All of that can be true, and yet, in front of the boxes, you should take two boxes (if there is a choice of course).
If that’s your attitude, you’re the kind of person who two boxes, and the predictor will pretty consistently predict that, which makes you the kind of person who walks away with only $1000.
Is that more correct than being the kind of person who walks away with $1mil? I wouldn’t say so. That’s a bizarre form of correct to me.
I am only talking about the rational choice in front of the boxes. Obviously before that, the rational thing is to appear as a one-boxer to trick the predictor, that is compatible with the rational choice being to take two boxes.
Is that more correct than being the kind of person who walks away with $1mil?
The most correct is to trick the predictor and take two boxes anyway.
Seems like you’re consistently losing 999k with that strategy, compared to the alternative. I’ll leave that kind of rationality to you. My kind of rationality leaves me with 1mil
True, the case of 100% accuracy is fundamentally different, and I find it hard to even grasp it, because I believe in indeterminism, and so that scenario kind of seems inherently contradictory. But yeah, if I knew for an absolute fact the predictor was 100% accurate, I would one-box. And that doesn’t really change my views on the normal versions where it doesn’t have perfect prediction.
I think we could probably have a separate section for the omniscient version where the entity is 100% correct. In this version, I am pretty sure everyone would one-box, as it is the obvious choice in that case. But there’s still something to be said about how and if it even makes sense for the predictor to be perfectly accurate…
It’s fine; I am not going to be playing a Newcomb game anytime soon, so I prefer to understand the problem rather than be irrational to win a hypothetical million dollars.
You need to make use of the actual possible winnings, and not just hide them behind a variable.
If you choose only Box 2 then there are two possible outcomes:
- You win $1,000,000
- You win $0
If you choose both boxes then there are two possible outcomes:
- You win $1,000
- You win $1,001,000
However, each outcome is not equally likely. Given the near-infallibility of the predictor, if you choose only Box 2 then P(win $1,000,000) is much greater P(win $0), and if you choose both boxes then P(win $1,000) is much greater than P(win $1,001,000).
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as I said before, your implications don’t follow. You are still saying “If 1+1 = 2 then it will rain tomorrow”.
if you choose only Box 2 then P(win $1,000,000) is much greater P(win $0)
Let’s decompose. 1 means one box, p is the prediction, c is the choice.
P(win $1,000,000) = P(p = 1,c = 1) = P(c = 1) \times P(p = 1 | c = 1)
P(win $0) = P(p = 2, c = 1) = P(c = 1) \times P(p = 2|c = 1)
We can remove the P(c = 1). You are saying P(p = 1|c = 1) > P(p = 2|c = 1)
This isn’t necessarily true. As I said, we only know P(c=1|p=1) is very high but depending on P(p = 1) the inequality could be true or false. And more importantly, it doesn’t even depend on whether you choose box 2 or two boxes.
What is true is that if you choose box 2 only you will win less money than if you chose two boxes. Only need to look at the three statements I wrote.
Right. Either way, I’m OB. If it’s 100%, I’m assured of $1M.
If it’s 99%, I’m still darned likely to get $1M. $1K isn’t so much that I won’t risk losing it for the chance of $1M.
If we remove the boxes language and you are in front of the table, and you are told: “You can either take all the money on the table or only some of it”. Would you still say you take only some of the money?
Are you removing all the words about the predictor on purpose? Where’d that stuff go?
It’s irrelevant. People are tricked by the fact they don’t see the money. My hope is that when you lay out the fact that there is money there and the choice is to take all of it or some of it, then people may realize the rational choice.
So you agree with this:
If you choose only Box 2 then there are two possible outcomes:
- You win $1,000,000
- You win $0
You just disagree that if I choose only Box 2 then P(win $1,000,000) > P(win $0).
So let’s compare two versions of the experiment. In version 1 the predictor is almost always right and in version 2 the predictor is almost always wrong.
In both versions I choose only Box 2.
I say that in version 1 I am more likely to win $1,000,000 than $0 and in version 2 I am more likely to win $0 than $1,000,000. It’s certainly not the case that I am as likely to win $1,000,000 in version 1 as in version 2. The reliability of the predictor is a relevant factor that you are wrong to ignore.
It’s clearly not irrelevant lol. It’s not irrelevant that the majority of people who use your strategy leave the room with 1000 and the majority who choose to one box leave the room with a million.
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As FlannelJesus says.
It depends on the base rate. But with the same base rate then you are right.
I got mixed up and that’s not really the problem so forget the last message.
This probability thing would work if what happens is: You make your choice, for example box 2. Then a random process with 99% chance of winning is run and you get the reward. If you take both boxes, a random process is launched with 1% of winning is run and you lose.
What you need to understand is the processes already happened and you already have the (potential) reward in front of you. The probabilities and the reliability of the predictor is irrelevant as they already made their prediction and already put the reward in front of you.
