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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