The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, 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 two rounds of choose-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). 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.
The two-round system first emerged in France and has since become the most common single-winner electoral system worldwide. 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. This has led to the rise of electoral reform movements (such as in France) which seek to replace the two-round system with other systems like rated voting.
In the United States, the first round is often called a jungle or top-two primary. Georgia, Louisiana, California, and Washington use the two-round system for most or all non-presidential elections, while Alaska and Maine use a similar instant-runoff system. In other states, the partisan primary system that is often described as a de facto two-round system, with primaries narrowing down the field to two main candidates.
Origins The French system of ballotage was first established as part of the reforms of the July 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". The rule has since gained substantial popularity in South America, Eastern Europe, and Africa, where it is now the dominant system.
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 a plurality of votes (more votes than anyone else), not necessarily a majority, to be elected.
Example
2002 French presidential election In the 2002 French presidential election, the two contenders described by the media as possible winners were Jacques Chirac and Lionel Jospin, who represented the largest two political parties in France at the time. However, 16 candidates were on the ballot, including Jean-Pierre Chevènement (5.33%) and Christiane Taubira (2.32%) from the Plural Left coalition of Jospin, who refused by excess of confidence to dissuade them.
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:
Jacques Chirac (Centre-right, Gaullist): 19.88% Jean-Marie Le Pen (Far-right, National Front): 16.86% Lionel Jospin (Centre-left, Socialist): 16.18%
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:
Jacques Chirac (Center-right, Gaullist): 82.21% Jean-Marie Le Pen (Far-right, National Front): 17.79% Despite the controversy over Jospin's early elimination, polls showed Chirac was preferred to Jospin by a majority of voters and that Chirac was the majority-preferred candidate, meaning the election was not spoiled.
2024 French legislative election French legislative elections allow more than two candidates to advance to the second round, leading to many triangular elections, such as in the 2024 French legislative election. 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.
Variants
Nonpartisan primary In the United States, a two-round system called the jungle primary is used in Louisiana in place of traditional primary elections to choose each party's candidate only in legislative, local, and some statewide races other than congressional ones. In this state, the first round is held on Election Day with runoffs occurring soon after if a candidate fails to receive at least 50% of the vote on election day. This system was first implemented for Louisiana federal congressional elections in 1978, having been introduced for state and local elections in 1975. Between a special election in 2006 and regular elections in 2010, a closed primary system was used for congressional races. The open primary system was subsequently restored but will be eliminated beginning in 2026 for all congressional elections and certain races for state positions in favor of closed primaries that are held months prior to the general election.
Washington adopted a two-round system in a 2008 referendum, called the nonpartisan blanket primary or top-two primary. California approved the system in 2010, which was first used for the 36th congressional district special election in February 2011. The first election (the primary) is held before 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 requires a second round if no candidate wins over 50% on Election Day. Georgia uses this system in addition to normal partisan primaries, which usually limit the field to two major candidates. Due to this, second rounds are rare, but a third-party or independent candidate drawing a small share of votes can still force one, as was seen in the 2022 United States Senate election in Georgia.
In Mississippi if a candidate for a statewide office receives less than 50% of the vote a runoff election is triggered.
In the states of Alabama, Arkansas, Georgia, Mississippi, Oklahoma, South Carolina, and Texas. If a candidate fails to receive 50% in a primary election a runoff is held. In addition a primary election runoff is held in North Carolina if requested by the second place candidate and the first place candidate fails to receive at least 30% of the vote.
In South Dakota a primary election runoff for a U.S. house, U.S. Senate, or state governor election is held if the first place candidate fails to receive at least 35% of the vote in a race with 3 or more candidates.
In Iowa a leading primary candidate must win at least 35% of the vote in a race with three or more candidates to automatically advance to the general election. If the leading primary candidate fails to receive 35% of the vote the general election nominee must be chosen by party convention or party committee, depending on the office.
Partisan primaries Partisan primaries which select candidates to the general election are a form of two-stage elections. The electoral system in the primary can differ by political party..
Party-list runoff A two-party vote is used for elections to the Bhutanese National Assembly, where the first round selects two parties that are allowed to compete in the second round. Then, a second round is held using single-member districts with first-past-the-post.Bhutanese National Assembly electoral system IPU
Armenia utilizes a conditional two-round party-list election, with the first round a party-list proportional representation and the conditional second round between the top two party-lists.
Exhaustive ballot
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 the United Kingdom, where local associations (LCAs) of the Conservative 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.
Contingent vote
The contingent or supplementary vote is a variant of instant-runoff voting (IRV) that has been used in Queensland and is used in the United 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
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 (called preferential voting). In the United States, it is known as ranked-choice voting and is used in a growing number of states and localities.
In Ireland it is known as the single transferable vote (STV) and is used for presidential 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. STV is often used for municipal elections in lieu of more party-based forms of proportional representation.
Approval voting with Runoff The Approval with runoff is a two-round system which uses approval voting in the first round and the top two candidates proceed to a runoff in the second round. The approval voting reduces the center squeeze effect for multiple candidates in the first round.
Compliance with voting method criteria
Most of the mathematical criteria by which voting methods are compared were formulated for voters with ordinal preferences. Some methods, like approval 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.