Condorcet methods
74-460: Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Instant-runoff voting ( IRV ) ( US : ranked-choice voting or RCV , AU : preferential voting , UK : alternative vote )
148-686: A center squeeze , which may sometimes prevent the election of a Condorcet winner. Whilst the Marquis de Condorcet early on showed that it did not satisfy his Condorcet winner criterion , which it may fail under certain scenarios, instant-runoff voting satisfies many other majoritarian criteria, such as the majority criterion , mutual majority criterion and the Condorcet loser criterion . Advocates have argued these properties are positive, because voting rules should encourage candidates to focus on their core support or political base, rather than building
222-501: A 'cycle'. This situation emerges when, once all votes have been tallied, the preferences of voters with respect to some candidates form a circle in which every candidate is beaten by at least one other candidate ( Intransitivity ). For example, if there are three candidates, Candidate Rock, Candidate Scissors, and Candidate Paper , there will be no Condorcet winner if voters prefer Candidate Rock over Candidate Scissors and Scissors over Paper, but also Candidate Paper over Rock. Depending on
296-400: A 68% majority of 1st choices among the remaining candidates and won as the majority's 1st choice. As noted above, sometimes an election has no Condorcet winner because there is no candidate who is preferred by voters to all other candidates. When this occurs the situation is known as a 'Condorcet cycle', 'majority rule cycle', 'circular ambiguity', 'circular tie', 'Condorcet paradox', or simply
370-507: A broad coalition. They also note that in countries like the United Kingdom without primaries or runoff elections , IRV can prevent spoiler effects by eliminating minor-party candidates in early rounds, and that unlike plurality, it is not affected by the presence of duplicate candidates (clones) . In instant-runoff voting, as with other ranked voting rules, each voter orders candidates from first to last. The counting procedure
444-592: 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. This also occurred in
518-477: A class of instant runoff- Condorcet hybrids. IRV is also completely immune to the burying strategy: ranking a strong opposition candidate lower can't get one's preferred candidate elected. 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
592-491: A contest between candidates A, B and C using the preferential-vote form of Condorcet method, a head-to-head race is conducted between each pair of candidates. A and B, B and C, and C and A. If one candidate is preferred over all others, they are the Condorcet Winner and winner of the election. Because of the possibility of the Condorcet paradox , it is possible, but unlikely, that a Condorcet winner may not exist in
666-530: 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 formerly for the elections for Mayor of London in the United Kingdom, voters rank a specified maximum number of candidates. In London,
740-614: A majority. Compared to a plurality voting system that rewards only the top vote-getter, instant-runoff voting mitigates the problem of wasted votes . However, it does not ensure the election of a Condorcet winner , which is the candidate who would win a direct election against any other candidate in the race. 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 . Some political scientists have found
814-415: 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
SECTION 10
#1732772323924888-742: A result of American influence, the term ranked-choice voting is often used in Canada as well. 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. IRV is occasionally referred to as Hare's method (after Thomas Hare ) to differentiate it from other ranked-choice voting methods such as majority-choice voting , Borda , and Bucklin , which use weighted preferences or methods that allow voter's lower preference to be used against voter's most-preferred choice. When
962-532: A result of a kind of tie known as a majority rule cycle , described by Condorcet's paradox . The manner in which a winner is then chosen varies from one Condorcet method to another. Some Condorcet methods involve the basic procedure described below, coupled with a Condorcet completion method, which is used to find a winner when there is no Condorcet winner. Other Condorcet methods involve an entirely different system of counting, but are classified as Condorcet methods, or Condorcet consistent, because they will still elect
1036-549: 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. The contingent vote , also known as "top-two IRV", is the same as IRV, except that if no candidate achieves
1110-437: 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
1184-523: A specific election. This is sometimes called a Condorcet cycle or just cycle and can be thought of as Rock beating Scissors, Scissors beating Paper, and Paper beating Rock . Various Condorcet methods differ in how they resolve such a cycle. (Most elections do not have cycles. See Condorcet paradox#Likelihood of the paradox for estimates.) If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent. For most Condorcet methods, those counts usually suffice to determine
1258-427: A voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible that every candidate has an opponent that defeats them in a two-candidate contest. The possibility of such cyclic preferences is known as the Condorcet paradox . However, a smallest group of candidates that beat all candidates not in
