This Paradox Splits Smart People 50/50

0:00 There is a problem that I can't bring up without starting a fight.

0:03 No, what?

0:04 It just seems so obvious to me.

0:06 Now I'm all screwed up, man.

0:07 (Casper laughs)- It has infiltrated every single

0:10 Veritasium meeting in the last two months.

0:12 It's trivial.

0:13 (laughs)- I didn't think you would fall for this side.

0:15 Just makes sense.

0:16 Let's go!

0:17 That's crazy!

0:18 And I even argued with Derek about it.

0:21 There's no way you're trying to convince me.

0:23 I don't care.

0:25 So, here's the setup.

0:26 You walk into a room, and there's a supercomputer and two boxes on the table.

0:31 One box is open, and it's got $1,000 in it.

0:34 (cash register ka-chings) There's no trick.

0:35 You know it's $1,000.

0:37 The other box is a mystery box, you can't see inside.

0:41 You also know that this supercomputer is very good at predicting people.

0:45 It has correctly predicted the choices of thousands

0:47 of people in the exact problem you're about to face.

0:51 Now, you don't know what that problem is yet,

0:53 but you do know that it has been correct almost every time.

0:57 Now, the supercomputer says you can either take both boxes,

1:01 that is the mystery box and the $1,000, or you can just take the mystery box.

1:07 So, what's in that mystery box?

1:09 Well, the supercomputer tells you that before you walked into the room,

1:13 it made a prediction about your choice.

1:16 If the supercomputer predicted you would just take the mystery

1:19 box and you'd leave the $1,000 on the table,

1:21 well, then it put $1 million (cash register ka-chings) into the mystery box.

1:25 But if the supercomputer predicted that you would take both boxes,

1:30 then it put nothing in the mystery box.

1:33 The supercomputer made its prediction before you knew about

1:36 the problem and it has already set up the boxes.

1:39 It's not trying to trick you, it's not trying to deprive you of any money.

1:43 Its only goal is to make the correct prediction.

1:47 So, what do you do?

1:48 Do you take both boxes or do you just take the mystery box?

1:52 Don't worry about how the supercomputer is making its prediction.

1:56 Instead of a computer, you could think of it as a super intelligent alien,

1:59 a cunning demon, or even a team of the world's best psychologists.

2:04 It really doesn't matter who or what is making the prediction.

2:07 All you need to know is that they are extremely accurate

2:11 and that they made that prediction before you walked into the room.

2:15 Pause the video now if you want to think about it.

2:17 (soft playful music) Got your answer?

2:23 So, I should just take two boxes, like, obviously.

2:26 I'm gonna say I'm just gonna take the $1 million and go with it.

2:29 Of course you take two boxes!

2:31 I would pick both boxes, I think.

2:33 I would not get the two boxes.

2:34 I think I'm taking both boxes.

2:36 Let's go!

2:36 (interviewee laughs) Okay.

2:37 This is seeming less paradoxical than I thought because I

2:40 should just go in and take the mystery box only.

2:44 No!

2:45 What?

2:46 There are two camps, one-boxers who would take only the mystery box,

2:51 and two-boxers who take both.

2:54 But as American philosopher Robert Nozick wrote, "To almost everyone,

2:57 it is perfectly clear and obvious what should be done.

3:00 The difficulty is that these people seem to divide almost evenly on the problem,

3:04 with large numbers thinking that the opposite half is

3:08 just being silly." This is known as Newcomb's paradox,

3:11 named for its inventor, William Newcomb.

3:14 The Guardian newspaper polled over 31,000 people about this problem in 2016.

3:19 53.5% were one-boxers and 46.5% were two-boxers.

3:25 Now, if you find it hard to see why anyone would pick the opposite side,

3:29 well, here are the arguments for each camp.

3:33 Look, I'm a reasonable guy and I like money,

3:35 so I'm gonna do whatever gets me the most money.

3:38 So, let's go weigh the outcomes of both of these decisions.

3:42 First, I'm gonna say that the probability that the computer

3:45 predicted my decision correctly is gonna be C, so the computer got it right.

3:49 And because of that, the probability it got it wrong is gonna be 1- C.

3:54 So, let's look at what happens if I try to two-box.

