Newcomb's Problem

[Mise]

This has nothing to do with probability, as has been made clear repeatedly earlier.

The success rate of Omega is fairly strong evidence that one of (a), (b) or (c) is true.

But if you deny (a), (b) and (c), then no, probability doesn't matter to you.

I still haven't seen anyone successfully tackle my "random number generator" corollary

You're assuming that true randomness exists... I see no more reason to believe that the world is NOT deterministic than to believe that it is.

But like I said, you're just denying all three of the above. So it makes sense that if you assume true randomness, AND successfully use it, then Omega can't make a prediction.

And even then, it doesn't prove that Omega CAN'T make the prediction, if you DIDN'T use your true random generator. The universe could be deterministic insofar as your actions can be determined, but not the outcome of your truly random number generator. You would have to prove that your actions are truly and fundamentally unpredictable, which is not an easy job.

(Actually, you'd have to prove that this specific action was unpredictable. There's lots of actions that I can predict fairly successfully... Maybe this is one that Omega can predict?)

 

[Sidhe]

The fact is the only way you could come to a conclusion is by using past events to predict the future, unless your an idiot and believe that Omega is just the luckiest bastard on the planet. Presented with that situation only a mollusc - who was given no more information than that in the OP - would chose anything different, assuming he didn't have two weeks to go away and talk cavernous amounts of philosophical BS until people got bored that is, in which case he may well come back and gun down Omega and steal his boxes. Which is what I suggested he do earlier.

Something tells me though I should of just stuck with my first answer then I'd of gotten something meaningful out of this excuse to wave your arms about and talk about things that you have no idea exist and therefore no way of saying its a paradox or anything else. It is if you believe in x it isn't if you believe in y.

Like I said in my second post it depends completely on how you set up the parameters as to what the answer is. Thus it's about that, not about a decision per se.

But that said given that situation most people would chose to be rational not start vacillating on whether determinism or randomness exists, or some unknowable predictive process is in effect. Because they would be forced to make a choice based on something tangible, and most people would go for logic or common sense. Not fortnight long exercise in how many knots you can tie a simple experiment in if you invent enough reason to. Which whilst is academically interesting, it doesn't really gel with reality, because presumable Omega hasn't given you the option of disappearing off for two weeks. You'd have to rationally at least assume that probability is your only friend, because that has real predictive power, and because anything else is supposition and needlessly superfluous to your decision in the here and now, when it happens.

 

[Gogf]

Bollocks quite frankly.

If it has nothing to do with logic and probability then it is a meaningless thread.

OK tell me it has to do with fairy tales and moonbeams and arm waving philosophical crap? Rather than a decision based on real concerns, given real events, given real meaning. Perhaps we should of said does God exist? And then we can proceed?

My rather voluminous arse it doesn't boil down to maths.

Sidhe, perhaps you misread my post that you quote, but nowhere did I say "it has nothing to do with logic." What I did say is that probability is irrelevant.

 

[Gogf]

The success rate of Omega is fairly strong evidence that one of (a), (b) or (c) is true.

But if you deny (a), (b) and (c), then no, probability doesn't matter to you.

I haven't read every single post in this thread. What the heck are (a), (b), and (c)?

 

[Gogf]

Like I said, if Omega doesn't cheat. You are assuming he cheats by putting the money in after you make your decision, which is what makes taking box B a better decision. Otherwise it is obviously better to take both, if he doesn't cheat. This is of course based on the assumption that Omega can't be tricked by half-belief - you can't falsely pretend to be a one boxer and then change. You must hope he thought wrong and you get a million and a thousand or you just get your thousand instead of nothing.

Untrue. If you consider the puzzle with Perfy's explanation in mind, it is clear that taking one box is better (this from a former two-boxer).

 

[Gogf]

Omega has to cheat.

You could just flip a coin when presented with the boxes.

How could he predict that without cheating?

Okay, this is a neat way to give yourself a 50% chance of choosing the right box, but why do that when you can guarantee yourself a 100% chance of getting $1,000,000?

 

[Kennigit]

Perhaps I'm misunderstanding mise, but as I understand it, you say that determinism (a) supports the one box arguement.

Ironically, I'd say that the two box arguement actually supports determinism more: a two boxer argues that the boxes are determined and nothing will change. The values of the boxes are pre-determined (ie. the determinism).

 

[Gogf]

First, you work out the probability that an alien who has been right a hundred times out of a hundred will be right the next time. Basically, find the improbability of 100 correct answers arising from pure guesswork. Call this P. This will give you the chance that the alien is simply guessing. If he is guessing, the chance that he is wrong is given by P/2.

