The triangular election () is a characteristic of the French electoral system as a consequence of the country's two-round voting system for elections to the National Assembly. Such a triangular election occurs when three candidates from the first round have reached the retention threshold, and none of them withdraws from the second round. The winner of this election is determined by a relative majority. Depending on the elimination thresholds adopted for the first round, the second round may also give rise to a quadrangular election (4) or even a quinquangular (5) or sexangular election (6).
A particularly notable triangular election took place during the 2024 French legislative election between the ', New Popular Front, and the Union of the Far-Right.
The first triangular elections appeared with the establishment of the two-round majority single-member constituency system. This electoral system was put in place during the legislative elections of 1852, and then kept during the Second French Empire and the French Third Republic, from the elections of 1876.
This voting method was originally considered favourable to the Legitimists, Orleanists, and Bonapartists, three political movements of the French right wing who suffered from division. Indeed, in the case of an incomplete bipolarisation of the vote, where a divided bloc withdraws in favour of the best of them during the second round, the triangular configuration is then more favourable to the political camp which has two qualified candidates.
This election system influences the politics of France more generally, as in order to be represented in the National Assembly without being able to win alone, you must have the support of other parties, in theory making the result more representative .
The occurrence of triangular races depends on the voting method of the elections, and more particularly on the qualification threshold for the second round.
Source:
In the 2021 French regional elections there were several run-offs, with the second round preventing the National Rally from winning any regions.
The number of three-way races per decade in various elections has never stabilised around any value. This is because of many influencing factors, sometimes favouring three-way races, sometimes causing the number of second rounds with more than two candidates to fall.
The higher the election threshold required to qualify for the second round, the fewer candidates there will be who will reach the second round and therefore the fewer three-way races.
The 12.5% threshold has not always been the same.
There were no more sexangular or quinquangular elections after the threshold change of 1966, and the number of quadrangular elections also shrank drastically.
If the threshold for remaining in the second round is a percentage of votes cast, which is the case for and municipal elections for municipalities with more than 1,000 inhabitants, then it is easier for a list or for a candidate to succeed in crossing this threshold, because too low a turnout would have no influence on the election.
Indeed, in the case of and legislative elections where a percentage threshold of registered voters is in force, candidates wishing to qualify for the second round are dependent on abstention.
The voter turnout is a significant factor influencing the number of three-way races in and legislative elections.
In the context of a 12.5% threshold of registered voters, for three candidates to qualify, the third must also win at least one eighth of the votes of registered voters. But this assumes that at least three eighths (37.5%) of registered voters go to the polls. Thus, a high abstention rate precludes any three-way race in the second round. The higher the turnout, the more it favours the possibility of there being a triangular election. However, when comparing historical statistics of the participation rate and the number of second rounds with more than two candidates during the legislative elections under the Fifth Republic, no correlation is evident.
The graph demonsxtrates two things:
Another factor influencing the number of triangular races is the presence of partisanship, which in France is known as bipolarisation or tripolarisation.
To better understand the subject, here are some historical explanations concerning the influence of these phenomena on French parliamentary life between 1958 and 1997:
The relationship between bipolarization, tripolarization and the number of second rounds is therefore as follows:
In the event of bipolarization, voters shift massively to two political camps, in a more or less balanced way. In this situation, other candidates will then receive very few votes: in general, they will not reach the threshold for the second round. Bipolarization thus favours duels between two parties.
On the other hand, in the event of tripolarization, the votes of the French are distributed among three political groups, again in a more or less balanced way. Thus, in this situation and with a fairly good turnout, three candidates will remain into the second round. Tripolarization thus favours triangular elections.
When superimposing this influence factor on the curve of second rounds with more than two candidates during the legislative elections (1958-1997), the correlation is stronger.
A final crucial factor in understanding the number of triangular elections is withdrawal from the second round.
In the case 2024 French legislative election, 89 triangular races were recorded. This number represents only ten more than in the 1997 French legislative election, in a context where the National Front collected far fewer votes than the National Rally, and where the tripolarization of French political was similar to 2024. This was because before withdrawals, the number of three-way races was 306, a figure more in line with the context of tripolarization and high participation at the time. In the end, no less than two thirds of the three-way races were cancelled because candidates withdrew. The reason was that while the National Rally came out on top in the first round in many constituencies, the presidential majority and the new popular front withdrew their candidates who came in third place, in order to block the extreme right and form a "Republican Front". This practice of withdrawing the least well-placed candidates to prevent the first from winning the election was known before, but in a much less widespread manner.
To summarize the factors impacting the number of triangular elections and their influence, here is a summary table:
<nowiki>*</nowiki>Note that in the case of regional and municipal elections (of more than 1000 inhabitants) where the retention threshold is calculated from the number of votes cast, the participation rate has no influence on the number of three-way races.