Instant-runoff voting (IRV), also known as ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV),[1] is a multi-round elimination method where the loser of each round is determined by the first-past-the-post method.[2][3] In academic contexts, the term instant-runoff voting is generally preferred as it does not run the risk of conflating the method with methods of ranked voting in general.

IRV is counted in steps. In each step, IRV looks at every ballot's top non-eliminated candidate and eliminates the candidate with the fewest top rankings. It falls into the plurality-with-elimination family of voting systems, alongside first-past-the-post and systems based on runoff elections. It contrasts with the rated voting and majority-rule methods of elections.

IRV has been used in Australia,[4] for the president of Ireland,[5] and for the National Parliament of Papua New Guinea.[6]

## Election procedure

### Process

In instant-runoff voting, as with other ranked election methods, each voter orders candidates from first to last. On their ballot, voters mark a "1" beside their first-round vote; a "2" beside their alternative, who receives their vote if the first candidate is eliminated; a "3" beside their next alternative; and so on, until every candidate has been ranked.[7]

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, reassign votes held by the eliminated candidate to the highest available choice. Return to step 1.

Sometimes, this algorithm is described with an early-stopping rule, which elects a candidate as soon as their score exceeds half the remaining votes. This is because when a candidate has over half the votes, it is no longer mathematically possible for another candidate to defeat them (see Droop quota), allowing the process to be stopped early without counting the remaining votes. As a result, IRV is often mistakenly referred to as electing "majority winners".[citation needed]

However, this is an implementation detail, and does not mean candidates are supported by most voters. Note that without early stopping, IRV eventually reassigns all active votes to the winner, creating the appearance of unanimity (which is clearly impossible). It is possible for a candidate to win an instant-runoff election despite no support (i.e. complete opposition) from more than half of voters, even when there is an alternative majority-approved candidate, as in the 2022 Alaska's special election. This effect occurs when some voters truncate their ballots if they do not support any of the candidates in the final round.[8] In practice, most close IRV races do not elect a majority-approved candidate because of this effect.[9]

Social choice theorists generally define a majority-preferred candidate or majority winner as one who would defeat any one of their opponents in a one-on-one majority vote. Instant-runoff voting does not always elect the majority-preferred candidate in this sense either (see #Examples).[citation needed]

### 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.[10] However, it does not ensure the election of a Condorcet winner, which is the candidate who would win a direct election against any other candidate in the race.

### 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.[11] Since Australia has compulsory voting, however, it is difficult to tell how many ballots are deliberately spoiled.[12]

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.[13]

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.[14]

### Resistance to strategy

#### 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. Preference deals between parties (where one party's voters agree to place another party's voters second, in return for their doing the same) are common.[15]

#### Spoiler effect

Proponents of IRV claim that IRV eliminates the spoiler effect, since IRV makes it safe to vote honestly for marginal parties: Under a plurality method, voters who sympathize most strongly with a marginal candidate are strongly encouraged to instead vote for a more popular candidate who shares some of the same principles, since that candidate has a much greater chance of being elected and a vote for the marginal candidate will not result in the marginal candidate's election. An IRV method reduces this problem, since the voter can rank the marginal candidate first and the mainstream candidate second; in the likely event that the fringe candidate is eliminated, the vote is not wasted but is transferred to the second preference.[citation needed]

However, when the third-party candidate is more competitive, they can still act as a spoiler under IRV,[16][17][18] 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).[19][better source needed] 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.[18] 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.[20][better source needed]

### 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.[citation needed] 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.[21]

### Criticism

#### Voter confusion and legitimacy of elections

Governor Paul LePage[22] and Representative Bruce Poliquin[23] claimed, ahead of the 2018 primary elections, that IRV would result in "one person, five votes", as opposed to "one person, one vote". Federal judge Lance Walker rejected these claims, and the 1st circuit court denied Poliquin's emergency appeal.[24]

#### Similarity to plurality

Most[quantify] instant-runoff voting elections are won by the candidate who leads in first-choice rankings, choosing the same winner as plurality voting.[citation needed] 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.[25]

#### Participation

The effect of IRV on voter turnout is difficult to assess. In a 2021 report, researchers at New America, a think tank based in Washington, D. C., said it may increase turnout by attracting more and more diverse candidates, but the impact would be realized most significantly by getting rid of the need for primaries.[26] The overall impact on diversity of candidates is difficult to detect.[27]

## 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 voters do not need to turn out several times to vote.[28] It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting.[29]

Britons and New Zealanders generally call IRV the "alternative vote" (AV).[30][31] Australians, who use IRV for most single winner elections, call IRV "preferential voting".[32] 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.[33][34] As a result of American influence, the term ranked-choice voting is often used in Canada as well.[35] American NGO FairVote has promoted the terminology "ranked-choice voting" to refer to IRV,[35][36] 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.[citation needed]

IRV is occasionally referred to as Hare's method[37] (after Thomas Hare) to differentiate it from other ranked-choice voting methods such as majority-choice voting, Borda, and Bucklin.