So yes in general, P(win $1,000,000) > P(win $0) if you want but this is including different predictions when you know you are only in a specific situation with a specific prediction.
You still haven’t told me which of the three statements is wrong.
Okay, so this is my response to all OBs hitherto involved, @noAxioms, @Michael, @Patterner and @FlannelJesus. I am also tagging you @Suny, since you’re in this conversation, but this obviously isn’t my explanation to you, since you aren’t an OB. I will respond to all of you by responding to noAxioms’ points, because my response is mostly the same. Also, at the end of this post, I will include a thought experiment to help show why TB-ism is rational in Version 1 of the Newcomb Scenario.
Yep, thanks for pointing that out!
The second question is very important to TBs, because any actually rational TB would change their answer if they could. So if you are a TB in Phase 1, with time available before the entity has made its prediction and filled the boxes (thus starting Phase 2), then you should do everything you can to stop being a TB within that time. For you, as someone who’s already (for now) an OB, you do not feel any need to do so. As such, I can imagine why the second question seems irrelevant.
Yes, in Version 1, there is a premise explicitly demanding you don’t know about this dilemma, not even in theory, before you find yourself in Phase 2. Right now, we know about this dilemma, so by the eighth premise, we couldn’t possibly be playing Version 1 of Newcomb’s Game right now. Though I’m not sure it would matter much to me, because I would need a penalty contract to become an OB anyways, and I am not about set one up for a hypothetical game that will never happen, as then there would be many such games I’d have to deal with. But I guess I could somehow magically give myself the OB philosophy right now, despite it being irrational (I don’t believe this would be possible for the vast majority of people, but it is a distracting possibility), and so I find that the eighth premise cleanly separates Version 1 from Version 2. In Version 2, I focus on not only people who know about Newcomb’s dilemma, but they know they will actually face it in the future, justifying their preparation.
To me, the preparation could not just be mental, I would need a penalizing contract. I cannot just teach myself to ignore the direction of causality and simple mathematics as preparation, so instead I must change the mathematical scenario by adding F. In so doing, I will make more money, by rationally making myself into an OB.
But, I don’t think anyone in their right mind disagrees with OB-ism in Version 2 of the Newcomb Scenario. So from here on out, I will focus on Version 1.
I don’t understand your point here. The point of Version 1’s extra premise is that you do not know about the dilemma in Phase 1. You only learn about the dilemma after the boxes’ contents have been determined.
How is it not valid there is some probability P that it predicted you were an OB? You say it knows about your nature with high certainty, and you happen to be an OB… so, that doesn’t mean P doesn’t exist, it just means P is close to 1. The analysis of expected utility remains the same, because P is still just… a constant number, some probability. What is you point here?
So, this is the funny part. If we are in Phase 1 of the Newcomb game, then you are right. It is not to your advantage to stop being an OB. And in my case, as a TB, it is to my advantage to become an OB. But this is now explicitly Version 2 of the game. We are not in Phase 1 of Version 1 of the Newcomb Game, because there is no decision-making in Phase 1 regarding Version 1 of the Newcomb Game, by definition of Version 1.
In Version 1, by the time you are reflecting on your OB-vs-TB nature, the boxes’ contents have already been determined, and you can do nothing to change them. Whether you get that $1M is out of your control at that point in time, but whether you get that $1000 is very much still in your control, at that same point in time.
Obviously, we’ll hope that that $1M is in Box 2, but either way, you should be grabbing both Box 1 and Box 2 at this point. I know this sounds paradoxical, but if you really break down the causal picture, you realize all the strangeness here arises from playing a game that rewards a past nature of irrationality, which is then correlated with a present nature of irrationality, and this present irrationality is seen as a choice to cause the reward… but the reward has already been caused. You’ve already won Phase 1 of the game, which means you will, by your nature, probably lose Phase 2 of the game by pointlessly leaving $1000 on the table… That’s still a good deal, if you look at the entire time-line, but it is a bad deal if you restrict your view to Phase 2.
If I could choose to be the person who wins Phase 1 instead of Phase 2 (all other aspects of myself remaining equal of course), then I would chose so.
…But if I could choose so, I would not be playing Version 1 of the Newcomb Game, I would be playing a different version. And as said, in those other versions, I am OB all the way, even if becoming so requires a little extra work from me.
Oh, but which you want to be… is irrelevant in Phase 2, Version 1. That is a future-oriented attitude, but your winnings have already been determined, and you will never play this game again (by the seventh premise).
Instead, ask, which do you wish that you were? And well, you may wish that you were an OB in Phase 1, but you cannot affect this fact. In Phase 2, if you act as an OB, that is correlated with you having been an OB in Phase 1. But acting as an OB in Phase 2 does not cause the $1M to be in the box, because it was already there!
