Instant-runoff voting

Instant-runoff voting (IRV; US: ranked-choice voting (RCV), AU: preferential voting, UK/NZ: alternative vote) is a single-winner ranked voting election system where multi-round eliminations is used to simulate a series of runoff elections. When no candidate has a majority of the votes in the first round of counting, in each following round, the candidate with the fewest first-preferences (among the remaining candidates) is eliminated, and their votes transferred if possible. This continues until one candidate accumulates a majority of the votes still in play.

Instant runoff voting falls under the plurality-based voting rule family, in that under certain conditions the candidate with the least votes (by plurality) is eliminated,^[1] making use of secondary rankings as contingency votes. Thus it is related to the two-round runoff system and the exhaustive ballot.^[2]^[3] IRV could also be seen as a single-winner equivalent of single transferable voting.

Unlike first-past-the-post voting, IRV is a sequential procedure.^[4] Unlike contingent voting (AKA supplementary voting), which has just two rounds of counting at most, IRV may entail numerous rounds of counting.

Instant-runoff voting (IRV) has been used 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, and to elect the head of state in India, Ireland, and Sri Lanka.

The rule was first studied by the Marquis de Condorcet, who observed it could eliminate the majority-preferred candidate (Condorcet winner).^[5]^[6]^[7]^[8] Since then, instant-runoff voting has been criticized for failing other criteria, including its ability to eliminate candidates for having too much support or too many votes.^[9] Instant-runoff voting may exhibit a kind of Independence of irrelevant alternatives violation called a center squeeze,^[10]^[11] which causes it to favor uncompromising alternatives over more-moderate ones,^[12]^[13] which may in turn hinder a recovery from increasing polarization between the candidates and limit free entry.^[14]

Some advocates of instant-runoff voting have argued these properties are positive, as voting rules should encourage candidates to appeal to their core support or political base rather than a broad coalition.^[15] They also note that in countries like the UK without primaries or runoffs, instant-runoff voting can prevent spoiler effects by eliminating minor-party candidates. Unlike a plurality vote system where votes are non-transferable, instant-runoff voting also avoids some kinds of vote-splitting by near-identical (clone) candidates. IRV has also been advocated for as a natural and practical generalization of the two-round system.^[16]

^ 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.
^ Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.
^ 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. arXiv:2308.08430. doi:10.1007/s10602-024-09442-3. ISSN 1572-9966.
^ Gladyshev, Vulnerability of Voting Paradoxes. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3471868
^ 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.
^ 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.
^ 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.
^ 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.
^ 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.
^ Nurmi, Hannu (December 1996). "It's not just the lack of monotonicity1". Representation. 34 (1): 48–52. doi:10.1080/00344899608522986. ISSN 0034-4893.
^ Atkinson, Nathan; Ganz, Scott C. (30 October 2022). "The flaw in ranked-choice voting: rewarding extremists". The Hill. Retrieved 14 May 2023. However, ranked-choice voting makes it more difficult to elect moderate candidates when the electorate is polarized, if the moderate's base of support is smaller than the base of support of extreme candidates. For example, in a three-person race, the moderate candidate may be preferred by a majority of voters to each of the more extreme candidates. However, voters with far-left and far-right views will rank the candidate in second place rather than in first place. Since ranked-choice voting counts only the number of first-choice votes (among the remaining candidates), the moderate candidate would be eliminated in the first round, leaving one of the extreme candidates to be declared the winner.
^ 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.
^ Robinette, Robbie (1 September 2023). "Implications of strategic position choices by candidates". Constitutional Political Economy. 34 (3): 445–457. doi:10.1007/s10602-022-09378-6. ISSN 1572-9966.
^ Atkinson, Nathan; Ganz, Scott (2024). "Robust Electoral Competition: Rethinking Electoral Systems to Encourage Representative Outcomes". SSRN Electronic Journal. Elsevier BV. doi:10.2139/ssrn.4728225. ISSN 1556-5068.
^ 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.
^ Nanson, E. J. (1882). "Methods of election: Ware's Method". Transactions and Proceedings of the Royal Society of Victoria. 17: 206. This method is a perfectly feasible and practicable one for elections on any scale ... [i]t is a simple and obvious extension of the French system...

[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. arXiv:2308.08430. doi:10.1007/s10602-024-09442-3. ISSN 1572-9966.

[4] Gladyshev, Vulnerability of Voting Paradoxes. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3471868

[:03-5] 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.

[:03223-6] 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.

[:223223-7] 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.

[:85223-8] 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.

[9] 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.

[:733-10] Nurmi, Hannu (December 1996). "It's not just the lack of monotonicity1". Representation. 34 (1): 48–52. doi:10.1080/00344899608522986. ISSN 0034-4893.

[:03244-11] Atkinson, Nathan; Ganz, Scott C. (30 October 2022). "The flaw in ranked-choice voting: rewarding extremists". The Hill. Retrieved 14 May 2023. However, ranked-choice voting makes it more difficult to elect moderate candidates when the electorate is polarized, if the moderate's base of support is smaller than the base of support of extreme candidates. For example, in a three-person race, the moderate candidate may be preferred by a majority of voters to each of the more extreme candidates. However, voters with far-left and far-right views will rank the candidate in second place rather than in first place. Since ranked-choice voting counts only the number of first-choice votes (among the remaining candidates), the moderate candidate would be eliminated in the first round, leaving one of the extreme candidates to be declared the winner.

[:8524-12] 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.

[:2423-13] Robinette, Robbie (1 September 2023). "Implications of strategic position choices by candidates". Constitutional Political Economy. 34 (3): 445–457. doi:10.1007/s10602-022-09378-6. ISSN 1572-9966.

[a790-14] Atkinson, Nathan; Ganz, Scott (2024). "Robust Electoral Competition: Rethinking Electoral Systems to Encourage Representative Outcomes". SSRN Electronic Journal. Elsevier BV. doi:10.2139/ssrn.4728225. ISSN 1556-5068.

[15] 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.

[:03223b-16] Nanson, E. J. (1882). "Methods of election: Ware's Method". Transactions and Proceedings of the Royal Society of Victoria. 17: 206. This method is a perfectly feasible and practicable one for elections on any scale ... [i]t is a simple and obvious extension of the French system...

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