Énigme : gagner des élections grâce aux mathématiques

Le Point

Les mathématiques sont souvent considérées comme un drôle de langage avec lequel certains peuvent s'amuser pendant des heures, tandis que d'autres ont des poussées d'urticaire rien qu'à son évocation. Pourtant, les maths sont partout dans notre vie. Et ces dernières recèlent parfois d'étranges casse-têtes.  C'est à ces énigmes que s'est attaqué Antoine Houlou-Garcia, chercheur associé à l'EHESS, auteur de "21 énigmes pour comprendre (enfin !) les maths" (Albin Michel, 2022) et de "Il était une fois le zéro" (Alisio, 2023). Dans une série de vidéos, le fondateur de la chaîne YouTube Arithm'Antique décrypte pour Le Point certains de ces problèmes mathématiques qui ont traversé l'Histoire ou régissent notre quotidien. Au programme de cet épisode : comment gagner des élections grâce aux mathématiques ?#énigmes #mathématiques #logique  Suivez nous sur : - Youtube : https://www.youtube.com/c/lepoint/ - Facebook : https://www.facebook.com/lepoint.fr/ - Twitter : https://twitter.com/LePoint - Instagram : https://www.instagram.com/lepointfr - Tik Tok : https://www.tiktok.com/@lepointfr - LinkedIn : https://www.linkedin.com/company/le-point/posts/ - www.lepoint.fr

Transcript

00:00 Are you ready to face the challenge of 5 mathematical puzzles?

00:03 It starts now!

00:04 The first puzzle is based on real facts.

00:07 We are in the Senate of the State of Virginia in the United States in 1980 to be precise.

00:12 Before explaining the puzzle, I will explain the context.

00:15 The Senate of Virginia has 40 senators.

00:17 For an amendment, that is, a law, to be accepted,

00:20 this amendment must obtain an absolute majority of votes, that is, 21 votes.

00:25 In the case where we would have an equality 20 for 20 against, and only in this case,

00:31 the lieutenant governor is brought to vote to break the equality,

00:35 what is called the "tie break" in English.

00:37 In our case in 1980, an amendment was debated in the Senate of Virginia

00:41 aimed at prohibiting any discrimination based on the sex of a person.

00:45 We are precisely oriented towards a case of equality 20 favorable, 20 unfavorable.

00:51 So the lieutenant governor will be brought to vote,

00:55 and we already know that the lieutenant governor is in favor of this amendment.

00:59 So the amendment will pass, it is a certainty.

01:02 Except that in reality we are still before the vote.

01:05 We know the opinions of some and others, but no one has voted yet.

01:09 The vote will take place in an hour.

01:10 And it turns out that a senator unfavorable to the amendment will succeed in making him fail.

01:17 The question is the following, knowing that this senator has done nothing illegal,

01:21 has not killed anyone, has not bought anyone,

01:23 knowing also that no one has changed their mind,

01:26 how did this senator manage to fail the amendment?

01:30 I'll give you a few seconds to think, you can pause the video if you want,

01:33 and then I'll give you the answer.

01:35 So, did you find the answer?

01:45 In fact, to find it, you have to think about this senator who absolutely wants to fail the amendment.

01:51 What can he do? Three things.

01:52 The first is simply to vote "no" to the amendment proposal.

01:56 This is what we expect him to do.

01:58 This is the most obvious thing.

02:00 The second thing he can do is vote "yes" to the amendment.

02:03 Well, that would be weird since he is against it.

02:05 And then there is a third thing he can do, it is to abstain.

02:08 So, oddly, abstaining in general does not make us win.

02:12 But let's look at the electoral mechanism behind this,

02:15 which mathematically implies some surprising things.

02:18 The senator who is against the amendment abstains.

02:22 So, we no longer have an equality of 20-20,

02:25 we now have a dissymmetry of 20-favorable, 19-disfavorable.

02:31 Of course, the majority has the favorable side.

02:35 But does it have the absolute majority?

02:37 No, the absolute majority is 21 votes.

02:40 And this 21st vote, the favorable side of the amendment,

02:43 hopes to get it thanks to the vote of the governor lieutenant.

02:46 Except that since there is no equality of 20-20,

02:49 the governor lieutenant has no way to vote.

02:54 By abstaining, he leaves the score at 20-19,

02:58 which does not allow the governor lieutenant to vote to reverse the balance,

03:02 nor the favorable side, which certainly has the majority but not the absolute majority, to win.

03:07 And that's how, with a little bit of arithmetic,

03:10 we manage to win elections that we were in to lose.

03:14 If you want to know more about some mathematical manipulations of voting,

03:17 you can consult "21 Enigmes pour Comprendre Enfin les Maths"

03:21 that I had the pleasure of co-writing with Thierry Maugenet.

03:24 (upbeat music)

03:27 (upbeat music)

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