1332-421: Is a single-winner , multi-round elimination rule that uses ranked voting to simulate a series of runoffs with only one vote. In each round, the candidate with the fewest votes is eliminated, and their votes are transferred to their next available preference until one of the options reaches a majority of the remaining votes. Instant runoff falls under the plurality-with-elimination family of voting methods, and
1406-407: Is also a Condorcet method, even though the voters do not vote by expressing their orders of preference. There are multiple rounds of voting, and in each round the vote is between two of the alternatives. The loser (by majority rule) of a pairing is eliminated, and the winner of a pairing survives to be paired in a later round against another alternative. Eventually, only one alternative remains, and it
1480-499: Is also referred to collectively as Condorcet's method. A voting system that always elects the Condorcet winner when there is one is described by electoral scientists as a system that satisfies the Condorcet criterion. Additionally, a voting system can be considered to have Condorcet consistency, or be Condorcet consistent, if it elects any Condorcet winner. In certain circumstances, an election has no Condorcet winner. This occurs as
1554-411: Is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner , is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately;
SECTION 20
#17327723239241628-412: Is an election between four candidates: A, B, C, and D. The first matrix below records the preferences expressed on a single ballot paper, in which the voter's preferences are (B, C, A, D); that is, the voter ranked B first, C second, A third, and D fourth. In the matrix a '1' indicates that the runner is preferred over the 'opponent', while a '0' indicates that the runner is defeated. Using a matrix like
1702-424: 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
1776-401: 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: The preferences of each region's voters are: To find the Condorcet winner every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing
1850-513: Is known as ambiguity resolution, cycle resolution method, or Condorcet completion method . Circular ambiguities arise as a result of the voting paradox —the result of an election can be intransitive (forming a cycle) even though all individual voters expressed a transitive preference. In a Condorcet election it is impossible for the preferences of a single voter to be cyclical, because a voter must rank all candidates in order, from top-choice to bottom-choice, and can only rank each candidate once, but
1924-440: Is no preference between candidates that were left unranked. Some Condorcet elections permit write-in candidates . The count is conducted by pitting every candidate against every other candidate in a series of hypothetical one-on-one contests. The winner of each pairing is the candidate preferred by a majority of voters. Unless they tie, there is always a majority when there are only two choices. The candidate preferred by each voter
1998-510: Is taken to be the one in the pair that the voter ranks (or rates) higher on their ballot paper. For example, if Alice is paired against Bob it is necessary to count both the number of voters who have ranked Alice higher than Bob, and the number who have ranked Bob higher than Alice. If Alice is preferred by more voters then she is the winner of that pairing. When all possible pairings of candidates have been considered, if one candidate beats every other candidate in these contests then they are declared
2072-404: Is the winner. This is analogous to a single-winner or round-robin tournament; the total number of pairings is one less than the number of alternatives. Since a Condorcet winner will win by majority rule in each of its pairings, it will never be eliminated by Robert's Rules. But this method cannot reveal a voting paradox in which there is no Condorcet winner and a majority prefer an early loser over
2146-422: Is then as follows: It is possible for a candidate to win an instant-runoff race without any support from more than half of voters, even when there is an alternative majority-approved candidate; this occurs when some voters truncate their ballots to show they do not support any candidates in the final round. In practice, candidates who do not receive a majority of votes in the first round usually do not finish with
2220-685: Is thus closely related to rules like the exhaustive ballot and two-round runoff system . IRV has found some use in national elections in several countries , predominantly in the Anglosphere . It is used to elect members of the Australian House of Representatives and the National Parliament of Papua New Guinea as well as the President of India , the President of Ireland , and the President of Sri Lanka . The rule
2294-437: 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 . The system has had a mixed reception among political scientists and social choice theorists . Some have suggested that the system does not do much to decrease
Instant-runoff voting - Misplaced Pages Continue
2368-426: The Marquis de Condorcet , who championed such systems. However, Ramon Llull devised the earliest known Condorcet method in 1299. It was equivalent to Copeland's method in cases with no pairwise ties. Condorcet methods may use preferential ranked , rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks
2442-457: 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. 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
