Two-round system

The two-round system is known as runoff voting in the United States, where the second round is known as a runoff election. Run-off voting is also sometimes used as a generic term to describe any method involving 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 they use an exhaustive ballot system (often called a runoff voting method) 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.

In both rounds of an election conducted using runoff voting, the voter simply marks his/her favorite 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. In the second round, each voter is entirely free to change the candidate he or she votes for, even if his/her preferred candidate has not yet been eliminated but he or she has merely changed his/her mind.

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 the first and second places 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 isn't obtained, etc.. 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.

The President of Germany was popularly elected in 1925 and 1932 by a two-round system; in the second round, a candidate could run even if they had not done so in the first round, and they did not require an absolute majority to win. In both elections, the communist candidate, Ernst Thälmann, did not withdraw and ran in the second round. In 1925, that probably ensured the election of Paul von Hindenburg (with only 48.3% of the vote), rather than Wilhelm Marx, the centrist candidate. Hindenburg had not run in the first round of the 1925 election.

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 can't 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 can't 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 don't 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,[8] 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 won't 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's less likely that a large electorate has information about all the other voters than that a small electorate has.

Runoff voting is intended to reduce the potential for eliminating "wasted" votes by tactical voting. Under the first past the post (plurality) method voters are encouraged to vote tactically by voting for only one of the two leading candidates, because a vote for any other candidate will not affect the result. Under runoff voting this tactic, known as "compromising", is sometimes unnecessary because, even if a voter's favourite candidate is eliminated in the first round, they will still have an opportunity to influence the result of the election by voting for a more popular candidate in the second round. However the tactic of compromising can still be used in runoff voting because it is sometimes necessary to compromise as a way of influencing which two candidates will survive to the second round. In order to do this it is necessary to vote for one of the three leading candidates in the first round, just as in an election held under the plurality method it is necessary to vote for one of the two leading candidates.

Runoff voting is also vulnerable to another tactic called "push over". This is a tactic by which voters vote tactically for an unpopular "push over" candidate in the first round as a way of helping their true favourite candidate win in the second round. The purpose of voting for the push over, in theory, is to ensure that it is this weak candidate, rather than a stronger rival, who survives to challenge a one's preferred candidate in the second round. But in practice, such a tactic may prove counter-productive. If so many voters give their first preferences to the "weak" candidate that it ends up winning the first round, it is highly likely they will gain enough campaign momentum to have a strong chance of winning the runoff, too, and with it, the election. At the very least, their opponent would have to start taking the so-called weak candidate seriously, particularly if the runoff follows quickly after the first round.

Runoff voting can be influenced by strategic nomination; this is where candidates and political factions influence the result of an election by either nominating extra candidates or withdrawing a candidate who would otherwise have stood. Runoff voting 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 withdrawing candidates a political faction can avoid the spoiler effect, whereby a candidate "splits the vote" of its supporters. A famous example of this spoiler effect occurred in the 2002 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, an important faction may have an interest in helping fund the campaign of smaller factions with a very different political agenda, so that these smaller parties end up weakening their own agenda.

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.

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, he or she 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.

In large-scale public elections the two rounds of runoff voting are held on separate days, and so involve voters going to the polls twice. In smaller elections, such as those in assemblies or private organisations, it is sometimes possible to conduct both rounds in quick succession. However the fact that it involves two rounds means that, for large elections, runoff voting is more expensive than some other electoral methods. It may also lead to voter fatigue and a reduced turn-out in the second round. In runoff voting, the counting of votes in each round is simple and occurs in the same way as under the plurality methods. Ranked voting systems, such as instant-runoff voting, involve a longer, more complicated count.

• Ranked voting systems
• Keynesian beauty contest
• List of electoral systems by country

• ACE Project: Two Round System
• A Handbook of Electoral System Design from International IDEA
• Electoral Design Reference from the ACE Project