Two-round system

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

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

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.

Examples

French presidential elections

2002

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 (Centre-right, Gaullist): 82.21%
• Jean-Marie Le Pen (Far-right, National Front): 17.79%

German Weimar Republic

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.

Variant

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]

Similar methods

Voting systems

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 then the candidate(s) with the fewest votes is eliminated and excluded from further ballots. The process of exclusion and reballot 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. EB often elects a different winner from runoff voting. Because the two-round system excludes more than one candidate after the first round, it is possible for a candidate to be eliminated who would have gone on to win the election under EB.

A hybrid system of EB is used by the

Instant-runoff voting

Instant-runoff voting (IRV) (also known as preferential voting or ranked-choice 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 (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 single transferable vote (STV) and is used for presidential elections and parliamentary elections. However, 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. STV is used in Northern Ireland, Malta, the Australian senate and various other jurisdictions in Australia.^[2] It is often used for municipal elections in lieu of more party-based forms of proportional representation.

Variants of instant-runoff voting can be designed to reflect the same rules as a two-round voting system. If no single candidate has an absolute majority of votes then only the two highest polling candidates progress to the second count, while all other candidates are excluded and their votes redistributed according to the recorded preferences for continuing candidates. One variant that works this way is called the Contingent vote, detailed below.

Contingent vote

The contingent vote is a variant of instant-runoff voting that has been used in the past in Queensland, Australia. Under the contingent vote voters cast only one vote, by ranking all of the candidates in order of preference. However it involves only two rounds of counting and uses the same rule for eliminating candidates as the two-round system. After the first round all but the two candidates with most votes are eliminated. Therefore, one candidate always achieves an absolute majority in the second round. Because of these similarities the contingent vote tends to elect the same winner as the two-round system, and may produce different results to instant-runoff voting.

A variant of the contingent vote, called the

In the United States, the Louisiana primary, introduced in

In

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.

Tactical voting and strategic nomination

Runoff voting is intended to reduce the potential for eliminating "wasted" votes by

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.

Impact on factions and candidates

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

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^[who?] 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^{[citation needed]} 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^{[citation needed]} 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.

Practical implications

In smaller elections, such as those in assemblies or private organizations, it is sometimes possible to conduct both rounds in quick succession. More commonly, however, large-scale public elections the two rounds of runoff voting are held on separate days, and so involve voters going to the polls twice and governments conducting two elections.

Voter fatigue/suppression

Holding two elections typically leads to voter fatigue and a reduced turnout, especially in the second round. Voter fatigue by design can also be called voter suppression.

Costs

One of the strongest criticisms against the two-round voting system is that the cost to the taxpayer required to conduct two ballots can be nearly twice that of holding a single ballot.^[5] The reason the cost is probably not quite double is that an instant-runoff ballot method, for example, may have more-expensive voting machines (at least until more places adopt this method) and the longer vote-counting time could pose additional costs to election administrators.^[6][7]

Political instability

The two-round voting system also has the potential to cause political instability between the two rounds of voting, adding further to economic impact.^{[clarification needed]}

Simple to tally

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.

Usage

The two-round system is the most common way used to elect heads of state (presidents) of countries worldwide, a total of 84 countries elect their heads of state directly with a two-round system as opposed to only 21 countries that used single-round plurality (first-past-the-post).^[8]

Heads of state elected by TRS in direct popular elections

^[9]

Legislative chambers exclusively elected by TRS in single-member districts

Sub-national legislatures:

Legislatures elected by TRS in multi-member districts (majority block voting)

Sub-national legislatures:

Legislatures partially elected by TRS (mixed systems)

Other examples of use

Two-round voting is also used in

Historically it was used to elect the Reichstag in the German Empire between 1871 and 1918 and the Storting of Norway from 1905 to 1919, in New Zealand in the 1908 and 1911 elections,^[11][12] and in Israel to elect the Prime Minister in the 1996, 1999 and 2001 elections.^[13]

See also

• Ranked voting systems
• Keynesian beauty contest
• List of electoral systems by country
• Arrow's impossibility theorem

References