The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is an electoral system used to elect a single candidate, where voters cast a single vote for their preferred candidate. It is used widely around the world, including in elections for the President of France and Finland, and especially in a political party's primary elections, in which it selects candidates to present to the public. When the number of rounds is unlimited, then it is sometimes known as an elimination ballot.
It generally ensures a majoritarian result, not a simple plurality result as under First past the post. Under the two-round election system, the election process usually proceeds to a second round only if in the first round no candidate received a simple majority (more than 50%) of votes cast, or some other lower prescribed percentage. Under the two-round system, usually only the two candidates who received the most votes in the first round, or only those candidates who received above a prescribed proportion of the votes, are candidates in the second round. Other candidate are excluded from the second round.
The two-round system is widely used in the election of legislative bodies and directly elected presidents, as well as in other contexts, such as in the election of political party leaders or within companies.
The second round of voting must be held after there is sufficient time to count and verify the results of the first round. Second rounds may be held on the same day in smaller settings, or up to three months later, as in the US state of Georgia. France traditionally has a two-week break before the second round.
In the preliminary election, voters select their preferred candidate. If one candidate reaches the election threshold (usually fifty percent of the positive votes plus one), they are elected.
Otherwise, in a two round system, the top candidates (usually the top two) are placed on a secondary ballot. Whoever receives the most votes on the second ballot is declared elected.
In an elimination ballot, successive rounds of voting are held until a candidate wins a majority of the positive votes. After each inconclusive round, those candidates at the bottom whose votes together do not add up to the votes of the next candidate are eliminated (so barring ties at least one candidate is eliminated each round).
Runoff voting can be condensed into a single preference ballot paper, at which point it becomes instant-runoff voting or an "alternative vote". A simplified model of a two round system is the supplementary vote.
A runoff ballot is not the same thing as a primary election. In a runoff ballot, all candidates are placed on the initial ballot and all voters are allowed to participate in the vote, whereas primaries are generally internal measures within a political party.
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.
The candidates for the capital are:
- Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
- Nashville, with 26% of the voters, near the center of Tennessee
- Knoxville, with 17% of the voters
- Chattanooga, with 15% of the voters
The preferences of the voters would be divided like this:
|42% of voters
(close to Memphis)
|26% of voters
(close to Nashville)
|15% of voters
(close to Chattanooga)
|17% of voters
(close to Knoxville)
Assuming each voter voted for their preferred city (for a more sophisticated approach, see below), the first ballot results would be as follows:
- Memphis: 42%
- Nashville: 26%
- Knoxville: 17%
- Chattanooga: 15%
In a two round runoff, Knoxville and Chattanooga are eliminated, while Nashville and Memphis advance to the second ballot.
The voters from Knoxville and Chattanooga prefer Nashville to Memphis, so the results of the second ballot would be:
- Nashville: 58%
- Memphis: 42%
Nashville would then be declared the winner.
Note on strategy: A two round runoff encourages candidates to unite to make the top two cut. Since Chattanooga and Knoxville both prefer each other second, knowing their divided vote might eliminate them both, they might work together before the election and decide for only Chattanooga to run. That would cause the defeat of Nashville (third place) and Chattanooga could win the final runoff round against Memphis. Something similar would happen with a multi-round elimination ballot.
In an elimination ballot, Chattanooga would be eliminated after the first round, and the second round would be:
- Memphis: 42%
- Knoxville: 32%
- Nashville: 26%
Nashville would then be eliminated and the third round of the elimination ballot would be:
- Knoxville: 58%
- Memphis: 42%
So Knoxville would win.
Potential for Tactical Voting
The runoff system encourages voters to "compromise" by not voting for their favorite candidate in their first round. In the above two-round example, if all voters from Chattanooga "compromised" for Knoxville in the first round, Knoxville would advance to the second round, where it would defeat Memphis. This would be a better result for the Chattanooga voters than sincere voting would get them. The Memphis supporters voters could respond by voting for Nashville instead of Memphis as a way to prevent Knoxville or Chattanooga winning.
Runoff voting can also encourage voters to vote for "push-overs", in order to set up a more favorable second-round matchup.
Impact of vote-splitting on two-round systems
A two-round runoff voting system, in practice, may work as a system of primary elections in countries where there are two major partisan blocks, by choosing for the second round of election a candidate in each block. While this is the usual outcome, different situations may arise in the presence of coalitions fielding multiple candidates, protest votes and third parties.
A striking example, which attracted considerable media attention, was that of the 2002 French presidential election. The two major contenders, respectively leading a left-wing and a right-wing coalition, were Lionel Jospin and Jacques Chirac. However, the left-wing coalition fielded three additional candidates representing minor parties in the coalition. Furthermore, part of the left-wing vote went to candidates from far-left parties, presumably to protest Jospin's policies, deemed too centrist. A third important candidate was Jean-Marie Le Pen, a controversial politician often described as racist and fascist-leaning. On the first round of elections:
- Jacques Chirac obtained 19.88% of the vote; added to other candidate in the same coalition François Bayrou's 6.84%, this makes 26.72%;
- Lionel Jospin obtained 16.18% of the vote; added to other candidates in the same coalition Robert Hue (3.37%), Noël Mamère (5.25%), Christiane Taubira (2.32%), this makes 27.12%.
While it is not established that voters for minor candidates of each coalition would have voted for the major candidate of the same coalition, these sums would tend to indicate that Jospin had a slight edge over Chirac. Le Pen, however, obtained 16.86% and thus went to the second round of election against Chirac. Since the vast majority of the electorate disapproves of Le Pen's policies, Chirac then won by an enormous majority (82.21%). In the last decades, normal second rounds in French presidential elections were settled around 50% for each side.
Impact on factions and candidates
Between each round of voting, discussion and dealing is possible; policy concessions and withdrawals can be negotiated. Accordingly, runoff votes in some form are advocated as part of most deliberative democracy proposals. Other electoral reform and grassroots democracy advocates prefer instant-runoff voting which let larger groups participate in the process by ballot - the French participation of the whole electorate in a runoff vote is a rare exception and permits some dealing between parties who have lost and those who seek their support.
The one-ballot "instant runoff" proposals are the opposite of such 'deliberative' processes, as there is no time nor place for explicit discussion and dealing as the power relationships become clear. Polls can take the place of early rounds of balloting, but are nowhere near as statistically valid as a formal vote.
The runoff voting rule satisfies a weak form of the dominant mutual third property, and thus a weak form of the mutual majority criterion: if over 1/3rd of voters vote for a candidate that pairwise beats all candidates not in a certain set of candidates most-preferred by the 1/3rd of voters (because they are a solid coalition), then someone from that set of candidates (i.e. the one that gets over 1/3rd of the votes) will win in the runoff.  Instant-runoff voting satisfies a stronger version of the property.
Sometimes Top Two Runoff (TTR) is also used as the name of an automatic one-round variation, which works by having voters rank the candidates, finding the two candidates ranked 1st by the most voters, and then using the rankings to figure out which of the two is preferred by a majority and electing that one. This method is more properly called the contingent vote.
It has been theorized that when runoff elections are held with the possibility of a candidate with a majority winning in the first round itself, that this actually incentivizes voters to do Favorite Betrayal to make a frontrunner have an "extra chance" to win (i.e. the frontrunner, who might lose in the runoff due to lower turnout or other factors, will instead win in the first round). Thus, it has been argued by some that a second round should always be held even if someone gets a majority in the first round. This could be modified to allow a candidate with a supermajority (say, 60%) to win in the first round, however, since the larger the majority, the less such incentive is likely to exist.
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