Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where one or more eliminations are used to simulate multiple runoff elections. In each round, the candidate with the fewest first-preference votes among the remaining candidates is eliminated. This continues until only one candidate is left. Instant runoff falls under the plurality-with-elimination family of voting methods, and is thus closely related to methods like the two-round system and party primary.
Instant-runoff voting is used in the national elections of several countries, especially countries which were formerly part of the British Empire. It is used to elect members of the Australian House of Representatives and the National Parliament of Papua New Guinea, and to elect the head of state in India, Ireland, and Sri Lanka.
The system was first discussed by the Marquis de Condorcet, who showed the rule could eliminate the majority-preferred candidate (Condorcet winner). Other critics of instant-runoff voting have pointed to further mathematical pathologies, including the ability of certain implementations to have the potential to eliminate candidates for having too much support or too many votes. Like first-past-the-post voting (FPTP), instant-runoff is vulnerable to a kind of spoiler effect called a center squeeze, which causes it to favor uncompromising alternatives over more-moderate ones, encouraging polarization.
Advocates of instant-runoff voting often argue these properties are positive, as winner-take-all methods can leave a large portion of the electorate without representation. For example, in a race that tabulates votes using a simple majority, if a candidate wins with only 40% of the vote, this means that the majority (60%) of the electorate did not vote for the winning candidate. In countries without primaries or runoffs, like the United Kingdom, instant-runoff voting is seen as preventing spoiler effects by eliminating minor-party candidates because it avoids some kinds of vote-splitting by nearly identical (clone) candidates. IRV has also been described as a natural extension of the two-round system or primary elections that avoids multiple rounds of voting. Some advocates also argue that voting methods should encourage candidates to appeal to their core support or political base rather than a broad coalition.
Election procedure
In instant-runoff voting, as with other ranked voting methods, each voter orders candidates from first to last. The counting procedure is then as follows:
If there is more than one candidate left, eliminate the one with the fewest voters ranking them first. Reassign votes held by the eliminated candidates to the next-highest preference on each ballot paper (setting aside any with no remaining preferences). Return to step 1.
This procedure is often described as stopping when a candidate reaches a majority, but there is no guarantee that any candidate will reach more than half the votes. (In practice, most candidates who do not have a majority in the first round do not achieve a majority under IRV.)
Properties and pathologies Center squeeze
Wasted votes and Condorcet winners Compared to a plurality voting system that rewards only the top vote-getter using non-transferable votes, 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.
Some advocates of instant-runoff voting argue that the failure to elect a Condorcet winner is positive, as it enables instant-runoff voting to pass later-no-help and later-no-harm, which together render the method immune to burying strategy. FairVote, in particular, has stated that they "believe [later-no-harm] is necessary in the context of high-stakes, competitive elections".
Resistance to strategy Instant-runoff voting has notably high resistance to tactical voting but less to strategic nomination.
Party strategizing and strategic nomination In Australia, preference deals (where one party's voters agree to place another party's voters second, in return for their doing 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 the first place. Spatial model simulations indicate that instant runoff rewards strategic withdrawal by candidates.
Tactical voting
Gibbard's theorem demonstrates that no (deterministic, non-dictatorial) voting method can be entirely immune from tactical voting. This implies that instant-runoff voting is susceptible to tactical voting in some circumstances. In particular, when there exists a Condorcet winner who instant-runoff voting fails to elect, voters who prefer the Condorcet winner to the instant-runoff voting winner have an incentive to use the compromising strategy. instant-runoff voting is also sometimes vulnerable to a paradoxical strategy of ranking a candidate higher to make them lose, due to instant-runoff voting failing the monotonicity criterion.
Research suggests that instant-runoff voting is highly resistant to strategic voting. In a test of multiple methods, instant runoff was found to be the second-most-resistant to tactical voting, after a class of instant runoff-Condorcet hybrids. Instant-runoff voting 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 instant-runoff voting 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.
Spoiler effect
Proponents of instant-runoff voting claim that instant-runoff voting eliminates the spoiler effect, since instant-runoff voting 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. Instant-runoff voting 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 instant-runoff voting, 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 second-favorite first and their favorite second, rather than first (favorite betrayal). This is the same bracketing effect exploited by Robinette and Tideman in their research on strategic campaigning, where a candidate alters their campaign to cause a change in voter honest choice, resulting in the elimination of a candidate who nevertheless remains more preferred by voters. This occurred in the 2022 Alaska's at-large congressional district special election. If Republican Sarah Palin, who lost in the end, had not run, the more centrist Republican candidate, Nick Begich, would have defeated the winning Democratic candidate, Mary Peltola, because the ballot data shows that the votes for the two Republican candidates would have been combined behind Begich and would have exceeded those of Peltola. This did not happen in the IRV election due to the way 15,000 Begich supporters marked their back-up preferences across party lines.
This may be observed when a candidate leads in the first count but is in the end unsuccessful. For example, in the 2009 Burlington, Vermont, mayoral election, if Kurt Wright, the Republican candidate who lost in the end, had not run, the Democratic candidate, Andy Montroll, would have defeated the winning Progressive candidate, Bob Kiss. In that sense, the Republican candidate was a spoiler—albeit for an opposing Democrat, rather than some political ally—even though he led in first-choice support.
Failed criteria
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 instant-runoff voting does not meet this criterion.
Instant-runoff voting 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 instant-runoff voting winner was the Condorcet winner, including a San Francisco election in which the instant-runoff voting winner was in third place in first choice rankings.
Two notable Condorcet failures occurred with the 2009 Burlington mayoral election and the 2022 Alaska's at-large congressional district special election.
Independence of irrelevant alternatives The independence of irrelevant alternatives criterion states that "the election outcome remains the same even if a candidate who cannot win decides to run." Instant-runoff voting violates this. 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 the Minimax Condorcet method.
Monotonicity criterion The monotonicity criterion says that a voter ranking a candidate higher on their ballot should not cause that candidate to lose and conversely, that a voter ranking a candidate lower on their ballot should not help that candidate win. The exact probability of a monotonicity failure depends on the circumstances, but with 3 major candidates, the probabilities range from 15 percent under the impartial culture model to 8.5 percent in the case of a strict left–right spectrum.
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 A to B. Instant-runoff voting fails this criterion. In his 1984 study, mathematician Depankar Ray found that in elections where instant-runoff voting elects a different candidate from plurality, that there was an estimated 50 percent probability that some voters would have received a more preferable outcome if they had not participated.
Reversal symmetry criterion