Two-round system
The two-round system, 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. The two-round system is in the family of plurality voting systems that also includes single-round plurality. Like instant-runoff 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 and the no-show paradox. 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.
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.
In the United States, the first round is often called a jungle or top-two primary. Georgia, California, and Washington use the two-round system for all non-presidential elections. Mississippi also uses it for state offices. 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.
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, 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 and Christiane Taubira 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 : 19.88%
- Jean-Marie Le Pen : 16.86%
- Lionel Jospin : 16.18%
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 voted for Chirac, who won with a very large majority:
- Jacques Chirac : 82.21%
- Jean-Marie Le Pen : 17.79%
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 which makes the result similar to top-two two-round systems.Variants
Two-party runoff vote
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.Top-two primaries
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.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 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 can have a second round after Election Day if the winner of the first round does not get more than 50%. However normal partisan primaries are used so it is rare to have more than 2 competitive candidates in the first round.
Exhaustive ballot
The exhaustive ballot 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 of the Conservative Party use EB to elect their prospective parliamentary candidates. 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 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
, 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. 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 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, 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.
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.If the voters determine their preferences before the election and always vote directly consistent to them, they will emulate the contingent 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 a game. 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, 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 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 the perfect 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.