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Thetwo-round system (TRS or2RS), sometimes calledballotage,top-two runoff, ortwo-roundplurality,[1] is a single-winnerelectoral system which aims to elect a member who has support of the majority of voters. The two-round system involves two rounds ofchoose-one voting, where the voter marks a single favorite candidate in each 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 ofplurality voting systems that also includessingle-round plurality (FPP). Likeinstant-runoff (ranked-choice) voting and first past the post, it elects one winner.[2][3]
The two-round system first emerged inFrance and has since become the most common single-winnerelectoral system worldwide.[1][4] Despite this, runoff-based rules like the two-round system and RCV have faced criticism fromsocial choice theorists as a result of their susceptibility tocenter squeeze (a kind ofspoiler effect favoring extremists) and theno-show paradox.[5][6][7] This has led to the rise ofelectoral reform movements which seek to replace the two-round system with other systems likerated 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 ajungle ortop-two primary.Georgia,Louisiana,California, andWashington[note 2] use the two-round system for all non-presidential elections.Mississippi uses it for state offices.[10] Most other states use apartisan 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 andMaine use theInstant-runoff voting system, a single-winner ranked-choice voting (RCV) system, which, unlike TRS, does not require voters to engage in multiple rounds of voting.)
The French system ofballotage was first established as part of the reforms of theJuly Monarchy, with the term appearing in the Organic Decree of 2 February 1832 of the French government, which mandated a second-round election "when none of the candidates obtains an absolute majority".[14] The rule has since gained substantial popularity inSouth America,Eastern Europe, andAfrica, where it is now the dominant system.[14]
Some variants of the two-round system use slightly different rules for eliminating candidates before the second round, allowing more than two candidates to proceed to the second round in some cases. Under such systems, in the second round it is sufficient for a candidate to receive aplurality of votes (more votes than anyone else), not necessarily a majority, to be elected.
In the2002 French presidential election, the two contenders described by the media as possible winners wereJacques Chirac andLionel Jospin, who represented the largest two political parties in France at the time. However, 16 candidates were on the ballot, includingJean-Pierre Chevènement (5.33%) andChristiane Taubira (2.32%) from thePlural Left coalition of Jospin, who refused by excess of confidence[clarification needed] to dissuade them.[citation needed]
With the left vote divided among a number of candidates, a third contender,Jean-Marie Le Pen, unexpectedly obtained slightly more than Jospin in the first round:
The other candidates received smaller percentages on the first round.
Because no candidate had obtained an absolute majority of the votes in the first round, the top two candidates went into the second round. Most supporters of the parties which did not get through to the second round (and Chirac's supporters) voted for Chirac, who won with a very large majority:
Despite the controversy over Jospin's early elimination, polls showed Chirac was preferred to Jospin by a majority of voters and that Chirac was themajority-preferred candidate, meaning the election was notspoiled.
French legislative elections allow more than two candidates to advance to the second round, leading to manytriangular elections, such as in the2024 French legislative election.[15] It is common for all but two candidates to withdraw from the second round (so they don't spoil the chances of another similar candidate) which makes the result similar to top-two two-round systems.
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A two-party vote is used for elections to theBhutanese National Assembly, where the first round selects two parties that are allowed to compete in the second round. Then, a second round is held usingsingle-member districts withfirst-past-the-post.[16]
In the United States, a two-round system called thejungle primary and used inLouisiana in place of traditional primary elections to choose each party's candidate. In this state, the first round is held onElection Day with runoffs occurring soon after.
Washington adopted a two-round systemin a 2008 referendum, called thenonpartisan blanket primary or top-two primary.Californiaapproved the system in 2010, which was first used for the36th congressional district special election in February 2011. The first election (the primary) is heldbefore the general election in November and the top two candidates enter the general election. The general election is always held, even if a candidate gets over 50%.
Georgia can have a second round after Election Day if the winner of the first round does not get more than 50%.[17] However normal partisan primaries are used so it is rare to have more than 2 competitive candidates in the first round.
The exhaustive ballot (EB) is similar to the two-round system, but involves more rounds of voting rather than just two. If no candidate receives an absolute majority in the first round, the candidate with the fewest votes is eliminated. This continues until one candidate has an absolute majority. Because voters may have to cast votes several times, EB is not used in large-scale public elections. Instead it is used in smaller contests such as the election of the presiding officer of an assembly; one long-standing example of its use is in theUnited Kingdom, where local associations (LCAs) of theConservative Party use EB to elect their prospective parliamentary candidates (PPCs). Exhaustive ballot is also used by FIFA and the International Olympic Committee to select hosts.