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.[38] State law in South Carolina[39] and Arkansas[40] use "instant runoff" to describe the practice of having certain categories of absentee voters cast ranked-choice ballots before the first round of an election and counting those ballots in any subsequent runoff elections.

## History and use

### History

This method was first discussed by the Marquis de Condorcet in 1788, who quickly rejected it after showing it would often eliminate a candidate preferred by a majority of voters.[41][42]

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

### Global use

#### 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[43]
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[44] (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.[45][46][47][48]

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

### 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.[49] 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[50] and Riddick's Rules of Procedure,[51] 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. Because holding many rounds of voting on separate days is generally expensive, the exhaustive ballot is not used for large-scale, public elections.

A more practical form of runoff voting is the two-round system, which excludes all but the top-two candidates after the first round, rather than gradually eliminating candidates over a series of rounds. Eliminations can occur with or without allowing and applying preference votes to choose the final two candidates. A second round of voting or counting is only necessary if no candidate receives an overall majority of votes. This method is used in Mali, France and the Finnish and Slovenian presidential election.

### Contingent vote

The contingent vote, also known as "top-two IRV" or the "supplementary vote", is the same as IRV, except that if no candidate achieves a majority in the first round of counting, all but the two candidates with the most votes are eliminated, and the second preferences for those ballots are counted. As in IRV, there is only one round of voting.

Under a variant of contingent voting used in Sri Lanka, and the elections for Mayor of London in the United Kingdom, voters rank a specified maximum number of candidates. In London, the supplementary vote allowed[lower-alpha 1] 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.[52] Louisiana uses it only for members of the United States Service or who reside overseas.[53][better source needed][needs update]
• 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.[49]

### 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.[54][better source needed]

### Variations

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

In an optional preferential voting system, voters can give a preference to as many candidates as they wish. They may make only a single choice, known as "bullet voting", and some jurisdictions accept a single box marked with an "X" (as opposed to a numeral "1") as valid for the first preference. This may result in exhausted ballots, where all of a voter's preferences are eliminated before a candidate is elected, such that the "majority" in the final round may only constitute a minority fraction of all ballots cast. Optional preferential voting is used for elections for the President of Ireland as well as some elections in New South Wales and Queensland.[55][56]

In a full-preferential voting method, voters are required to mark a preference for every candidate standing.[57] 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.[58]

A version of instant-runoff voting applying to the ranking of parties was first proposed for elections in Germany in 2013[59] as spare vote.[citation needed]

## 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.[citation needed]

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.[citation needed]

### 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.[60]

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.[61][better source needed] 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".[citation needed]

### Pathologies of IRV

#### Condorcet winner criterion

The Condorcet winner criterion states that "if a candidate would win a head-to-head competition against every other candidate, then that candidate must win the overall election". It is incompatible with the later-no-harm criterion, so IRV does not meet this criterion.

IRV is more likely to elect the Condorcet winner than plurality voting and traditional runoff elections. The California cities of Oakland, San Francisco and San Leandro in 2010 provide an example; there were a total of four elections in which the plurality-voting leader in first-choice rankings was defeated, and in each case the IRV winner was the Condorcet winner, including a San Francisco election in which the IRV winner was in third place in first choice rankings.

Systems which fail Condorcet but pass mutual majority can exclude voters outside the mutual majority from the vote, essentially becoming an election between the mutual majority.[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. This is less likely to happen than under plurality, but much more likely than under ranked pairs or score voting.[citation needed]

#### Monotonicity criterion

The monotonicity criterion says that ranking a candidate higher on your ballot should not cause them to lose. The exact probability of a monotonicity failure depends on the circumstances, but with 3 major candidates, the probabilities range from 14.5 percent under the impartial culture model[citation needed] to 8.5 percent in the case of a strict left–right spectrum,[62] quickly approaching 100 percent for more than a handful of candidates.