2516-569: 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. State law in South Carolina and Arkansas use "instant runoff" to describe
2590-606: The supplementary vote allowed voters to express first and second preferences only. Sri Lankan voters rank up to three candidates to elect the president of Sri Lanka . Condorcet method Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A Condorcet method ( English: / k ɒ n d ɔːr ˈ s eɪ / ; French: [kɔ̃dɔʁsɛ] )
2664-477: The "alternative vote" (AV). Australians, who use IRV for most single winner elections, call IRV "preferential voting". While this term is widely used by Australians, it is somewhat of a misnomer . Depending on how "preferential" is defined, the term would include all voting systems, apply to any system that uses ranked ballots (thus both IRV and STV), or would exclude IRV (IRV fails positive responsiveness because ballot markings are not interpreted as "preferences" in
2738-428: The 1st circuit court denied Poliquin's emergency appeal. Often instant-runoff voting elections are won by the candidate who leads in first-count vote tallies so they choose the same winner as first-past-the-post voting would have. In Australia federal elections, the 1972 election had the largest number of winners who would not have won under first past the post but still only 14 out of 125 seats filled were not won by
2812-544: The Condorcet winner if there is one. Not all single winner, ranked voting systems are Condorcet methods. For example, instant-runoff voting and the Borda count are not Condorcet methods. In a Condorcet election the voter ranks the list of candidates in order of preference. If a ranked ballot is used, the voter gives a "1" to their first preference, a "2" to their second preference, and so on. Some Condorcet methods allow voters to rank more than one candidate equally so that
2886-430: The Condorcet winner to the IRV winner have an incentive to use the compromising strategy. IRV is also sometimes vulnerable to a paradoxical strategy of ranking a candidate higher to make them lose, due to IRV failing the monotonicity criterion . Research suggests that IRV is very resistant to tactical voting. In a test of multiple methods, instant runoff was found to be the second-most-resistant to tactical voting, after
2960-464: The Condorcet winner. As noted above, if there is no Condorcet winner a further method must be used to find the winner of the election, and this mechanism varies from one Condorcet consistent method to another. In any Condorcet method that passes Independence of Smith-dominated alternatives , it can sometimes help to identify the Smith set from the head-to-head matchups, and eliminate all candidates not in
3034-555: The Copeland winner has the highest possible Copeland score. They can also be found by conducting a series of pairwise comparisons, using the procedure given in Robert's Rules of Order described above. For N candidates, this requires N − 1 pairwise hypothetical elections. For example, with 5 candidates there are 4 pairwise comparisons to be made, since after each comparison, a candidate is eliminated, and after 4 eliminations, only one of
Instant-runoff voting - Misplaced Pages Continue
3108-640: The Schulze method, use the information contained in the sum matrix to choose a winner. Cells marked '—' in the matrices above have a numerical value of '0', but a dash is used since candidates are never preferred to themselves. The first matrix, that represents a single ballot, is inversely symmetric: (runner, opponent) is ¬(opponent, runner). Or (runner, opponent) + (opponent, runner) = 1. The sum matrix has this property: (runner, opponent) + (opponent, runner) = N for N voters, if all runners were fully ranked by each voter. [REDACTED] Suppose that Tennessee
3182-411: The basis for defining preference and determined that Memphis voters preferred Chattanooga as a second choice rather than as a third choice, Chattanooga would be the Condorcet winner even though finishing in last place in a first-past-the-post election. An alternative way of thinking about this example if a Smith-efficient Condorcet method that passes ISDA is used to determine the winner is that 58% of
3256-605: The candidates from most (marked as number 1) to least preferred (marked with a higher number). A voter's ranking is often called their order of preference. Votes can be tallied in many ways to find a winner. All Condorcet methods will elect the Condorcet winner if there is one. If there is no Condorcet winner different Condorcet-compliant methods may elect different winners in the case of a cycle—Condorcet methods differ on which other criteria they satisfy. The procedure given in Robert's Rules of Order for voting on motions and amendments
3330-496: The complete order of finish (i.e. who won, who came in 2nd place, etc.). They always suffice to determine whether there is a Condorcet winner. Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size. Such ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties. For example, with Copeland's method , it would not be rare for two or more candidates to win
3404-424: The context in which elections are held, circular ambiguities may or may not be common, but there is no known case of a governmental election with ranked-choice voting in which a circular ambiguity is evident from the record of ranked ballots. Nonetheless a cycle is always possible, and so every Condorcet method should be capable of determining a winner when this contingency occurs. A mechanism for resolving an ambiguity
