Instant-runoff voting

For the proportional electoral system applying ranked ballots to multi-member constituencies, see single transferable vote.
For ranked methods in general, see ranked voting.

A joint Politics and Economics series
Social choice and electoral systems
Single-winner methods
Single vote - plurality methods

Condorcet methods

Positional voting

Cardinal voting

Proportional representation
Party-list

Quota-remainder methods

Approval-based committees

Fractional social choice

Semi-proportional representation

Mixed systems
By results of combination
By mechanism of combination

By ballot type

Paradoxes and pathologies
Spoiler effects

Pathological response

Strategic voting

Paradoxes of majority rule

Social and collective choice
Impossibility theorems

Positive results

icon Mathematics portal

Instant-runoff voting (IRV) (US: ranked-choice voting or RCV, AU: preferential voting, UK: alternative vote), is a single-winner, multi-round elimination rule that uses ranked voting to simulate a series of runoff elections. In each round, the last-place finisher according to a plurality vote is eliminated, and the votes supporting the eliminated choice 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,[1] and is thus closely related to rules like the exhaustive ballot and two-round runoff system[2][3]

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 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).[4][5][6] IRV is known to exhibit other mathematical pathologies, which include non-monotonicity[7] and the No-show paradox.[8][9] Like some other commonly-used systems, IRV also exhibits a kind of independence of irrelevant alternative violation called a center squeeze,[10][11] 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 a broad coalition.[12] 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).

  1. ^ Nurmi, Hannu (June 2005). "Aggregation problems in policy evaluation: an overview". European Journal of Political Economy. 21 (2): 287–300. doi:10.1016/j.ejpoleco.2004.08.001. ISSN 0176-2680.
  2. ^ Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.
  3. ^ Hyman, Ross; Otis, Deb; Allen, Seamus; Dennis, Greg (1 September 2024). "A majority rule philosophy for instant runoff voting". Constitutional Political Economy. 35 (3): 425–436. doi:10.1007/s10602-024-09442-3. ISSN 1572-9966.
  4. ^ Condorcet, Jean-Antoine-Nicolas de Caritat (1788). "On the Constitution and the Functions of Provincial Assemblies". Complete Works of Condorcet (in French). Vol. 13 (published 1804). p. 243. En effet, lorsqu'il y a plus de trois concurrents, le véritable vœu de la pluralité peut être pour un candidat qui n'ait eu aucune des voix dans le premier scrutin.
  5. ^ Nanson, E. J. (1882). "Methods of election: Ware's Method". Transactions and Proceedings of the Royal Society of Victoria. 17: 206. The method was, however, mentioned by Condorcet, but only to be condemned.
  6. ^ Campbell, D.E.; Kelly, J.S. (2000). "A simple characterization of majority rule". Economic Theory. 15 (3): 689–700. doi:10.1007/s001990050318. JSTOR 25055296. S2CID 122290254.
  7. ^ Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN 0092-5853. JSTOR 2110496.
  8. ^ Stensholt, Eivind (2018). "What is Wrong with IRV?". SSRN Electronic Journal. doi:10.2139/ssrn.3272186. ISSN 1556-5068.
  9. ^ Ray, Depankar (1986). "On the practical possibility of a 'no show paradox' under the single transferable vote". Mathematical Social Sciences. 11 (2): 183–189. doi:10.1016/0165-4896(86)90024-7.
  10. ^ Nurmi, Hannu (December 1996). "It's not just the lack of monotonicity1". Representation. 34 (1): 48–52. doi:10.1080/00344899608522986. ISSN 0034-4893.
  11. ^ McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853. JSTOR 3088418. As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
  12. ^ Hyman, Ross; Otis, Deb; Allen, Seamus; Dennis, Greg (September 2024). "A Majority Rule Philosophy for Instant Runoff Voting". Constitutional Political Economy. 35 (3): 425–436. arXiv:2308.08430. doi:10.1007/s10602-024-09442-3. ISSN 1043-4062.