Thecontingent orsupplementary vote is a variant of instant-runoff voting (IRV) that has been used inQueensland and is used in theUnited Kingdom to elect mayors. Like IRV, voters vote once and rank candidates. Unlike IRV, contingent voting election system involves only two rounds of counting at most. After the first round of counting all but the two candidates with most votes are eliminated, with their votes transferred. With only two candidates progressing on to the second round of counting, one candidate achieves a majority in the second round and wins. The contingent vote tends to elect the same candidate that the two-round system and instant-runoff voting system do.
Instant-runoff voting (IRV), like the exhaustive ballot, involves multiple reiterative counts in which the candidate with fewest votes is eliminated each time. Whilst the exhaustive ballot and the two-round system both involve voters casting a separate vote in each round, under instant-runoff, voters vote only once. This is possible because, rather than voting for only a single candidate, the voter ranks all of the candidates in order of preference. These preferences are then used to transfer the votes of those whose first preference has been eliminated during the course of the count. Because the two-round system and the exhaustive ballot involve separate rounds of voting, voters can use the results of one round to decide how they will vote in the next, whereas this is not possible under IRV. Because it is necessary to vote only once, IRV is used for elections in many places. For such as Australian general and state elections (calledpreferential voting). In the United States, it is known asranked-choice voting and is used in a growing number of states and localities.
InIreland it is known as thesingle transferable vote (STV) and is used forpresidential elections and parliamentary by-elections. STV as applied in multi-member districts is a proportional voting system, not a majoritarian one; and candidates need only achieve a quota (or the highest remaining fraction of a quota), to be elected. Multi-winner STV is used in Northern Ireland, Malta, the Australian senate and various other jurisdictions in Australia.[18] STV is often used for municipal elections in lieu of more party-based forms of proportional representation.
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Most of the mathematical criteria by which voting methods are compared were formulated for voters with ordinal preferences. Some methods, likeapproval voting, request information than cannot be unambiguously inferred from a single set of ordinal preferences. The two-round system is such a method, because the voters are not forced to vote according to a single ordinal preference in both rounds.
If the voters determine their preferences before the election and always vote directly consistent to them, they will emulate thecontingent vote and get the same results as if they were to use that method. Therefore, in that model of voting behavior, the two-round system passes all criteria that the contingent vote passes, and fails all criteria the contingent vote fails.
Since the voters in the two-round system do not have to choose their second round votes while voting in the first round, they are able to adjust their votes as players in agame. More complex models consider voter behavior when the voters reach a game-theoretical equilibrium from which they have no incentive, as defined by their internal preferences, to further change their behavior. However, because these equilibria are complex, only partial results are known. With respect to the voters' internal preferences, the two-round system passes the majority criterion in this model, as a majority can always coordinate to elect their preferred candidate. Also, in the case of three candidates or less and a robust political equilibrium,[19] the two-round system will pick the Condorcet winner whenever there is one, which is not the case in the contingent vote model.
The equilibrium mentioned above is a perfect-information equilibrium and so only strictly holds in idealized conditions where every voter knows every other voter's preference. Thus it provides an upper bound on what can be achieved with rational (self-interested) coordination or knowledge of others' preferences. Since the voters almost surely will not have perfect information, it may not apply to real elections. In that matter, it is similar to theperfect competition model sometimes used in economics. To the extent that real elections approach this upper bound, large elections would do so less so than small ones, because it is less likely that a large electorate has information about all the other voters than that a small electorate has.
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The two-round system is intended to reducetactical voting. Under the single-winnerplurality voting election system (also known as first past the post),Vote splitting can occur and the choice of just a minority of voters can be elected. Voters who favor less-popular candidates are encouraged to vote tactically, or "compromise", by voting for one of the two leading candidates, because a vote for any other candidate does not have as good a chance of affecting the result and also prevents the voter from indicating which of the two leading candidates they prefer. Under TRS if there are only three (viable) candidates, this is unnecessary: even if a voter's favorite candidate is eliminated in the first round, they will still have an opportunity to influence the result by voting for their second-favorite in the second round. However if there are more than three candidates, there is a reason for the voter to compromise and vote for a leading candidate in the first round, in order to avoid the chance that only candidates the voter dislikes advance to the second round and have chance to be elected.