3478-509: The emergence of a consensus candidate with broad support. The book instead recommends repeated balloting until some candidate manages to win a majority of votes. Two other books on American parliamentary procedure, The Standard Code of Parliamentary Procedure and Riddick's Rules of Procedure , take a similar stance. 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
3552-474: The eventual winner (though it will always elect someone in the Smith set ). A considerable portion of the literature on social choice theory is about the properties of this method since it is widely used and is used by important organizations (legislatures, councils, committees, etc.). It is not practical for use in public elections, however, since its multiple rounds of voting would be very expensive for voters, for candidates, and for governments to administer. In
3626-425: The first place. Spatial model simulations indicate that instant runoff rewards strategic withdrawal by candidates. Gibbard's theorem demonstrates that no (deterministic, non-dictatorial) voting method can be entirely immune from tactical voting. This implies that IRV is susceptible to tactical voting in some circumstances. In particular, when there exists a Condorcet winner who IRV fails to elect, voters who prefer
3700-521: The first-count leader. 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. The overall impact on diversity of candidates is difficult to detect. Instant-runoff voting derives its name from
3774-470: The following sum matrix: When the sum matrix is found, the contest between each pair of candidates is considered. The number of votes for runner over opponent (runner, opponent) is compared with the number of votes for opponent over runner (opponent, runner) to find the Condorcet winner. In the sum matrix above, A is the Condorcet winner because A beats every other candidate. When there is no Condorcet winner Condorcet completion methods, such as Ranked Pairs and
SECTION 50
#17327723239243848-921: The form of the single transferable vote . Henry Richmond Droop then proposed applying the system to single-winner contests. (He also invented the Droop quota , which equates to a simple majority in a single-winner contest.) Nonpartisan primary system with IRV in the second round (among top four candidates) in Alaska. In the United States, the sequential elimination method used by IRV is described in Robert's Rules of Order Newly Revised as an example of ranked-choice voting that can be used to elect officers. Robert's Rules note that ranked-choice systems (including IRV) are an improvement on simple plurality but recommend against runoff-based rules because they often prevent
3922-454: The group, known as the Smith set , always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcet winner, and is thus said to be "Smith-efficient". Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat,
3996-539: The impact of wasted votes relative to plurality. Research has found IRV causes lower confidence in elections and does not substantially affect minority representation, voter turnout , or long-run electoral competition . Opponents have also noted a high rate of repeals for the system. Governor Paul LePage and Representative Bruce Poliquin 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
4070-474: The likely event that the fringe candidate is eliminated, the vote is not wasted but is transferred to the second preference. However, when the third-party candidate is more competitive, they can still act as a spoiler under IRV, by taking away first-choice votes from the more mainstream candidate until that candidate is eliminated, and then that candidate's second-choice votes helping a more-disliked candidate to win. In these scenarios, it would have been better for
4144-425: The one above, one can find the overall results of an election. Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition . The sum of all ballots in an election is called the sum matrix. Suppose that in the imaginary election there are two other voters. Their preferences are (D, A, C, B) and (A, C, B, D). Added to the first voter, these ballots would give
4218-419: The original 5 candidates will remain. To confirm that a Condorcet winner exists in a given election, first do the Robert's Rules of Order procedure, declare the final remaining candidate the procedure's winner, and then do at most an additional N − 2 pairwise comparisons between the procedure's winner and any candidates they have not been compared against yet (including all previously eliminated candidates). If
4292-415: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Exhausted vote In the alternative vote , ballot exhaustion occurs when a voter's ballot can no longer be counted, because all candidates on that ballot have been eliminated from an election. Contributors to ballot exhaustion include: This may occur because the voter chooses not to fill out
4366-474: 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. 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. IRV was later independently reinvented by Thomas Hare (of England) and Carl Andrae (of Denmark) in
4440-426: The procedure's winner does not win all pairwise matchups, then no Condorcet winner exists in the election (and thus the Smith set has multiple candidates in it). Computing all pairwise comparisons requires ½ N ( N −1) pairwise comparisons for N candidates. For 10 candidates, this means 0.5*10*9=45 comparisons, which can make elections with many candidates hard to count the votes for. The family of Condorcet methods
