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Two-round system

The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate. The first round is held using simple plurality to choose the top-two candidates, and then in the second round the winner is chosen by majority vote. The two-round system is widely used in the election of legislative bodies and directly elected presidents.

For other types of runoff-voting systems, see Runoff voting (disambiguation).

Second rounds may be held on the same day in smaller settings, or up to one month later, as in the US state of Georgia. France traditionally has a two-week break before the second round.

Terminology[edit]

The two-round system is known as runoff voting in the United States, where the second round is known as a runoff election.


Runoff voting may also sometimes be used as a generic term to describe any voting method that involves a number of rounds of voting, with eliminations after each round. By this broader definition the two-round system is not the only form of runoff voting, and others include the exhaustive ballot and instant-runoff voting. However, the subject of this article is the two-round system. In Canada, for example, when there are more than two candidates for political-party leadership, an exhaustive-ballot system (often called a runoff-voting method) is used where one candidate must win a simple majority (over half). Candidates with the fewest votes or candidates who want to move their support to other candidates may also move to remove themselves from the next vote.

Voting and counting[edit]

In both rounds of an election conducted using runoff voting, the voter simply marks their preferred candidate. If no candidate has an absolute majority of votes (i.e. more than half) in the first round, then the two candidates with the most votes proceed to a second round, from which all others are excluded. In the second round, because there are only two candidates, and absent a tie vote, one candidate will achieve an absolute majority. Voters may change the candidate they support in the second round.


Some variants of the two-round system use a different rule for choosing candidates for the second round, and allow more than two candidates to proceed to the second round. Under such methods, it is sufficient for a candidate to receive a plurality of votes (more votes than anyone else) to be elected in the second round. In Czech and Kenyan presidential elections, the candidates in first and second place are permitted to stand in the second round, with all other candidates eliminated, thus providing the contingency for a first- or second-place tie; a plurality is then sufficient to be elected. However, in Ghana, which also employs this contingency method, the majority requirement still holds in the second round, and a third round would be held if it is not obtained. Under some variants of runoff voting, there is no formal rule for eliminating candidates, but candidates who receive fewer votes in the first round are expected to withdraw voluntarily.

Jacques Chirac (Centre-right, Gaullist): 19.88%

Jean-Marie Le Pen (Far-right, National Front): 16.86%

Lionel Jospin (Centre-left, Socialist): 16.18%

Variant[edit]

A variant of the two-round system, where only the top two parties from the first round enter the second round where they are eligible for seats, is applied for elections to the Bhutanese National Assembly. The second round is held under first-past-the-post voting.[1]

Compliance with voting method criteria[edit]

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.


Since the two-round system requires more information from each voter than a single ordinal ballot provides, one cannot fit the criteria that are formulated expressly for voters with ordinal preferences without making a generalization as to how the voters will behave. The same problem exists in Approval voting, where one has to make assumptions as to how the voters will place their approval cutoffs.


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,[4] 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 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.

Impact on factions and candidates[edit]

Runoff voting 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 favourite candidate has been eliminated. Under runoff voting, 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, runoff voting is advocated, in various forms, by some supporters of deliberative democracy.


Runoff voting is designed for single-seat constituencies. Therefore, like other single-seat methods, if used to elect a council or legislature it will not produce proportional 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, runoff voting 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 a parliamentary system, it is more likely to produce single-party governments than are PR methods, which tend to produce coalition governments. While runoff voting is designed to ensure that each individual candidate elected is supported by a majority of those in their constituency, if used to elect an assembly it does not ensure this result on a national level. As in other non-PR methods, the party or coalition which wins a majority of seats will often not have the support of an absolute majority of voters across the nation.

Majoritarianism[edit]

The intention of runoff voting is that the winning candidate will have the support of an absolute majority of voters. Under the first past the post method the candidate with most votes (a plurality) wins, even if they do not have an absolute 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 an absolute majority of votes.


Critics argue that the absolute majority obtained by the winner of runoff voting is an artificial one. Instant-runoff voting and the exhaustive ballot are two other voting methods that create an absolute majority for one candidate by eliminating weaker candidates over multiple rounds. However, in cases where there are three or more strong candidates, runoff voting will sometimes produce an absolute majority for a different winner than the candidate elected by the other two.


Advocates of Condorcet methods argue that a candidate can claim to have majority support only if they are the "Condorcet winner" – that is, the candidate who would beat every other candidate in a series of one-on-one elections. In runoff voting 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 runoff election due to insufficient support in the first round.


Runoff advocates counter that voters' 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, runoffs require a high showing among the full field of choices in addition to a strong showing 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.

Ranked voting systems

Keynesian beauty contest

List of electoral systems by country

Arrow's impossibility theorem

ACE Project: Two-Round System

from International IDEA

A Handbook of Electoral System Design