choice voting is often used in Canada as well.[17] American NGO FairVote has promoted the terminology "ranked choice voting" to refer to IRV, a choice that has caused controversy and accusations that the organization is attempting to obscure the existence of other ranked-choice methods that could compete with IRV.[18][19]

IRV is occasionally referred to either as Hare's method[20] (after Thomas Hare) or as Ware's method, after the American William Robert Ware, to differentiate it from other ranked-choice voting methods such as Condorcet, Borda, or Bucklin voting.

When the single transferable vote (STV) method is applied to a single-winner election, it becomes IRV; the government of Ireland has called IRV "proportional representation" based on the fact that the same ballot form is used to elect its president by IRV and parliamentary seats by proportional representation (STV), but IRV is a non-proportional winner-take-all (single-winner) election method, while STV elects multiple winners.[21] State law in South Carolina[22] and Arkansas[23] 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

Compared to a plurality voting system that rewards only the top vote-getter, instant-runoff voting mitigates the problem of wasted votes.[24] However, it does not eliminate this problem, or 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:

In IRV for a polarized election between left, right, and center, the votes for B are not wasted, but the consensus candidate (B) is not elected
Simple election example
First choice A B C
Second choice B A C B
Voters 36% 10% 20% 34%
  • 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 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 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, for instance in 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. This can happen in a scenario where candidate B is a compromise candidate between polarizing candidates A and C.

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,[25] and the rate of spoiled ballots is sometimes five times more common than plurality voting elections.[26][unreliable source?] Since Australia has compulsory voting, however, it is difficult to tell how many ballots are deliberately spoiled.[27] 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.[28]

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.[29]

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.[30] 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.[31]

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.[citation needed]

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.[32] 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 infamous example, the Minor Party Alliance successfully manipulated this system to win several seats in 2016, despite receiving almost no first-preference votes.

Tactical voting

See also: Tactical voting § Instant runoff 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",[33] and Australian political analyst Antony Green dismissing suggestions of tactical voting.[34] 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 hybrids, and did not resist strategic withdrawal by candidates well.[35] 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).[36]

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.[37] 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".[38] 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.[37] 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

Main article: 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 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,[39][40][41][42] 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,[43][44][45][46][47][48][49] 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).[50][51] 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.[37][52][49] 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.[53][54]

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.[55] 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.[56]

Proportionality

IRV is a single-winner application of the proportional voting system known as STV, with a Droop quota (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.[3] 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.[57]

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.[58] IRV is more likely to result in legislatures where no single party has an absolute majority of seats (a hung parliament),[citation needed] 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

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.[59] The argument that IRV represents plural voting is sometimes used in arguments over the "fairness" of the method, and has led to frequent legal challenges in the United States.[60]

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".[61] 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".[62] Federal judge Lance Walker rejected this claim, and the 1st circuit court denied Poliquin's emergency appeal, leading to Poliquin dropping his claim.[63]

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.[64]

Participation

The effect of IRV on voter turnout is difficult to assess. In a lengthy 2021 report, researchers at New America, a think tank based in Washington, D. C., said:[65]

With our sample of cases largely limited to municipal and often nonpartisan elections (in relatively engaged localities), the best we can say for RCV [ranked-choice voting], independent of timing considerations, is that it may increase local turnout from a pathetic baseline to a slightly less pathetic level by attracting more, and more diverse, candidates. However, if RCV is able to combine the primary and the general election into a single election, held in November alongside other national elections, it is likely to have a more powerful effect in boosting turnout.

The report concluded:[66]

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.

History and use

Main article: History and use of instant-runoff voting

History

This method was considered by the Marquis de Condorcet as early as 1788, though only to condemn it for its ability to eliminate a candidate preferred by a majority of voters.[67][68]

IRV can be seen as a special case of the single transferable vote 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 by American architect William Robert Ware, who suggested it could also be used for single-winner elections.[69][70] Ware noted that the vote counting took only two or three hours, less time than required to count votes in the previous university election when limited voting was used and each voter cast five votes.[71] Unlike the single transferable vote in multi-seat elections, however, the only votes transferred are cast by backers of candidates who have been eliminated. There are no transfers of surplus votes as under STV.

