Countries such as France or Argentina have an election system where the top two candidates proceed to a final runoff round. Historically speaking and across all (or a large number of) such countries, how often does the candidate who came second in the first round end up winning in the second round?
I'm primarily interested in top-level elections, which are listed in this Wiki article. But if there's only data for sub-national level elections, I'll accept that as well.
It's not uncommon. Worldwide 1945-2020 according to an article in Political Studies Review:
About 30% of all second-round competitions in presidential and semi-presidential regimes result in the runner-up winning. Fifty-three of the 181 second-round elections saw the ‘surprising’ electoral comeback of the candidates who placed second in the first round. It is worth noting that a significant percentage of all the runoffs in semi-presidential and presidential regimes are won by the candidate who finished second in the first round. Comebacks at the presidential elections were reported in 34 of 73 countries included in the research.
A footnote further points out significant regional variation:
From about one-quarter in Latin America (24%), and 21.6% of cases in Africa, to about one-third in Europe (31.6%). In Asia (54%) and Oceania (50%), a full half of runoff elections have been concluded with a comeback.
I have gone through all presidential elections since 1990, in the countries that are currently part of the EU. (This means some elections took place before ascension to the EU.) In most EU countries, the president has only limited power, with the notable exeption of France. All have a separately elected head of government (minister president).
Six countries are monarchies (Belgium, Denmark, Luxemburg, Netherland, Sweden, Spain). In seven countries (Estonia, Germany, Greece, Hungary, Italy, Latvia and Malta), presidential elections are held in parliament or a special electoral body. They are extremely divers, from first-past-the-post in the third round in Germany to the extremely complicated Estonian system with multiple supermajority votes in first the parliament, then in an electoral college (that can nominate new candidates). Only one of them, Hungary, uses a runoff second round vote.
Legend:
| Country | A | B | C |
|---|---|---|---|
| Hungary | 6 | 1 | 1 |
Fourteen countries have presidential elections by popular vote. Of them, Ireland is a special case as it uses a instant runoff system. Formally, the winner might not be picked in the second counting round, but quite probably in the last round when only two candidates remain.
| Country | A | B | C |
|---|---|---|---|
| Ireland | 2 | 2 | 1 |
The other countries use a runoff in the second round:
| Country | A | B | C |
|---|---|---|---|
| Austria | 4 | 0 | 2 |
| Bulgaria | 0 | 7 | 0 |
| Croatia | 2 | 4 | 1 |
| Cyprus | 1 | 4 | 3 |
| Czechia¹ | 0 | 3 | 0 |
| Finland | 1 | 4 | 0 |
| France | 0 | 5 | 1 |
| Lithuania | 2 | 2 | 3 |
| Poland | 1 | 5 | 1 |
| Portugal | 7 | 0 | 0 |
| Romania | 1 | 4 | 3 |
| Slovakia² | 0 | 3 | 2 |
| Slovenia | 2 | 4 | 2 |
| Sum | 21 | 45 | 18 |
¹Czechia elected the president in parliament until 2008. The first public vote took place in 2013.
²Slovakia elected the president in parliament until 1998. The first public vote took place in 1999.