3:56 There is a C chance of me getting $1,000

3:59 and a 1- C chance of me getting $1,001,000.

4:03 If I add these two together, I get a weighted sum,

4:06 which is gonna tell me how much I can expect to get if I try to two-box.

4:10 This is also known as expected utility or the EU of two-boxing.

4:15 And I can just simplify this expression a tiny bit.

4:18 So, let's look at what happens if I try to one-box now.

4:20 There's a C chance of me getting $1 million

4:22 and there's a 1- C chance of me getting nothing.

4:25 So, we can cancel this out, simplify this to just $1 million times C.

4:31 If I equate these two expressions,

4:33 I'm gonna get the C at which these two expected utilities are equal,

4:36 and it turns out that the C at which this happens is 0.5005,

4:41 or 50.05%, which means if the computer is

4:46 better at predicting than what is basically random,

4:50 then the expected utility of one-boxing is gonna be higher.

4:54 Now, I know that the computer is much better at predicting

4:56 than that because it accurately predicted thousands of people before me,

5:00 which means I'm sticking with my one box.

5:04 Here's my $1 million.

5:05 Take that, Casper.

5:07 Thank you very much.

5:09 So, I should go in and take the mystery box and leave the other.

5:11 'Cause I'm assuming that its prediction is pretty good, it's a supercomputer.

5:15 Okay, so you're saying it's not paradoxical because the choice is obvious.

5:18 I'm very surprised.

5:19 Why?

5:20 Because to me, the answer is also obvious,

5:22 and to me, the answer is you take both boxes.

5:25 So, here's how I think about the problem in a way that actually makes sense.

5:28 You know that the supercomputer has already set up the boxes,

5:31 so whatever I decide to do now,

5:33 it doesn't change whether there's zero or $1 million in that mystery box,

5:38 and that gives us four possible options that I've written down here.

5:41 If there is $0 in a mystery box,

5:44 then I could one-box and get $0 or I could two-box and get $1,000,

5:49 but there could also be $1 million in a mystery box.

5:52 And in that case, I would get $1 million if

5:55 I one-box or I would get $1,001,000 if I two-box.

6:00 So, I'm always better off by picking both boxes.

6:03 This is known as strategic dominance where I always pick the dominant strategy,

6:08 which in this case is to two-box.

6:11 So, give me those boxes.

6:13 The two-boxer argument makes a lot of sense to me.

6:16 Once you explain it, I'm like, "Okay, yeah,

6:19 I can see why exactly you're right." But I can also see that just having

6:24 those thoughts in your brain are what

6:26 might allow the computer to give you nothing.

6:28 I think I'm grateful that I just don't have those thoughts.

6:32 It's so funny because I was totally expecting you to go two box.

6:36 No way.

6:37 No way, man.

6:38 It seems like there are two perfectly

6:40 reasonable approaches that give two completely different answers,

6:44 and that's because your choice actually reveals

6:47 something fundamental about how you make decisions.

6:50 It comes down to these two statements.

6:52 First, as far as you know,

6:54 basically everyone who has taken one box has walked away a millionaire,

6:58 and everyone who has taken two has walked away poor.

7:01 Second, the supercomputer made its prediction

7:04 before you even knew about the problem.

7:07 The boxes are already set up,

7:09 so your decision now can't change if the million is in there or not.

7:14 Both of these statements are true,

7:16 but there's a hidden assumption in each that divides people.

7:20 We pick both and the computer picks both?

7:23 You just get the $1,000.

7:24 I think I would just pick the mystery box.

7:26 Just the mystery box, probably.

7:28 Yeah.

7:28 I might be taking the mystery box.

7:30 Just the mystery box?

7:31 Yeah, it might be.

7:33 Okay, why?

7:35 I don't know, I guess the supercomputer is right, no?

7:38 Here's the hidden assumption for us one-boxers.

7:40 My expected utility calculations are based on probabilities that are

7:44 using prior evidence of how accurate the supercomputer is,

7:48 because the thousands of people that it accurately predicted before me

7:52 is evidence enough for me that when I go for one box,

7:56 there's gonna be $1 million waiting in there for me.

7:58 This is based on something called evidential decision theory.

8:02 And using this decision theory, you get these expected utilities,

8:06 and my choice is obvious from there.