#### Participation criterion

The participation criterion says that candidates should not lose as a result of having "too many voters"—a set of ballots that all rank A>B should not switch the election winner from B to A. IRV fails this criterion: about 50 percent of elections where IRV elects a different candidate from plurality involve participation failures.[63]

#### 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.[citation needed]

## Examples

### 1990 Irish presidential election

The 1990 Irish presidential election provides a simple example of how instant-runoff voting can produce a different result from first-past-the-post voting and prevent some spoiler effects associated with plurality voting. The three major candidates were Brian Lenihan of Fianna Fáil, Austin Currie of Fine Gael, and Mary Robinson of the Labour Party. After the first count, Lenihan had the largest share of first-choice rankings. Currie had the fewest votes and was eliminated. After this, Robinson received 82 percent of Currie's votes, thereby overtaking Lenihan.

Irish presidential election, 1990[64]
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%
Close

### 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.[65] In the 7th round, Hibbins narrowly defeated Coalition candidate Clem Newton-Brown by a margin of 277 votes.

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

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 Eliminated
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
Close

### 2009 Burlington mayoral election

Burlington mayoral election, 2009 (round-by-round analysis of votes)
Candidates 1st round 2nd round 3rd round
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
Close

Under Burlington's second-ever IRV mayoral election in 2009, the winner, Bob Kiss, was elected over the more popular Andy Montroll as a result of a first-round spoiler effect.

FairVote touted the 2009 election as one of its major success stories,[66] claiming it helped the city save on costs of a traditional runoff[66][67] and prevented a spoiler effect,[68] although later analysis showed that without Wright in the election, Montroll would have defeated Kiss in a one-on-one race.[69]

Mathematicians and voting theorists criticized the election results as revealing several pathologies associated with instant-runoff voting, noting that Kiss was elected as a result of 750 votes cast against him (ranking Kiss in last place).[70][71]

Several electoral reform advocates branded the election a failure after Kiss was elected, despite 54 percent of voters voting for Montroll over Kiss,[72] violating the principle of majority rule.[69][73][74][75]

Locals argued the system was convoluted,[67] turned the election into a "gambling game" by disqualifying Montroll for having won too many votes,[71][75] and "eliminated the most popular moderate candidate and elected an extremist".

Burlington mayoral election, 2009 (summary analysis)
Party Candidate Maximum
round
Maximum
Share in
maximum
round
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%
Close

## Comparison to other voting systems

Comparison of single-winner voting systems
Criterion

Method
Majority 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
Anti-plurality No Yes No No No No No No No Yes Yes No No Yes Single mark
Approval Yes No No No No No No Yes[Tn 2] Yes Yes Yes No Yes Yes Appr­ovals
Baldwin Yes Yes Yes Yes Yes Yes No No No No No No No No Ran­king
Black Yes Yes No Yes Yes No No No No Yes No No No No Ran­king
Borda No Yes No No Yes No No No No Yes Yes No Yes No Ran­king
Bucklin Yes Yes Yes No No No No No No Yes No No Yes No Ran­king
Coombs Yes Yes Yes No Yes No No No No No No No No Yes Ran­king
Copeland Yes Yes Yes Yes Yes Yes Yes No No Yes No No No No Ran­king
Dodgson Yes No No Yes No No No No No No No No No No Ran­king
Highest median Yes Yes[Tn 3] No[Tn 4] No No No No Yes[Tn 2] Yes Yes No[Tn 5] No Yes Yes Scores
Instant-runoff Yes Yes Yes No Yes No No No Yes No No Yes Yes No Ran­king
Kemeny–Young Yes Yes Yes Yes Yes Yes Yes LIIA Only No Yes No No No No Ran­king
Minimax Yes No No Yes[Tn 6] No No No No No Yes No No[Tn 6] No No Ran­king
Nanson Yes Yes Yes Yes Yes Yes No No No No No No No No Ran­king
Plurality Yes No No No No No No No No Yes Yes Yes Yes No Single mark
Random ballot[Tn 7] No No No No No No No Yes Yes Yes Yes Yes Yes Yes Single mark
Ranked pairs Yes Yes Yes Yes Yes Yes Yes LIIA Only Yes Yes No[Tn 5] No No No Ran­king
Runoff Yes Yes No No Yes No No No No No No Yes Yes No Single mark
Schulze Yes Yes Yes Yes Yes Yes Yes No Yes Yes No[Tn 5] No No No Ran­king
Score No No No No No No No Yes[Tn 2] Yes Yes Yes No Yes Yes Scores
Sortition[Tn 8] No No No No No No No Yes No Yes Yes Yes Yes Yes None
STAR No Yes No No Yes No No No No Yes No No No No Scores
Tideman alternative Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No Ran­king
Table Notes
1. 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.
2. 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.
3. 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.
4. 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.
5. A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
6. 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.
7. Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.
Close