Under the two-round system, voters sometimes engage in "push over". A voter doing so votes for an unpopular "push over" candidate in the first round to ensure that it is this weak candidate, rather than a stronger rival, whom survives to challenge their preferred candidate in the second round. This can backfire if it removes too many votes for their preferred candidate, or the weak candidate's campaign may be energized by being advanced to the second round.
The two-round system can be influenced bystrategic nomination - this is where candidates and political factions influence the result of an election by nominating extra candidates or withdrawing a candidate who would otherwise have stood. TRS is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of compromising. This is because a candidate who knows they are unlikely to win can ensure that another candidate they support makes it to the second round by withdrawing from the race before the first round occurs, or by never choosing to stand in the first place. By reducing the size of its slate, a political faction can avoid thespoiler effect, whereby a party "splits the vote" of its supporters. A famous example of this spoiler effect occurred in the2002 French presidential election, when so many left-wing candidates stood in the first round that all of them were eliminated, and two right-wing candidates advanced to the second round. Conversely, a popular faction may fund the campaign of multiple smaller opposing candidates, in order to split the opposition votes among them.
The intention of two-round system is that the winning candidate will have the support of amajority of the votes cast. Under the first past the post method, the candidate with most votes (a plurality or a majority) wins, even if they do not have a majority (more than half) of votes. The two-round system tries to overcome this problem by permitting only two candidates in the second round, so that one must receive a majority of votes counted.
Critics argue that the majority obtained by the winner under the two-round system is an artificial one. Instant-runoff voting and the exhaustive ballot are two other voting methods that create a majority for one candidate by eliminating weaker candidates and then transferring votes based on back-up preferences. However, in cases where there are three or more strong candidates, the TRS will sometimes produce a majority for a different winner than the candidate elected by a majority produced under instant-runoff voting or the exhaustive ballot.
Advocates ofCondorcet methods argue[citation needed] that a candidate can claim to have majority support only if they are the "Condorcet winner" – that is, the candidate whose vote tally is greater than that of every other candidate in a series of one-on-one comparisons. In the two-round system, in the last round, the winning candidate is only matched, one-on-one, with one of the other candidates. When a Condorcet winner exists, the candidate does not necessarily win a TRS election due to insufficient support in the first round.
Two-round system advocates counter[citation needed] that the voter's first preference is more important than lower preferences because that is where voters are putting the most effort of decision and that, unlike Condorcet methods, to win under the TRS requires a good showing among the full field of candidates in the first round and also a plurality in the final head-to-head competition. Condorcet methods can allow candidates to win who have minimal first-choice support and can win largely on the compromise appeal of being ranked second or third by more voters.
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The two-round system encourages candidates to appeal to a broad cross-section of voters. This is because, in order to win an absolute majority in the second round, it is necessary for a candidate to win the support of voters whose favorite candidate has been eliminated. Under the two-round system, between rounds of voting, eliminated candidates, and the factions who previously supported them, often issue recommendations to their supporters as to whom to vote for in the second round of the contest. This means that eliminated candidates are still able to influence the result of the election. This influence leads to political bargaining between the two remaining candidates and the parties and candidates who have been eliminated, sometimes resulting in the two successful candidates making policy concessions to the less successful ones. Because it encourages conciliation and negotiation in these ways, the two-round system is advocated, in various forms, by some supporters ofdeliberative democracy.
The two-round system is designed for single-seat constituencies. Therefore, like other single-seat methods, if used to elect a council orlegislature it will not produceproportional representation (PR). This means that it is likely to lead to the representation of a small number of larger parties in an assembly, rather than a proliferation of small parties. In practice, the two-round system produces results very similar to those produced by the plurality method, and encourages a two-party system similar to those found in many countries that use plurality. Under aparliamentary system, it is more likely to produce single-party governments than are PR methods, which tend to producecoalition governments. While the two-round system is designed to ensure that each individual candidate elected is supported by a majority of voters in the constituency, it does not ensure majority rule on a national level when it comes to electing an assembly. As in other non-PR methods, the party or coalition that wins a majority of seats often will not have the support of a majority of voters across the nation.
InAustralian politics, thetwo-party-preferred vote (TPP or 2PP) is the result of the final round of an election or opinion poll after preferences have been distributed to the highest two candidates, who in some cases can be independents.[citation needed] For the purposes of TPP, the Liberal/National Coalition is usually considered a single party, with Labor being the other major party. Typically the TPP is expressed as the percentages of votes attracted by each of the two major parties, e.g. "Coalition 45%, Labor 55%", where the values include both primary votes and preferences. The TPP is an indicator of how much swing has been attained/is required to change the result, taking into consideration later preferences.