8:10 And it turns out a lot of you actually thought the same way.

8:12 We polled our audience, got more than 24,000 responses,

8:16 and it turns out two thirds of you are one-boxers.

8:20 I know, it's crazy.

8:21 I don't trust this.

8:22 It's looking to be like you're less

8:23 and less rational with these results, Casper.

8:26 So, your argument is kind of that if you one-box,

8:28 it will have predicted that you were gonna

8:30 one-box and you'll walk out with the money.

8:32 That is pretty convincing.

8:34 Casper, I'm starting to really doubt this two box side of things.

8:37 How could you not be a two-boxer?

8:39 Gregor has this really funny way of thinking about things,

8:42 but I make my decision based off something else,

8:45 something a little more rational because I believe that whatever

8:48 I do now can't influence and change the past.

8:52 I only take into account things that I can actually influence.

8:55 And clearly, whatever I do now,

8:58 whatever I think now is not gonna change whether that $1 million is gonna be

9:01 in the mystery box or not because it was

9:03 already set up before I learned about the problem.

9:07 This is known as causal decision theory,

9:09 where you only take into account things that you can actually cause.

9:12 And so, with this, your expected utility calculation changes,

9:16 and that's because you need to use a different probability,

9:19 one where you could actually cause that $1

9:22 million to be in the mystery box or not.

9:24 So, right before the supercomputer made its prediction,

9:27 there was some probability that it thought I was going to one-box.

9:32 I know, it's weird, but bear with me.

9:34 So, let's say that probability is P, then that's the probability that I'm going

9:38 to use in my expected utility calculation.

9:41 And the expected utility to one-box is just gonna be 0+ $1 million times P.

9:48 That's pretty good, but the expected utility for two-boxing

9:51 is gonna be $1,000+ $1 million times P.

9:57 But that's just the same as the expected

9:59 utility for one-boxing plus an extra $1,000.

10:02 So, no matter what the computer predicted,

10:04 my expected utility is always higher by picking both boxes.

10:09 So, of course, you're gonna two-box.

10:10 Anyone in their right mind would pick both boxes.

10:13 It's made the prediction before you're in there,

10:16 whether I have facing this thing being 90%,

10:18 100%, it actually doesn't really matter.

10:20 I think you guys are imposing your will on-- Yes, it does!

10:22 He's cooking, bro.

10:23 Like, yeah, you guys think that your decision,

10:26 whatever you think now is gonna change the past.

10:29 That's called wishful thinking.

10:30 Yeah, like, come on, I'm two boxes.

10:32 I'm two boxes.

10:33 It only makes sense.

10:34 I'm back with Casper.

10:36 Exactly, welcome to camp two-boxers.

10:38 (laughs)- I'm not losing $1 million.

10:40 It was never in the room, man.

10:41 You're gonna walk into a room and there's either money

10:43 in the room or there isn't money in the room.

10:44 Your question is, do you pick it up?

10:46 Of course.

10:46 We're trying to do you a favor here!

10:48 You're not doing me a favor 'cause your decision making does not affect...

10:52 Like, your little thought does not change God's mind, bro.

10:55 Henry, if you convinced yourself that you're a one-boxer,

10:58 you've convinced the machine.

11:00 I don't believe that.

11:01 What do you mean you don't-- I don't believe you

11:03 convincing yourself should impact what the machine thinks of you.

11:05 Because often, you're just walking into a room

11:07 and it's already made the prediction.

11:08 You can't impact it, you know?

11:10 So, whatever you think is more important,

11:12 whether that's the evidence of the supercomputer's accuracy

11:15 or the fact that the boxes are already set up,

11:18 well, that affects how you calculate the expected utility.

11:21 And because both of those assumptions are true, both camps have valid answers.

11:26 But if there's no right answer, then is this just a meaningless problem?

11:30 Well, not really.

11:32 Because it actually reveals a surprising amount about three important questions.

11:37 Does free will exist?

11:38 What does it mean to be rational?

11:40 And is there an ideal way to act in life?

11:44 For example, the only way you're going to win this game

11:47 is to already be the kind of person to one-box,

11:50 but then two-box at the last second anyways.

11:52 That's the only way you're gonna get $1,001,000.

