Instant-runoff voting

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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 introducing last-candidate elimination.[2][3] In the United Kingdom, it is generally called the alternative vote (AV).[4] In the United States and Australia, IRV is sometimes referred to simply as ranked-choice voting (RCV)[5] or preferential voting[6][7] respectively, though such terms are considered misnomers because of the wide variety of ranked-choice (preferential) voting systems other than IRV.

IRV elections are a virtual (instant) variation on multiple-round voting. 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,[8] as well as the lower houses in most states, and in some local government elections. It is the method used to elect the president of India, the president of Ireland,[9] and (in a modified form) the National Parliament of Papua New Guinea.[10] When used in city elections, the mayor is often elected through IRV.[11] 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[edit]

Process[edit]

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.[12]

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[edit]

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.[13] It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting.[14]

Britons and New Zealanders generally call IRV the "alternative vote" (AV).[15][16] while in Canada it is called "ranked choice voting".[17] Australians, who use IRV for most single winner elections, call IRV "preferential voting".[18] Jurisdictions using IRV such as San Francisco, California, Maine, Alaska, and Minneapolis, Minnesota have codified 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.[19][20]

IRV is occasionally referred to (rather confusingly) either as Hare's method[21] (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. American NGO FairVote uses the terminology "ranked choice voting" to refer to IRV in the case of single-winner offices, a choice that has caused controversy because it conflates instant runoff with[clarification needed].[22][23]

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.[24] State law in South Carolina[25] and Arkansas[26] 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[edit]

Wasted votes and Condorcet winners[edit]

Compared to a plurality voting system that rewards only the top vote-getter, instant-runoff voting mitigates the problem of wasted votes.[27] 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 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[edit]

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,[28] and the rate of spoiled ballots is sometimes five times more common than plurality voting elections.[29][unreliable source?] Since Australia has compulsory voting, however, it is difficult to tell how many ballots are deliberately spoiled.[30] 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.[31]

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.[32]

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.[33] 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.[34]

Resistance to strategy[edit]

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[edit]

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.[35] 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[edit]

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",[36] and Australian political analyst Antony Green dismissing suggestions of tactical voting.[37] 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.[38] 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).[39]

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.[40] 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".[41] 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.[40] 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[edit]

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,[42][43][44][45] 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,[46][47][48][49][50][51][52] 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).[53][54] 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.[40][55][52] 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.[56][57]

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.[58] 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.[59]

Proportionality[edit]

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.[60]

Australia[edit]

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.[61] 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[edit]

Voter confusion and legitimacy of elections[edit]

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.[62] 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.[63]

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".[64] 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".[65] Federal judge Lance Walker rejected this claim, and the 1st circuit court denied Poliquin's emergency appeal, leading to Poliquin dropping his claim.[66]

Similarity to plurality[edit]

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.

Participation[edit]

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:[67]

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:[68]

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[edit]

History[edit]

This method was considered by Condorcet as early as 1788, though only to condemn it for its ability to eliminate a candidate preferred by a majority of voters.[69][70]

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.[71][72] 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.[73] 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).[74] 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.[75]

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.[76] (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.)[77]

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.[78] IRV continued to benefit the Coalition until the 1990 election, when for the first time Labor obtained a net benefit from IRV.[79]

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.[80]

In 2000, Bosnia used IRV for its election.[80]

Global use[edit]

National level elections[edit]

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[81]
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[82] (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.[83][84][85][86]

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

Robert's Rules of Order[edit]

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[87] and Riddick's Rules of Procedure,[88] take a similar stance.

Similar methods[edit]

Runoff voting[edit]

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.

Exhaustive ballot[edit]

A method closer to IRV is the exhaustive ballot. In this method—one 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.[89] 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[edit]

The simplest form of runoff voting is the two-round system, 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[edit]

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. 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[edit]

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.[90] Louisiana uses it only for members of the United States Service or who reside overseas.[91]
  • 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, 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.[2]

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 of cast ballots.[92]

Comparison to first-past-the-post[edit]

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.[93]

Variations[edit]

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.[94][95]

In a full-preferential voting method, voters are required to mark a preference for every candidate standing.[96] 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.[97]

A version of instant-runoff voting applying to the ranking of parties was first proposed for elections in Germany in 2013[98] as spare vote.[99]

Voting method criteria[edit]

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[edit]

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.[100]

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.[101] 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[edit]

Condorcet winner criterion[edit]

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.[102]

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, Vermont,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.

Consistency criterion[edit]

The consistency 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[edit]

The independence of irrelevant alternatives 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.[103] This is much less likely to happen than under plurality.[citation needed]

Monotonicity criterion[edit]

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[104] claims failure is unlikely, at a less than 0.03 percent chance per election. Some critics[105] argue in turn that Allard's calculations are wrong and the probability of monotonicity failure is much greater, at 14.5 percent under the impartial culture election model in the three-candidate case, or 7 to 10 percent in the case of a left-right spectrum. Lepelley et al. find a 2 to 5 percent probability of monotonicity failure under the same election model as Allard.[106] 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[edit]

The participation criterion states that "the best way to help a candidate win must not be to abstain".[107] 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.[108] Depankar Ray finds a 50 percent probability that, when IRV elects a different candidate than Plurality, some voters would have been better off not showing up.[109]

Reversal symmetry criterion[edit]

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.[108]

Examples[edit]

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[edit]

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 second choice candidate for that voter becomes their new first choice, and their original third choice becomes their new second choice. This results in the Round 2 votes as seen below. This gives Sue three votes, which is a majority.