The first known use of an IRV-like method in a governmental election was in the 1893 general election in the Colony of Queensland (in present-day Australia).[72] The variant used for this election was a "contingent vote", where all candidates but two are eliminated in the first round, with one of the last two elected by majority after votes of the others are transferred. Queensland used contingent voting until 1942, one of the longest uses of the system anywhere.[73]

IRV in its true form (what was called Alternative Voting at the time) was first used in Western Australia, in the 1908 state election. To form up a majority behind one candidate, candidates are dropped one by one. The lower houses of all Australian states (except Tasmania and ACT) and the Australian House of Representatives are elected through IRV. The last state to adopt AV was Queensland in 1962, It had switched from contingent voting to single-member plurality in 1942.[74] (Multi-winner STV of the Hare-Clark version was introduced for the Tasmanian House of Assembly at the 1909 state election. ACT used modified d'Hondt (a party-list PR system) to 1995 when it adopted STV.)[75]

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 vote in conservative country areas, allowing Labor candidates to win without a majority of the vote. The conservative government of Billy Hughes introduced IRV (in Australia called "preferential voting") as a means of allowing competition between the Coalition 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.[76] IRV continued to benefit the Coalition until the 1990 election, when for the first time Labor obtained a net benefit from IRV.[77]

In 1990, for example, the small Baltic state of Estonia held its first post-Soviet elections under a combination of IRV and STV — a system which had been popularized by Rein Taagepera, an expatriate Estonian political scientist from the University of California.[78]

In 2000, Bosnia used IRV for its election.[78]

Global use

Main article: History and use of instant-runoff voting § Use by country

National level elections

Country Body or office Type of body or office Electoral system Total seats Notes
Australia House of Representatives Lower chamber of legislature IRV 151
Ireland President Head of State IRV
Dáil Éireann Lower chamber of legislature Single transferable vote (STV), by-elections using IRV 158[79]
Papua New Guinea National Parliament Unicameral legislature IRV 109
United States President (via Electoral College) Head of State and Government Alaska and Maine use IRV to select the state winner. In Maine, 2 electors are allocated to the winner and the others (currently 2) are allocated by congressional district, while in Alaska, the winner gets all electors of the state in the Electoral College system (as Alaska has only one at-large district, the effect is the same). 7 EVs[80] (out of 538)
House of Representatives Lower chamber of legislature IRV in Maine

Nonpartisan primary system with IRV in the second round (among top four candidates) in Alaska.[81][82][83][84]

3 (out of 435)
Senate Upper chamber of legislature 4 (out of 100)

Robert's Rules of Order

In the United States, the sequential elimination method used by IRV is described in Robert's Rules of Order Newly Revised as an example of ranked-choice voting that can be used to elect officers.[2] 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[85] and Riddick's Rules of Procedure,[86] take a similar stance.

Similar methods

Runoff voting

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

The runoff method closest to IRV is the exhaustive ballot. In this method—familiar to fans of the television show American Idol—one candidate is eliminated after each round, and many rounds of voting are used, rather than just two.[87] 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

Top-two IRV

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.[88] Louisiana uses it only for members of the United States Service or who reside overseas.[89]
  • 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.[2]

Comparison to first-past-the-post

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

Variations

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

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

In an optional preferential voting system, voters can give a preference to as many candidates as they wish. They may make only a single choice, known as "bullet voting", and some jurisdictions accept a single box marked with an "X" (as opposed to a numeral "1") as valid for the first preference. This may result in exhausted ballots, where all of a voter's preferences are eliminated before a candidate is elected, such that the "majority" in the final round may only constitute a minority fraction of all ballots cast. Optional preferential voting is used for elections for the President of Ireland as well as some elections in New South Wales and Queensland.[91][92]

In a full-preferential voting method, voters are required to mark a preference for every candidate standing.[93] 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.[94]

A version of instant-runoff voting applying to the ranking of parties was first proposed for elections in Germany in 2013[95] as spare vote.[96]

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.[97]

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.[98] 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".

Pathologies of IRV

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.[99] This is less likely than under plurality voting

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.[100]

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.[citation needed] 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.[99] This is less likely to happen than under plurality, but much more likely than under ranked pairs or score voting.

