Two-round system

The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality,^[1] is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves one or two rounds of choose-one voting, where the voter marks a single favorite candidate in each round. If no one has a majority of votes in the first round, the two candidates with the most votes in the first round move on to a second election (a second round of voting).^{[note 1]} The two-round system is in the family of plurality voting systems that also includes single-round plurality (FPP). Like instant-runoff (ranked-choice) voting and first past the post, it elects one winner.^[2]^[3]

The two-round system first emerged in France and has since become the most common single-winner electoral system worldwide.^[1]^[4] Despite this, runoff-based rules like the two-round system and RCV have faced criticism from social choice theorists as a result of their susceptibility to center squeeze (a kind of spoiler effect favoring extremists) and the no-show paradox.^[5]^[6]^[7] This has led to the rise of electoral reform movements which seek to replace the two-round system with other systems like rated voting, particularly in France.^[7]^[8]

As well, TRS means voters sometimes have to gather to vote a second time, and sometimes the intervening period of time is rife with discord.^[9]

In the United States, the first round is often called a jungle or top-two primary. Georgia, Louisiana, California, and Washington^{[note 2]} use the two-round system for all non-presidential elections. Mississippi uses it for state offices.^[10] Most other states use a partisan primary system that is often described as behaving like a two-round system in practice, with primaries narrowing down the field to two frontrunners.^[11]^[12]^[13] (Alaska and Maine use the Instant-runoff voting system, the ranked-choice voting (RCV) system, which unlike TRS does not require multiple rounds of voting.)

^ ^a ^b Sabsay, Daniel Alberto (1995). "El sistema de doble vuelta o ballotage" (PDF). Lecciones y Ensayos (62). Facultad de Derecho de la Universidad de Buenos Aires. ISSN 0024-0079. Archived (PDF) from the original on 2022-11-07. Retrieved 2024-07-18.
^ Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.
^ Martinelli, César (2002-10-01). "Simple plurality versus plurality runoff with privately informed voters". Social Choice and Welfare. 19 (4): 901–919. doi:10.1007/s003550200167. ISSN 1432-217X.
^ "El ballotage, con raíces históricas en Francia". El Día. 1 November 2015. Archived from the original on 2023-10-23. Retrieved 2024-07-18.
^ Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23–48. doi:10.2307/2110786. ISSN 0092-5853. JSTOR 2110786. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
^ Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning
^ ^a ^b Keskin, Umut; Sanver, M. Remzi; Tosunlu, H. Berkay (August 2022). "Monotonicity violations under plurality with a runoff: the case of French presidential elections". Social Choice and Welfare. 59 (2): 305–333. doi:10.1007/s00355-022-01397-4.
^ Balinski, Michel; Laraki, Rida (2020-03-01). "Majority judgment vs. majority rule". Social Choice and Welfare. 54 (2): 429–461. doi:10.1007/s00355-019-01200-x. ISSN 1432-217X.
^ Advantages and disadvantages of Two-Round System https://aceproject.org/ace-en/topics/es/esd/esd01/esd01e/esd01e01/mobile_browsing/onePag accessed April 25, 2025
^ "Electoral systems in Mississippi". Ballotpedia. Retrieved 2025-02-12.
^ Santucci, Jack; Shugart, Matthew; Latner, Michael S. (2023-10-16). "Toward a Different Kind of Party Government". Protect Democracy. Archived from the original on 2024-07-16. Retrieved 2024-07-16. Finally, we should not discount the role of primaries. When we look at the range of countries with first-past-the-post (FPTP) elections (given no primaries), none with an assembly larger than Jamaica's (63) has a strict two-party system. These countries include the United Kingdom and Canada (where multiparty competition is in fact nationwide). Whether the U.S. should be called 'FPTP' itself is dubious, and not only because some states (e.g. Georgia) hold runoffs or use the alternative vote (e.g. Maine). Rather, the U.S. has an unusual two-round system in which the first round winnows the field. This usually is at the intraparty level, although sometimes it is without regard to party (e.g. in Alaska and California).
^ Gallagher, Michael; Mitchell, Paul (2005-09-15). "The American Electoral System". The Politics of Electoral Systems. OUP Oxford. p. 192. ISBN 978-0-19-153151-4. American elections become a two-round run-off system with a delay of several months between the rounds.
^ Bowler, Shaun; Grofman, Bernard; Blais, André (2009), "The United States: A Case of Duvergerian Equilibrium", Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States, New York, NY: Springer, pp. 135–146, doi:10.1007/978-0-387-09720-6_9, ISBN 978-0-387-09720-6, retrieved 2024-08-31, In effect, the primary system means that the USA has a two-round runoff system of elections.