11:57 But some would argue that that itself is impossible.

12:00 If the predictor is so good,

12:02 let's say it's 100% accurate, then that's not even possible.

12:06 Would you say that's true?

12:08 Yeah.

12:09 Then a follow-up question is, if such a perfect predictor would exist,

12:13 does that mean that free will doesn't exist?

12:17 Because you're saying there's nothing you can do in between walking

12:20 into that room and making your decision

12:23 that ends up changing what was predetermined.

12:27 That's right, and maybe this reveals where I'm coming from, and I

12:30 think where I'm coming from is maybe free will doesn't exist.

12:33 I come down in this point of like free will is an illusion,

12:36 but our world operates in a way

12:39 that is indistinguishable from free will being real,

12:43 and therefore, you have to act as though it's real, as though it's 100% real.

12:49 Interesting.

12:50 If we think that free will is not real and it's an illusion,

12:53 and then you have someone who's committing crimes and then you wanna say,

12:57 "Well, that's not his fault." Therefore, instead of putting, you know,

13:01 murderers in jail for 25 years,

13:03 we're just gonna give them some gardening classes or so.

13:06 Like, the problem is,

13:07 that then changes the environment where everyone knows you can

13:11 kill someone and you can go to, like, do the gardening.

13:13 So, you can't change the system based on the knowledge that it's an illusion.

13:16 Whether we do or don't have free will, you have to live as though it exists.

13:21 So, you've still gotta make a choice, one box or two boxes?

13:25 Which brings us to our second question, what does it mean to be rational?

13:30 I'm the guy who acted rationally and doesn't

13:32 believe his thoughts can influence the past.

13:35 But your rational choice will have given you a $1,000.

13:39 I know, yeah, it's tough.

13:40 It's tough.

13:42 [Gregor] Let's see what I can buy with $1 million.

13:44 None of these look great.

13:45 I think we can be more creative.

13:46 Private island sounds pretty nice.

13:48 All right, Casper, what do you wanna go buy with 1,000, man?

13:51 (Casper laughs) (Henry laughs)- [Casper] This is

13:53 known as the "Why Ain'cha Rich?" argument,

13:55 which boils down to one super annoying question,

13:59 if you're so smart, then why ain'cha rich?

14:02 You know, if winning is getting more money,

14:04 then of course the one-boxers are gonna end up better off than the two-boxers.

14:08 But maybe it's not about who wins, but about what's rational.

14:12 In their 1978 paper, philosophers Gibbard and Harper argue that the rational

14:17 choice is to pick both boxes.

14:19 Although they do admit that two-boxers will fare worse.

14:23 They instead say that the game is rigged.

14:25 And "if someone is very good

14:27 at predicting behavior and rewards predicted irrationality richly,

14:31 then irrationality will be richly rewarded." But I

14:34 think that's a bit of a cop out,

14:36 because really, Newcomb's paradox reveals something surprising,

14:40 that sometimes in order to be a rational person, you must act irrationally.

14:46 There's one question of what's a rational person.

14:48 There's another question of what's a rational act.

14:51 Most of the time, rational people do rational acts, sometimes they just don't.

14:55 And I think this is analogous to the situation in the prisoner's dilemma.

15:02 [Casper] In the prisoner's dilemma,

15:03 you and another player compete for money by either cooperating or defecting.

15:07 If you both cooperate, (audio chimes) then you get three coins each.

15:10 (coins clinking) But if you defect (audio chimes) and your opponent cooperates,

15:13 then you get five coins (coins clinking) and they get nothing.

15:16 And if you both defect, (buzzer buzzes) you get one coin each.

15:19 (coins clink) So, no matter what your opponent does,

15:21 you are always better off by defecting.

15:24 But if you play this game not once, but repeatedly, then everything changes.

15:29 All of a sudden, you're better off by cooperating.

15:33 What's a rational society?

15:34 A rational society is full of cooperators.

15:37 What's a rational person?

15:39 Maybe a rational person is a defector.

15:41 And normally, you might expect a rational society is made up of rational people,

15:46 but I think it's familiar that rationality at one

15:48 level isn't compatible with rationality at the other level.

15:51 So, while the rational act is the two box,

15:53 a rational society would actually be full of one-boxers.