Being an OB in Phase 2 does not cause you to be an OB in Phase 1. However, being an OB in Phase 2 is highly causally correlated with being an OB in Phase 1. Being an OB in Phase 1 is EXCLUSIVELY that which causes you to likely win the $1M. As such, being an OB in Phase 2 is merely correlated with winning the $1M, but it cannot CAUSE it. (Again, we’re assuming you cannot impact the past here)
And it is the fact that you had this irrational stance in Phase 1 that caused Box 2 to likely contain the $1M. That does not change that fact by the time you’re in Phase 2, it is completely irrational to leave that $1000 on the table.
As you said, you agree it’s there. When you are in Phase 2, there are no risks regarding the $1M anymore. It is impossible for you to lose your $1M by also taking Box 1. Of course, if you thought like that during Phase 1, you’d lose out on $1M.
And if you find yourself thinking like that in Phase 2, then you’ve discovered some bad news… you’re a TB. And if you’re a TB in Phase 2, you were probably a TB in Phase 1, which means Box 2 probably doesn’t have the $1M.
But you cannot change this fact at this point. So, you might as well take both boxes.
Consider instead this hypothetical game here; The Irrationality Game.
The Irrationality Game
You enter a room, and there is an entity with a rationality-meter. The game works like this; the entity scans you, and if you are irrational, then you win $1M. If you are rational, you win $1000.
Rational people will lose this game compared to irrational people. They are still (by definition) more rational than the winners. This is a game were “playing well” does not mean playing rationally, because nobody is playing this game rationally, nor irrationally.
If you are playing a game where your choices are not deliberate, then you are not playing (ir)rationally. Perhaps you think being rational or irrational is a deliberate choice. Well even so, why would you chose to generally be irrational (thus losing lots of value) just so you can win The Irrationality Game on the extreme off-chance you ever play it? When the contestants of the Irrationality Game show up, they will not win because they play more rationally… by definition. Winning usually means being more rational, but not always. Being rational means winning the highest number of the right kinds of games, in general. Being maximally rational does not mean winning every conceivable game, as that is incompatible with being maximally rational.
Now, maybe you would disagree that the Newcomb Game is such a game. But if you do, then you are thinking about Version 2 of the game. In Version 1, we have that Phase 1 is essentially the same game as the Irrationality Game.
Phase 2 is thus, for those who are rational, just the choice to collect their $1000 prize, which they almost always will do, because they are rational. Phase 2, for the irrational people, is just the choice to reject an additional $1000 dollars, which they almost always will do, because they are irrational in this way. That’s why they’re winning the $1M in the first place. They think their actions now can impact their nature in the past.
You have to separate winning in a game like this from being rational, because games like these are special, contrived games in which winning is correlated with being irrational, by definition! And we should not change our definition of rationality because of this, because doing so will make us lose more money when applying it to all games. Rationality wins in general, that is why it is rationality. But in a game literally designed to punish rationality, of course it does not win.
I was using emphatic language for sake of comedy. I am aware that IQ and RQ are not the same, though that said, I am not sure how well IQ measures intelligence in the first place. But yeah, this is entirely off-topic. I did not actually mean OBs are dumb. This is all a silly (yet important) thought experiment, and so I think a little silliness on our part is warranted as we discuss this.
That’s your problem, you do not see that the counter-intuitive combinations of facts here are not contradictions. They are counter-intuitive products of counter-intuitive premises.
No, let me bring back my definition for rationality in this context.
In Version 1, do OBs use logic and rationality to maximize the money they make? No, because in Phase 1, they are not using anything in order to be an OB. They just are, unknowingly. They are playing Phase 1 well, but they not playing Phase 1 rationally, nor irrationally, because a precondition of that is knowing that you are playing.
So in Version 1, it is only Phase 2 that can be played rationally. TBs enter Phase 2, and they decide to take $1000 instead $0, clearly the rational choice. They lost compared to OBs, but that was because they were unknowingly playing Phase 1 badly. But they too were playing Phase 1 arationally. In Version 1, no-one can play Phase 1 (ir)rationally. This is key to seeing why there are no contradiction in recognizing TB-ism as rational.
A game that, unbeknownst to you, punishes you for being rational… is a game in which rational people will lose. That is trivial. Version 2, in a sense, does not heavily punish rational people, but it does require extra work from them compared to irrational people, because TBs have to set-up something extra to allow for a rational conversion into OB-ism.
They must do this because OB-ism pays better in the bigger picture, yet simultaneously, OB-ism pays worse in Phase 2 (assuming no preparation). But you don’t get Phase 2 without playing the whole game, and so TBs have their own rationality weaponized against them. But, they use that same rationality to defend against it, by for example creating a penalty.
The Time-Travelling Rhetorician
Alice is an OB. Bob is a TB. This is just who they are. In Phase 1, they are an OB and a TB, respectively.
