In two-round system, how common is that the two remaining candidates have more votes than all candidates (including both of them) on first round?

As this answer exemplifies, in the Brazilian 2014 Presidential Election, the sum of the votes of the remaining two candidates in the second round (~105.5 million) exceeds the sum of their's plus the other 9 candidates 3 weeks sooner (~104 million) with more than 1.5 million votes.

The analysis of the reasons (technical and political) in this particular case are interesting within itself, I want to know if similar situations have occurred in any other time with governments who hold elections in a two-round system.

• Your question is maybe using a slightly ambiguous example: the number of valid/effective votes may have gone up, but the number of cast votes actually went down. Sep 23, 2016 at 15:21
• Thanks for commenting @AndyT, I don't see it as ambiguous. Here, I want to know how common is to the number of valid/effective votes goes up. The probable reasons behind the contradiction you mention are interesting too. Maybe you already knows what they are to this case or maybe you are not interested. If you want to know, I/we could delve into it too... :-) Sep 23, 2016 at 19:34

It doesn't sound particularly unlikely - if the first round is to narrow it down to only two candidates, then there are often two clear candidates that will win. For the second election, you are actually voting for the actual result - at this point you want to make sure that the candidate you dislike doesn't get in (or the candidate you do like does get in) hence you are more motivated to vote.

See e.g. the French Presidential election in 2002. The first round had 28,498,471 votes, but only one of the two "expected" candidates got through. The average person really didn't want Le Pen to win, and 31,062,988 voted in the second round.

• Thanks for the answer @AndyT Good example, but is not it just an outstanding example? Sep 23, 2016 at 19:51

This is, as far as I know, nearly always the case in France, which uses a two-round system for almost all elections (including the regional elections, where it does not make much sense, but not the elections to the European parliament, where it's not possible).

The second round is widely seen as the one that matters. The results of the first round do change perceptions, influence negotiations between political parties and also determine how much public funds a party gets in the following years but who will make the threshold to reach the second round is often not in doubt so that the only thing deciding who gets elected is the result of the second round of voting (certainly for the presidential election - with one major exception, obviously - other elections are a bit more complex).

I could not find a convenient table tallying up voter turnout over a long period of time but I have checked the 2007 and 2012 presidential elections, 2004 and 2010 regional elections, and 2004 local elections on the official election website of the Interior ministry and the stats confirm my recollection.

For presidential elections, the difference isn't huge because turnout is already high and possibly also because many people still vividly recall what happened in 2002 (in France, you just need to say "April 21" without any other qualification and everybody who is old enough and cares at least a bit about politics should know you are speaking of the results of the 2002 presidential election). For regional elections, the difference can be up to 5 percentage points, which means over 2M people (out of population of 66M people, with slightly more than 46M registered voters).

EDIT: I found a Wikipedia article confirming this for the presidential and legislative elections. Note, however, that the table for the legislative, local (cantonales), and municipal elections are not directly comparable as a candidate or a list who gets more than 50% of the vote in the first round of voting is elected directly, which automatically depresses turnout in the second round (and, in municipal elections, many lists run unopposed because France has literally tens of thousands or really tiny municipalities).

If you treat the primary system in the US as a "two round" system, this almost always happens. Factors in the US include: parties often require one to register for that party to vote in their primaries; many states use caucuses, which are more time-consuming; and different states have primaries at different times, making the later voters less inclined to vote.