15:57 Now, I'm a fervent two-boxer,

15:59 but there are three ways that you can get me to one-box.

16:03 The first is if my choices now can actually change the past.

16:06 For example, say the supercomputer makes its prediction

16:09 by opening up some tiny wormhole to see the future.

16:12 Well, in that case, if I choose one box now,

16:14 that actually causes the $1 million to be

16:17 placed in there in the past, so I one-box.

16:19 Second, if there are multiple trials, because now with every game,

16:23 each of my choices builds up a reputation, so if I one-box,

16:27 then I'll be predicted as the kind of person to one-box,

16:29 and so I get the $1 million either in this round or a later one.

16:33 And third is, if I can pre-commit.

16:34 If I can talk to the computer to make my case before it makes its prediction,

16:39 then I will 100% one-box because staying true to my word is important to me,

16:43 and the supercomputer would know that.

16:45 If I put my word on it, I'll take the one box.

16:47 Yeah, 100% one box, yeah.

16:50 But there are some realistic scenarios where staying

16:52 true to a worse option could have deadly consequences.

16:56 On the 29th of August, 1949, the Soviet Union detonated the RDS-1 bomb

17:02 as part of their first nuclear weapons test.

17:04 This sent the US and the USSR into a furious arms race.

17:08 By the mid-1960s, the US had over 30,000 nuclear warheads,

17:13 and the USSR had just over 6,000.

17:16 Both sides were more than capable of destroying the other.

17:19 (explosion booms) The US Secretary of Defense at the time,

17:22 Robert McNamara, didn't advocate for disarmament.

17:25 Instead, he recommended a strategy of "assured destruction," where the US should

17:30 be able to deter a deliberate nuclear attack by "maintaining a highly

17:34 reliable ability to inflict an unacceptable degree of damage upon any single

17:40 aggressor." This strategy eventually became known

17:42 as mutually assured destruction, or MAD.

17:45 If either country attacked first,

17:47 the other would surely retaliate and lead to total annihilation of both sides.

17:52 (explosion booms) So, having that commitment to retaliate is beneficial.

17:56 It stops the attack from happening in the first place.

18:00 Now, say you are the US president during the Cold War.

18:03 You have publicly committed to retaliate if the US is ever attacked.

18:07 But you've just received word that the Soviets have launched their missiles.

18:11 It's not a system error, it is a real attack.

18:14 So, what do you do?

18:15 If you launch now, then at best, everyone in the US and USSR dies.

18:20 And at worst, you get a nuclear winter that kills nearly everyone on the planet.

18:25 Everyone in the whole world dies, then I probably don't launch.

18:28 But you did pre-commit.

18:30 Yep.

18:31 I don't like the outcome.

18:32 No, it's terrible.

18:33 I don't like the outcome of everyone on Earth dying, so I'm gonna just not.

18:37 When the country is electing their leader, which leader do you want to elect?

18:42 Do you want to elect someone who's crazy and is always gonna press that button,

18:46 or do you wanna elect someone who makes the seemingly

18:49 rational choice of saving people and not press that button?

18:52 I think you want someone who maintains

18:55 the posture of always pushing that button.

18:58 That's right.

18:59 And then you want someone who secretly will not actually push that button.

19:04 There is an inherent risk there,

19:06 which is that if anyone finds out, you're exposed.

19:10 There's this other game theory interaction, the game they call chicken.

19:13 You're both driving your cars at each other.

19:14 The worst thing is if neither of you swerves, because then you both die,

19:18 but you win if the other person swerves and you don't.

19:21 The best strategy in this game is to visibly

19:24 take the steering wheel out of your car

19:27 and throw it out the window so that the opponent can see that you've done that.

19:30 Now they know you cannot swerve.

19:32 You're this mad dog that's just going straight ahead.

19:36 And now they realize,

19:37 "Now my best action is just to swerve." And that similarly,

19:40 like what you want with the nuclear deterrent as they set up in "Dr.

19:45 Strangelove."- In the 1963 film, "Dr.

19:48 Strangelove or: How I Learned to Stop Worrying and Love

19:50 the Bomb," the Russians built the perfect doomsday device.