Monotonicity criterion

Further information: Monotonicity criterion § Instant-runoff voting and the two-round system are not monotonic

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[101] to 8.5 percent in the case of a strict left–right spectrum,[102] quickly approaching 100 percent for more than a handful of candidates.[101]

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.[103]

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.[104]

Examples

Tennessee capital election

Tennessee and its four major cities: Memphis in the far west; Nashville in the center; Chattanooga in the east; and Knoxville in the far northeast

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

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

The preferences of each region's voters are:

42% of voters
Far-West 		26% of voters
Center 		15% of voters
Center-East 		17% of voters
Far-East
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis


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

1st 2nd 3rd
Knoxville 17% 32% 58%
Memphis 42% 42% 42%
Nashville 26% 26% (eliminated)
Chattanooga 15% (eliminated)

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 center 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

See also: Irish presidential election, 1990

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. The three candidates were Brian Lenihan of the traditionally dominant Fianna Fáil party; Austin Currie of Fine Gael; and Mary Robinson, nominated by the Labour Party and the Workers' Party. After the first count, 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 preference ranked on each ballot; in this process, Robinson received 82 percent of Currie's votes, thereby overtaking Lenihan.

Irish presidential election, 1990[105]
Candidate Round 1 Round 2
Mary Robinson 612,265 38.9% 817,830 51.6%
Brian Lenihan 694,484 43.8% 731,273 46.2%
Austin Currie 267,902 16.9% (eliminated)
Exhausted ballots 9,444 0.6% 34,992 2.2%
Total 1,584,095 100% 1,584,095 100%

2014 Prahran election (Victoria)

Another real-life example of IRV producing results different from first-past-the-post can be seen in the 2014 Victorian general election in Prahran. In this 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.[106] In the 7th round, Hibbins narrowly defeated Coalition candidate Clem Newton-Brown by a margin of 277 votes.

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

2009 Burlington mayoral election

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

Under Burlington's second-ever IRV mayoral election in 2009, the winner, Bob Kiss, was elected over Andy Montroll even though he would have lost in a one-on-one election.[107][108][109][110]

The organization FairVote, which advocates for IRV, called the election a success, noting that the system prevented an unpopular first-round winner (Kurt Wright) from winning, as would have happened under a plurality voting system.[111]

However, the election prompted a storm of criticism from voting reform advocates and political scientists, who pointed out that Andy Montroll was more popular than Bob Kiss and would have beaten Kiss by a comfortable margin of 8 percent in a one-on-one election.[108][112][109] Backlash to the results led Burlington voters to repeal IRV in a 2010 referendum by a vote of 52 to 48 percent.[113][114]

The election was also a notable example of a participation and monotonicity failure, with Bob Kiss winning the election as a result of 750 ballots that ranked him in last place.[108] Removing these ballots, or moving Bob Kiss from last to first place, would have caused Kiss to lose the election (by defeating Wright, allowing Montroll to advance to the final round).[108]

Burlington mayoral election, 2009 (summary analysis)
Party Candidate Maximum
round 		Maximum
votes 		Share in
maximum
round 		Maximum votes
First round votesTransfer votes


Progressive Bob Kiss 3 4,313 48.0%
​​
Republican Kurt Wright 3 4,061 45.2%
​​
Democratic Andy Montroll 2 2,554 28.4%
​​
Independent Dan Smith 1 1,306 14.5%
​​
Green James Simpson 1 35 0.4%
​​
Write-in 1 36 0.4%
​​
Exhausted votes 606 6.7%
​​

Comparison to other voting systems

Comparison of single-winner voting systems
Criterion


Method
 Majority winner Majority loser Mutual majority Condorcet winner[Tn 1] Condorcet loser Smith[Tn 1] Smith-IIA[Tn 1] IIA/LIIA[Tn 1] Clone­proof Mono­tone Participation Later-no-harm[Tn 1] Later-no-help[Tn 1] No favorite betrayal[Tn 1] Ballot