Round 1 Round 2
Candidate a b c d e Votes a b c d e Votes
Bob 1 2 3 1 2 2 1 2 2 1 2 2
Sue 3 1 2 3 1 2 2 1 1 2 1 3
Bill 2 3 1 2 3 1

Tennessee capital election[edit]

Most instant-runoff voting elections are won by the candidate who leads in first-choice rankings, choosing the same winner as plurality voting; in 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.[110]

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 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.

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

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities and that everyone wants to live as near to the capital as possible.

The candidates for the capital are:

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

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
  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.

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

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

If one of the cities had achieved a majority vote (more than half), the election would end there. If this were a first-past-the-post election, Memphis would win because it received the most votes. But IRV does not allow a candidate to win on the first round without having an absolute majority of the vote. While 42 percent of the electorate voted for Memphis, 58 percent 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 percent 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):

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

In the first round, Memphis was first, Nashville was second and Knoxville was third. With Chattanooga eliminated and its votes redistributed, the second round finds Memphis still in first place, followed by Knoxville in second and Nashville has moved down to third place.

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:

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

Result: Knoxville, which was running third in the first tabulation, has moved up from behind to take first place in the third and final round. The winner of the election is Knoxville. However, if 6 percent 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 percent of voters in Memphis were to stay away from voting, the winner would be Nashville. This is an example of IRV failing the participation criterion.

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

1990 Irish presidential election[edit]

Irish presidential election, 1990[111]
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%)
Exhausted ballots 9,444 (0.6%) 34,992 (2.2%)
Total 1,584,095 (100%) 1,584,095 (100%)

The 1990 Irish presidential election provides an 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.

2014 Prahran election (Victoria)[edit]

A real-life example of IRV producing a result which differs from what would be expected under a first-past-the-post or the two-round voting system is the result for the seat of Prahran in the 2014 Victorian state election. In this instance, it was the candidate who initially finished third (Greens candidate Sam Hibbins) 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 candidate Neil Pharaoh) by 31 votes, and the first-ranked candidate (Liberal candidate Clem Newton-Brown) by 277 votes. It was not until the final round of counting that one of the two remaining candidates (Hibbins) had more than 50 percent of the total vote.[112]

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.

Candidate[112] Primary vote First round Second round Third round Fourth round Fifth round Sixth round
Clem Newton-Brown (LIB) 16,582 44.8% 16,592 16,644 16,726 16,843 17,076 18,363 49.6%
Neil Pharaoh (ALP) 9,586 25.9% 9,593 9,639 9,690 9,758 9,948
Sam Hibbins (GRN) 9,160 24.8% 9,171 9,218 9,310 9,403 9,979 18,640 50.4%
Eleonora Gullone (AJP) 837 2.3% 860 891 928 999
Alan Walker (FFP) 282 0.8% 283 295
Jason Goldsmith (IND) 247 0.7% 263 316 349
Steve Stefanopoulos (IND) 227 0.6% 241
Alan Menadue (IND) 82 0.2%
Total 37,003 100%

2009 Burlington mayoral election[edit]

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
James Simpson Green 35 +35 0 −35
Write-in 36 +36 0 −36
Exhausted pile 4 +4 151 +147 606 +455
TOTALS[113] 8980 +8980

Under the 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 winner (Andy Montroll).[114][115][116][117] As a result, Burlington voters later repealed IRV in 2010 by a vote of 52 percent to 48 percent.[118][119]

The organization FairVote, 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) 99.9 percent 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".[120]

However, the election was considered a failure by advocates of the Condorcet voting method, who point out that "in a head-to-head election, Andy Montroll should have beaten Bob Kiss by a 7.8% margin".[115][116][121]

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 favour, the participation criterion is violated. Wright voters were 40 percent, versus voters who placed Montroll and Kiss above Wright at 51.5 percent. 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)

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[edit]

Comparison of Voting Systems
Criterion: Majority Majority loser criterion Mutual majority criterion Condorcet winner Condorcet loser Smith ISDA LIIA Cloneproof Monotone Participation Reversal Later-no-harm Later-no-help Polynomial time Resolvability
Schulze Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes No No Yes Yes
Ranked pairs Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No No Yes Yes
Tideman alternative Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No Yes Yes
Kemeny–Young Yes Yes Yes Yes Yes Yes Yes Yes No Yes No Yes No No No Yes
Ranked robin Yes Yes Yes Yes Yes Yes Yes No No Yes No Yes No No Yes No
Nanson Yes Yes Yes Yes Yes Yes No No No No No Yes No No Yes Yes
Black Yes Yes No Yes Yes No No No No Yes No Yes No No Yes Yes
Instant-runoff voting Yes Yes Yes No Yes No No No Yes No No No Yes Yes Yes Yes
Smith//IRV Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No Yes Yes
Borda count No Yes No No Yes No No No No Yes Yes Yes No Yes Yes Yes
Baldwin Yes Yes Yes Yes Yes Yes No No No No No No No No Yes Yes
Bucklin Yes Yes Yes No No No No No No Yes No No No Yes Yes Yes
Plurality Yes No No No No No No No No Yes Yes No Yes Yes Yes Yes
Coombs Yes Yes Yes No Yes No No No No No No No No No Yes Yes
Minimax Yes No No Yes No No No No No Yes No No No No Yes Yes
Anti-plurality No Yes No No No No No No No Yes Yes No No No Yes Yes
Dodgson Yes No No Yes No No No No No No No No No No No Yes

See also[edit]

References[edit]

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  114. ^ 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.
  115. ^ a b 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!
  116. ^ 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.
  117. ^ 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.
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  120. ^ 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
  121. ^ "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.

External links[edit]

Practice[edit]

Demonstrations and simulations[edit]

Advocacy groups and positions[edit]

Opposition groups and positions[edit]