19:54 As soon as it detects a nuclear attack or any tampering,

19:57 it automatically triggers a large enough nuclear

19:59 explosion to kill everyone on the planet.

20:02 The tampering kill switch isn't there to prevent enemies from disabling it.

20:06 It's to prevent the Russians themselves from having second thoughts.

20:10 Now, the whole point of the device is to be so devastating

20:13 and automatic that the US would never even think about launching an attack.

20:18 But this only works if everyone knows that the device exists,

20:22 which is the whole point of the movie.

20:24 In both Newcomb's paradox and MAD,

20:26 the best outcome follows from a pre-commitment to a worse option.

20:30 That's what gets you at least $1 million in the former

20:33 and a tense but stable peace in the latter.

20:36 It's the commitment that's important.

20:38 So, maybe being rational isn't deciding about what to choose in the moment,

20:43 but it's about deciding what rules you're going to live by.

20:46 The question isn't how to act.

20:48 The question is what rules one ought to follow,

20:52 or how does one even decide what rules to follow?

20:54 Sometimes it's put in the form of, if

20:57 you knew that you were a robot with programming,

21:00 that you could set and you could rewire yourself

21:04 to make yourself obey one set of rules rather than another,

21:09 the question is, what sort of rules would you wire yourself to obey?

21:12 And what you would do is you would make

21:14 yourself into the kind of creature that sort of always

21:17 acts in line with the commitments that would've been

21:20 good to form had you even known about the problem.

21:23 When you're in a situation like the Newcomb case,

21:26 you would end up finding yourself think,

21:28 "If I had been able to make a pre-commitment,

21:31 what pre-commitment would've been the good one to make?

21:33 The good pre-commitment to make would've been to be a one-boxer.

21:37 And since I've already wired myself up to be the kind

21:41 of person that lives up to all the pre-commitments I would've made,

21:45 then I'm already, in effect, committed to one-boxing,

21:48 even though I didn't realize it."- I love this approach, because for me,

21:51 that kind of makes it an iterated problem,

21:55 but maybe more an iterated problem in life.

21:58 If I don't look at it as a single case and I

22:01 sort of almost think about it as for every future predictor,

22:05 for every future case, or like, almost building your own reputation, right?

22:09 Exactly.

22:10 Like, you always wanna live up to the commitments you've made,

22:13 so even if you haven't heard of it before,

22:16 you'd wanna stick to those ideal pre-commitments so that you

22:20 are acting in line with the best version of yourself.

22:23 Yeah, that would convince me to be a one-boxer.

22:26 It's rare to convince anyone to switch on the Newcomb problem.

22:29 (laughs)- The thing is,

22:31 even if I never run into another generous supercomputer again,

22:34 life doesn't end after I walk out of that room.

22:37 Like, I should always defect (audio chimes) in a one-shot prisoners

22:40 dilemma because I can only gain by betraying the other player.

22:43 (coins clinking) But when I play multiple rounds of the game,

22:45 like in life or in society, everything changes.

22:49 Suddenly, it pays to cooperate.

22:51 So, being the kind of person

22:52 that sticks to an ideal pre-commitment is beneficial.

22:56 So, maybe I was just a one-boxer kind of guy all along.

22:59 All it took was a little reframing and a new perspective.

23:03 (screen beeping and chirping)- The core of Newcomb's paradox is deciding if

23:09 a strong correlation that you know isn't causal should matter in your decision.

23:14 So, the question is, what do you do?

23:15 Do you pick both boxes or do you just pick the mystery box?

23:19 Might be taking the mystery box.

23:21 Mystery box.

23:22 I would pick both boxes, I think.

23:23 I also pick both boxes, so.

23:25 (laughs)- I'll take the mystery box.

23:27 Okay, why?

23:29 Okay, so you would pick just the mystery box and probably get the $1 million.

23:33 Yeah.

23:33 So that's based off,

23:35 I guess that it's almost always been correct, so there's this correlation.

23:38 Do we think that correlation is the same as causation?

23:43 But how can you tease out what's causation and what's just correlation?

23:47 That's a difficult problem that has applications far beyond thought experiments.

23:51 For example, how can you tell whether a drug really works

23:54 or if any beneficial effects are simply due to random chance?

23:58 (screen chirping) Big questions like these combined with hands-on

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