4514-469: The same number of pairings, when there is no Condorcet winner. A Condorcet method is a voting system that will always elect the Condorcet winner (if there is one); this is the candidate whom voters prefer to each other candidate, when compared to them one at a time. This candidate can be found (if they exist; see next paragraph) by checking if there is a candidate who beats all other candidates; this can be done by using Copeland's method and then checking if
SECTION 60
#17327723239244588-541: The same) between parties are common. Parties and candidates often encourage their supporters to participate in these preference deals using How-to-vote cards explaining how to use their lower rankings to maximize the chances of their ballot helping to elect someone in the preference deal before it may exhaust. Instant runoff may be manipulable via strategic candidate entry and exit, reducing similar candidates' chances of winning. Such manipulation does not need to be intentional, instead acting to deter candidates from running in
4662-426: The set before doing the procedure for that Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one of the paired candidates over the other candidate, and another pairwise count indicates how many voters have the opposite preference. The counts for all possible pairs of candidates summarize all the pairwise preferences of all
4736-454: The system contributes to higher rates of spoiled votes , partly because the ballot marking is more complex. Most jurisdictions with IRV do not require complete rankings and may use columns to indicate preference instead of numbers. In American elections with IRV, more than 99 percent of voters typically cast a valid ballot. A 2015 study of four local US elections that used IRV found that inactive ballots occurred often enough in each of them that
4810-410: 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 (favorite betrayal). This is the same bracketing effect exploited by Robinette and Tideman in their research on strategic campaigning, where a candidate alters their campaign to cause a change in voter honest choice, resulting in the elimination of
4884-490: The traditional sense. Under IRV (and STV), secondary preferences are used as back-up preferences/contingency votes). 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 that apply to IRV contests. 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. As
4958-486: The voter might express two first preferences rather than just one. If a scored ballot is used, voters rate or score the candidates on a scale, for example as is used in Score voting , with a higher rating indicating a greater preference. When a voter does not give a full list of preferences, it is typically assumed that they prefer the candidates that they have ranked over all the candidates that were not ranked, and that there
5032-420: The voters, a mutual majority , ranked Memphis last (making Memphis the majority loser ) and Nashville, Chattanooga, and Knoxville above Memphis, ruling Memphis out. At that point, the voters who preferred Memphis as their 1st choice could only help to choose a winner among Nashville, Chattanooga, and Knoxville, and because they all preferred Nashville as their 1st choice among those three, Nashville would have had
5106-448: The voters. Pairwise counts are often displayed in a pairwise comparison matrix , or outranking matrix , such as those below. In these matrices , each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Cells comparing a candidate to themselves are left blank. Imagine there
5180-446: 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. It is also known as the alternative vote, transferable vote, ranked-choice voting (RCV), single-seat ranked-choice voting, or preferential voting (but use of some of those terms may lead to misunderstanding as they also apply to STV.) Britons and New Zealanders generally call IRV
5254-532: The winner is the candidate preferred by a majority of voters. When results for every possible pairing have been found they are as follows: The results can also be shown in the form of a matrix: ↓ 2 Wins ↓ 1 Win As can be seen from both of the tables above, Nashville beats every other candidate. This means that Nashville is the Condorcet winner. Nashville will thus win an election held under any possible Condorcet method. While any Condorcet method will elect Nashville as
5328-434: 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. Instant-runoff voting has notably high resistance to tactical voting but less to strategic nomination . In Australia, preference deals (where one party's voters agree to place another party's voters second, in return for their doing
5402-523: The winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting , these systems would select Memphis and Knoxville respectively. This would occur despite the fact that most people would have preferred Nashville to either of those "winners". Condorcet methods make these preferences obvious rather than ignoring or discarding them. On the other hand, in this example Chattanooga also defeats Knoxville and Memphis when paired against those cities. If we changed
5476-452: Was first developed and studied by the Marquis de Condorcet , who came to reject it after discovering it could eliminate the majority-preferred candidate in a race (today often called a Condorcet winner ). IRV is known to exhibit other mathematical pathologies , which include non-monotonicity and the no-show paradox . Like some other commonly-used systems, IRV also exhibits a kind of independence of irrelevant alternative violation called
#923076