Triangular election in France

Legislative elections

Source:^[9]

• 1958: 235
• 1962: 129
• 1967: 65
• 1968: 49
• 1973: 96
• 1978: 1
• 1981: 1
• 1986: single-round proportional voting (no three-way race possible).
• 1988: 8
• 1993: 15
• 1997: 79 (105 before withdrawals)^[10]
• 2002: 10 ^[11]
• 2007: 1 (12 before withdrawals)^[12]
• 2012: 34 (46 before withdrawals)^[13]
• 2017:1^[14]
• 2022: 7 (8 before withdrawals)^[15]
• 2024: 89 (306 before withdrawals)^[16]

Regional elections

In the 2021 French regional elections there were several run-offs, with the second round preventing the National Rally from winning any regions.^[17]

The percentile threshold to be a candidate in the second round

Development over time

The 12.5% threshold has not always been the same.^[18]

• Following ordinances of 1958 and 1959 which re-established among other things the two-round system, the threshold was 5%.
• With law number 66-1022 of 1966 the threshold changed to 10%^[19].
• With law number 76-665 of 1976 the threshold changed to 12.5%, where it remained as of 2024.^[20]

There were no more sexangular or quinquangular elections after the threshold change of 1966, and the number of quadrangular elections also shrank drastically.^[9]

Voter turnout

The voter turnout is a significant factor influencing the number of three-way races in departmental elections [fr] 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.^[9][16][25]

The graph demonsxtrates two things:

• Turnout must be high enough to have many second rounds with more than two candidates (1958; 1962; 1973; 1997 and 2024)
• On the other hand, if participation is very high, this does not necessarily imply a large number of second rounds with more than two candidates (1978; 1981; 1993)

Bipolarization and tripolarization

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:

• Before 1970 there were not, strictly speaking, two major political forces in opposition. Indeed, the SFIO (then the FGDS) Socialists and the PCF Communists never stood down to help each other, although both parties were left-wing. Similarly, the currents ranging from the radicals to the moderate right opposed the candidates of the Gaullist party. A form of multi-party democracy dominated at that time.^[26]
• A bipolarization of parliamentary life was, on the other hand, fully evident between the elections of 1978 and 1986. Indeed, during this period, we find two large coalitions alternating in power: the Right (composed of the RPR and the UDF) and the Left (composed of the Socialists and the Communists)^[26][9].
• But from the 1986 elections, Jean-Marie Le Pen's National Front began to gain momentum in legislative elections. More particularly in 1997, his party made a fairly significant breakthrough. Although the FN's score was respectable in the first round, it won very few seats in the National Assembly, in particular because of withdrawals intended to form a "Republican Front" against the extreme right. This was not true tripolarization, because Le Pen's party had too little presence in the chamber, but it did entail the rise of a third camp in French political life^[26][27].

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.

• During the period when multipartyism dominated, many second rounds took place with more than two candidates. Also, in particular we we see quadrangular, quinquangular and sexangular vote: this would not happen again during the quarter-century after the 1973 elections, the last one characterised by multipartyism.
• During the period of bipolarization, the number of triangular races collapsed to a single occurrence in each election.
• Finally, as the National Front began to gain momentum around 1986, the number of second rounds with more than two candidates rose again, reaching a fairly high figure in 1997. Indeed, during these elections, FN made a breakthrough: the number of three-way contests peaked at 79 (105 before withdrawals).^[9]

Withdrawals

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.^[16] 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".^[16] 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.

Synthesis

To summarize the factors impacting the number of triangular elections and their influence, here is a summary table:

*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.^[21][22]