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

[SAB2322-1] Sabsay, Daniel Alberto (1995). "El sistema de doble vuelta o ballotage" (PDF). Lecciones y Ensayos (62). Facultad de Derecho de la Universidad de Buenos Aires. ISSN 0024-0079. Archived (PDF) from the original on 2022-11-07. Retrieved 2024-07-18.

[:02-3] Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). A simulation-based study of proximity between voting rules.

[:1322-4] Martinelli, César (2002-10-01). "Simple plurality versus plurality runoff with privately informed voters". Social Choice and Welfare. 19 (4): 901–919. doi:10.1007/s003550200167. ISSN 1432-217X.

[ED-RAÍCES2322-5] "El ballotage, con raíces históricas en Francia". El Día. 1 November 2015. Archived from the original on 2023-10-23. Retrieved 2024-07-18.

[Merrill_198422-6] Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23–48. doi:10.2307/2110786. ISSN 0092-5853. JSTOR 2110786. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.

[Merril_19852222-7] Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning

[:4-8] Keskin, Umut; Sanver, M. Remzi; Tosunlu, H. Berkay (August 2022). "Monotonicity violations under plurality with a runoff: the case of French presidential elections". Social Choice and Welfare. 59 (2): 305–333. doi:10.1007/s00355-022-01397-4.

[9] Balinski, Michel; Laraki, Rida (2020-03-01). "Majority judgment vs. majority rule". Social Choice and Welfare. 54 (2): 429–461. doi:10.1007/s00355-019-01200-x. ISSN 1432-217X.

[10] Advantages and disadvantages of Two-Round System https://aceproject.org/ace-en/topics/es/esd/esd01/esd01e/esd01e01/mobile_browsing/onePag accessed April 25, 2025

[12] "Electoral systems in Mississippi". Ballotpedia. Retrieved 2025-02-12.

[:0322-13] Santucci, Jack; Shugart, Matthew; Latner, Michael S. (2023-10-16). "Toward a Different Kind of Party Government". Protect Democracy. Archived from the original on 2024-07-16. Retrieved 2024-07-16. Finally, we should not discount the role of primaries. When we look at the range of countries with first-past-the-post (FPTP) elections (given no primaries), none with an assembly larger than Jamaica's (63) has a strict two-party system. These countries include the United Kingdom and Canada (where multiparty competition is in fact nationwide). Whether the U.S. should be called 'FPTP' itself is dubious, and not only because some states (e.g. Georgia) hold runoffs or use the alternative vote (e.g. Maine). Rather, the U.S. has an unusual two-round system in which the first round winnows the field. This usually is at the intraparty level, although sometimes it is without regard to party (e.g. in Alaska and California).

[14] Gallagher, Michael; Mitchell, Paul (2005-09-15). "The American Electoral System". The Politics of Electoral Systems. OUP Oxford. p. 192. ISBN 978-0-19-153151-4. American elections become a two-round run-off system with a delay of several months between the rounds.

[15] Bowler, Shaun; Grofman, Bernard; Blais, André (2009), "The United States: A Case of Duvergerian Equilibrium", Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States, New York, NY: Springer, pp. 135–146, doi:10.1007/978-0-387-09720-6_9, ISBN 978-0-387-09720-6, retrieved 2024-08-31, In effect, the primary system means that the USA has a two-round runoff system of elections.

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