Accordingly, the entity predicts that Alice will be an OB in Phase 2, and that Bob will be a TB in Phase 2. And in accordance with the game, when Alice walks into the room, Box 2 has $1M. Equivalently, when Bob walks into the room, Box 2 has $0.
And we’re looking at the typical case here. So, Alice only takes Box 2, because it is in her nature to do so. Bob also acts like he typically would, so he takes both Box 1 and Box 2.
Alice thinks she played better than Bob, and she did! But she did not play more rationally. The bulk of the money she won was determined by no choice of her own, during Phase 1, when her irrational nature as an OB was sensed by the entity. The opposite is true for Bob.
Now consider, a master rhetorician, who also time travels. He wants to prove Alice wrong. So, he time travels back to Phase 1. The entity has no way of predicting the time traveler’s influence, of course, because he is not a part of the data of the past. He is from the future, after all.
Alice is about to take only Box 2. But the time traveler convinces her to take both boxes. And so she does, and gains an extra $1000. This is cheating. If she needed a time-travelling rhetorician to become a TB, then we can not fault the entity for being wrong. The entity was right, because Alice truly was an OB. Her reaction to the actual Newcomb game was that of an OB. But the time traveler comes and gives her an ability to cheat, and as a result, she gets to eat her cake and have it too.
But this shows that she never needed to take only Box 2 in Phase 2. By the time she enters Phase 2, on the off-chance that she would act against her own nature, she could win an extra $1000, which is clearly more rational. But this is not likely, because one does not simply outsmart the entity. That does not change that fact this is nonetheless a demonstration of the real causal picture.
The time traveler also goes back to when Bob has entered Phase 2. Bob is about to take both boxes, but the time traveler convinces him not to. He convinces him to only take Box 2.
And so Bob does, and instead of winning $1000, he wins $0.
So, we see that for both Alice and Bob, once they are in Phase 2, their rational choice is to two-box (assuming they’re in Version 1 of the scenario).
Conclusion
I am trying to reiterate my points here in different ways, to attack the problem from different angles. Below, I will give the most concise argument for why two-boxing is rational.
Box 2 contains $1M due to your pre-disposition to being an OB. Box 2 contains $1M because the entity predicted you would be an OB. You won Phase 1 because of your irrational nature, not because of your (ir)rational playing.
In Phase 2, taking only Box 2 does not cause you to win the $1M. But taking only Box 2 is correlated with the cause for why Box 2 contains $1M. But to change your mind, however unlikely that is, does not risk that those $1M magically vanishes from Box 2. When you feel like taking only Box 2, you are presented with the good news that you are an OB. But these goods news are not the cause of Box 2 containing $1M, they are merely the indication thereof.
OBs are conflating correlation with causation. And it is precisely their nature of making this conflation that happens to win them $1M in Version 1 of the Newcomb game. But this conflation is nonetheless irrational, because in other, more realistic games, this irrationality will cost them money. Also, conflating correlation with causation is… simply false. Therefore, it is irrational.
We do not redefine what rationality is based on one contrived edge case. Rationality is what works best in general, and rationality is based in truth.
Conflating correlation with causation does not work best in general, therefore it is irrational. Heck, conflating correlation with causation doesn’t even work best in Phase 2 of V1 of Newcomb’s Game… because by then, you have already reaped the rewards of your past conflation of correlation and causation. At this point, it would only help you further to realize this conflation was irrational, even though it happened to win you an extra $1M in this case. If you truly only realized this in Phase 2, then you will $1M + $1000. This is of course unlikely.
If you redefine rationality or start believing in a different directionality of causation, all because of Version 1 of Newcomb’s scenario, then you are missing the bigger picture.
In V1, Phase 2, the only risk you are facing is leaving the $1000 on the table. You are not risking the $1M, because it is already there or already not there. Your decisions in Phase 2 cannot possibly change that.
It’s not irrelevant that the majority of people who use your strategy leave the room with 1000 and the majority who choose to one box leave the room with a million.
First, that’s not what I said was irrelevant; I said the “boxes” language and the fact that the money is hidden are irrelevant.
Second, what I am telling you is that all the people leaving the room with $1,000,000 could have left the room with $1,001,000 if they had taken the rational choice. Taking two boxes ALWAYS gets you more money if you are in the situation described in the problem.
But those factors that you left out are an important part of why one boxers consistently leave with 1000x more money than two boxers. So… they’re relevant.
I don’t think that’s the right diagnosis of one boxers. I think “whatever causes people to be one boxers seems to be also consistently causing the predictor to predict that you’re a one boxer.” There’s no confusion between causation and correlation there. There’s a root cause for both the prediction and the behaviour.
And really, it’s hard to argue the group of people leaving with more money is irrational. We can all acknowledge that, right? Like you can argue your it, but you have to make a really damn good argument, because leaving with more money is… rational