type

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



See also

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  95. ^ Breyer, Patrick (November 2013). "Alternative II: Einführung einer Ersatzstimme" (PDF). Anhörung zum Entwurf eines Gesetzes zur Abschaffung der Fünf-Prozent-Sperrklausel bei Landtagswahlen in Schleswig-Holstein [Hearing on the draft law to abolish the five percent threshold in state elections in Schleswig-Holstein (Discussion paper)] (Report) (in German). Piratenfraktion im Schleswig-Holsteinischen Landtag. (Drs. 18/385).
  96. ^ "Dual Level Voting - Granting equal votes in a proportional election with a threshold". www.dualvoting.com.
  97. ^ Nanson, E. J. (1882). "Methods of election". Transactions and Proceedings of the Royal Society of Victoria. 19: 207–208. although Ware's method cannot return the worst, it may return the next worst.
  98. ^ Green-Armytage, James (2004). "A Survey of Basic Voting Methods". Archived from the original on 3 June 2013.
  99. ^ a b "Burlington Vermont 2009 IRV mayoral election". RangeVoting.org. Retrieved 17 April 2011.
  100. ^ FairVote. "Understanding the RCV Election Results in District 10". FairVote.org. Archived from the original on 26 July 2011. Retrieved 17 April 2011.
  101. ^ a b Smith, Warren D. "Monotonicity and Instant Runoff Voting". Retrieved 4 May 2011.
  102. ^ Lepelley, Dominique; Chantreuil, Frederic; Berg, Sven (1996). "The likelihood of monotonicity paradoxes in run-off elections". Mathematical Social Sciences. 31 (3): 133–146. doi:10.1016/0165-4896(95)00804-7.
  103. ^ Ray, Depankar (1986). "On the practical possibility of a 'no show paradox' under the single transferable vote". Mathematical Social Sciences. 11 (2): 183–189. doi:10.1016/0165-4896(86)90024-7.
  104. ^ Smith, Warren D. "Lecture 'Mathematics and Democracy'". Retrieved 12 May 2011.
  105. ^ "Presidential Election November 1990". ElectionsIreland.org. Retrieved 23 November 2009.
  106. ^ "State Election 2014: Prahran District (Distribution of preference votes)". Victorian Electoral Commission.
  107. ^ Bouricious, Terry (13 March 2009). "Point/Counterpoint: Terry Bouricius Attempts To Rip Professor Gierzynski A New One Over Instant Runoff Voting Controversy (Now With All New Gierzynski Update!)". Vermont Daily Briefing. Archived from the original on 19 October 2015. Retrieved 27 September 2017. the 2009 election suffered from not only the 'thwarted majorities' or Condorcet's paradox, but also the 'no-show paradox' that shows that Wright voters who preferred Montroll over Kiss (that is, ranked Montroll 2nd) would have been better staying home and not voting at all.
  108. ^ a b c d Gierzynski, Anthony; Hamilton, Wes; Smith, Warren D. (March 2009). "Burlington Vermont 2009 IRV mayoral election". RangeVoting.org. Retrieved 1 October 2017. Montroll was favored over Republican Kurt Wright 56% to 44% ... and over Progressive Bob Kiss 54% to 46% ... In other words, in voting terminology, Montroll was a 'beats-all winner,' also called a 'Condorcet winner' ... However, in the IRV election, Montroll came in third!
  109. ^ a b Olson, Brian (2009). "2009 Burlington Mayor IRV Failure". bolson.org. Retrieved 1 October 2017. This is an IRV failure. The IRV result is clearly not what people actually wanted. More people liked Montroll over Kiss than the other way around, but IRV elected the loser.
  110. ^ Sheldon-hess, Dale (16 March 2009). "IRV Fails in Its Own Backyard". The Least of All Evils. Retrieved 27 September 2017. Montroll would have beaten any other candidate in a one-on-one election.
  111. ^ Bouricius, Terry (17 March 2009). "Response to Faulty Analysis of Burlington IRV Election". FairVote.org. Retrieved 1 October 2017. successfully prevented the election of the candidate who would likely have won under plurality rules, but would have lost to either of the other top finishers in a runoff
  112. ^ "Burlington's 2009 Mayoral Election: Did IRV Fail The Voters?". Integral Psychosis. 16 March 2009. Retrieved 1 October 2017. Montroll was the 'Beats-All winner' (aka the 'Condorcet winner') as he would have beaten both Wright (56% to 44%) and Kiss (54% to 46%) in head-to-head races, demonstrating that he was the preferred candidate by the majority of voters.
  113. ^ "Instant run-off voting experiment ends in Burlington". Rutland Herald Online. Archived from the original on 4 March 2016. Retrieved 15 December 2016.
  114. ^ "Burlington, Vermont, Question 4, Ranked-Choice Voting Amendment (March)". Ballotpedia.org. Retrieved 18 April 2021.

Practice

Demonstrations and simulations

Advocacy groups and positions

Opposition groups and positions

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