In smaller elections, such as those in assemblies or private organizations, it is sometimes possible to conduct both rounds in quick succession. More commonly, however, large-scale public elections the two rounds of runoff voting are held on separate days, and so involve voters going to the polls twice and governments conducting two elections. As a result, one of the most common criticisms against the two-round system is that the cost and difficulty of casting a ballot is effectively doubled.[20] However, the system may sometimes still be cheaper than holding aranked-choice runoff (RCV), as the counting of votes in each round is simple. By contrast,ranked-choice runoff voting involves a longer and more complex count that often requires a centralized count, as it is impossible totally or audit RCV results locally.[21][22]
The two-round voting system also has the potential to cause political instability between the two rounds of voting.[citation needed]
The two-round system is the most common way used to electheads of state (presidents) of countries worldwide, a total of 87 countries elect their heads of statedirectly with a two-round system as opposed to only 22 countries that used single-round plurality (first-past-the-post).[23]
Algeria
Argentina
Austria
Azerbaijan
Belarus
Benin
Bolivia (Double simultaneous vote for the presidential 1st round and legislative elections)
Brazil
Bulgaria
Burkina Faso
Burundi
Cape Verde
Central African Republic
Chad
Chile
Colombia
Republic of the Congo
Comoros
Costa Rica
Croatia
Cyprus
Czech Republic
Djibouti
Dominican Republic
East Timor
Ecuador
Egypt
Finland
France
Ghana
Guatemala
Guinea
Guinea-Bissau
Haiti
Indonesia
Iran
Ivory Coast
Kazakhstan
Kenya
Kyrgyzstan
Liberia
Libya
Lithuania
Madagascar
Malawi
Maldives
Mali
Mauritania
Moldova
Mongolia
Montenegro
Mozambique
Namibia
Niger
Nigeria
North Macedonia
Northern Cyprus
Palau
Peru
Poland
Portugal
Romania
Russia
São Tomé and Príncipe
Senegal
Serbia
Seychelles
Sierra Leone
Slovakia
Slovenia
Sudan
Syria
Tajikistan
Togo
Tunisia
Turkey
Turkmenistan
Uganda
Ukraine
Uruguay (Double simultaneous vote for the presidential 1st round and legislative elections)
Uzbekistan
Yemen
Zambia
Zimbabwe
Bahrain (lower house only)Comoros (unicameral)Republic of the Congo (lower house only)Czech Republic (upper house only)France (lower house only)
Gabon (both houses; lower house elected directly but upper house elected indirectly)Haiti (both houses)Mali (unicameral)Uzbekistan (lower house only)
Georgia (United States) (both houses)
Mississippi (United States) (both houses)
Montserrat (United Kingdom) (unicameral)
Texas (United States) (both houses)
Louisiana (United States) (both houses)
French Polynesia (France) – two-round majority bonus system (unicameral)
Italy – City councils (Majority bonus system)Egypt (both houses; single-member and small multi-member districts, alongsideparty-list proportional representation in large multi-member districts)France (upper house only; indirect elections in single-member and small multi-member districts, alongsideparty-list proportional representation in large multi-member districts)
Hungary (until 2010) (unicameral; single-member districts alongsideparty-list proportional representation in multi-member districts and compensatory seats nationwide)Lithuania (unicameral; single-member districts alongsideparty-list proportional representation nationwide)Tajikistan (unicameral; single-member districts alongsideparty-list proportional representation nationwide)
United States – Used inLouisiana for all elections, inGeorgia for special elections, andvariants used inAlaska,California, andWashington.Two-round voting is used inFrench departmental elections. InItaly, it is used to elect mayors, but also to decide which party or coalition receives amajority bonus in city councils.[25]
Historically it was used to elect theReichstag in theGerman Empire between 1871 and 1918 and theStorting of Norway from 1905 to 1919, inNew Zealand in the1908 and1911 elections,[26][27] and inIsrael to elect thePrime Minister in the1996,1999 and2001 elections.[28]El Salvador used a two-round system to elects itspresident until the2024 presidential election; a constitutional reform in 2025 abolished the two-round system.[29]
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
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
Finally, we should not discount the role of primaries. When we look at the range of countries withfirst-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 theUnited Kingdom andCanada (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 thealternative 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).
American elections become a two-round run-off system with a delay of several months between the rounds.
In effect, the primary system means that the USA has a two-round runoff system of elections.