Now, there are four cases:

a) Alien right, you pick B
b) Alien right, you pick both
c) Alien wrong, you pick B
d) Alien wrong, you pick B

a) If the alien is right, and you pick B, you have a reward of 1 million. The value of this case is (1-P/2)*(10^6).
b) If the alien is right, and you pick both, then the value of this case is (1-P/2)*(10^3)
c) If the alien is wrong, and you pick B, then you get nothing. The value of this case is (P/2)*0 = 0
d) If the alien is wrong, and you pick both, then you get the jackpot, valued at (P/2)*1001000

The condition of balance is: Val(a) + Val(c) = Val(b) + Val(d)

which is:

(1-P/2)*(10^6) + 0 = (1-P/2)*(10^3) + (P/2)*1001000

Which gives P = 0.999.

That is, both choices are equal only when the probability that the alien will be wrong 0.999 times every times he makes a choice - or, in layman's terms, that he is wrong every 999 out of 1000 times.

Now again, there are two choices. Either he knows, or he is guessing.

The probability that he is guessing is, or has made a hundred correct choices purely by guess work, is 2^(-100).

As this is clearly less than the required value of 0.999, we can safely conclude that the case in which we take only the box B is the correct one to choose in this scenario. It's not guaranteed, of course, but it's valued far more highly. Much more than trillions of times more highly, in fact.









Was that rough proof of correctness enough of a justification for me saying that we should pick choice B?

And do I win this thread?

No, you lose the thread, because your calculations have no basis in reality and this kind of thinking has been REPEATEDLY debunked. There are very good arguments for both sides—this is not one of them.

 

[Mise]

I haven't read every single post in this thread. What the heck are (a), (b), and (c)?

(a) determinism, (b) violation of causality, or (c) some law of nature that requires there to be $1m or not in box B as a result of a choice you make.

Ayatollah So re-jigged (c) as such:
"(but in (c), replace "result" with "logical consequence given the laws of nature")."

 

[Gogf]

(a) determinism, (b) violation of causality, or (c) some law of nature that requires there to be $1m or not in box B as a result of a choice you make.

Ayatollah So re-jigged (c) as such:
"(but in (c), replace "result" with "logical consequence given the laws of nature")."

I don't see what any of those have to do with "probability." Reread the post you originally replied to and what I was replying to in it.

 

[Mise]

I don't see what any of those have to do with "probability." Reread the post you originally replied to and what I was replying to in it.

Omega's 100% success rate makes it highly likely that at least one of (a), (b) or (c) is true... I mean, there's been some very... "creative"... explanations for how Omega could pick the right box. But to me, it just sounds completely absurd that one should go to such lengths to explain away the hard facts, when all one has to do is accept (a), (b) or (c). Personally, I find (a) and (c) quite easy to swallow. (b) not so much.

The probabilities previously calculated have no direct impact on which box you should pick, I agree. But they give a clear indication of what kind of universe we live in. If we live in a universe where none of those things is true, then picking two boxes is most rational. But the evidence suggests that at least one of them is true, and thus we should pick one box.

 

[Gogf]

Omega's 100% success rate makes it highly likely that at least one of (a), (b) or (c) is true... I mean, there's been some very... "creative"... explanations for how Omega could pick the right box. But to me, it just sounds completely absurd that one should go to such lengths to explain away the hard facts, when all one has to do is accept (a), (b) or (c). Personally, I find (a) and (c) quite easy to swallow. (b) not so much.

The probabilities previously calculated have no direct impact on which box you should pick, I agree. But they give a clear indication of what kind of universe we live in. If we live in a universe where none of those things is true, then picking two boxes is most rational. But the evidence suggests that at least one of them is true, and thus we should pick one box.

Okay, I think I agree with what you're saying here, but I really don't understand how it replies to "probability is not relevant here"!

 

[Mise]

Okay, I think I agree with what you're saying here, but I really don't understand how it replies to "probability is not relevant here"!

Well, it is relevant

TBH, I was just taking issue with both sides' dis/use of "probability".

 

[Syterion]

Untrue. If you consider the puzzle with Perfy's explanation in mind, it is clear that taking one box is better (this from a former two-boxer).

I don't understand that explanation.

 

[warpus]

You're assuming that true randomness exists... I see no more reason to believe that the world is NOT deterministic than to believe that it is.

But like I said, you're just denying all three of the above. So it makes sense that if you assume true randomness, AND successfully use it, then Omega can't make a prediction.

And even then, it doesn't prove that Omega CAN'T make the prediction, if you DIDN'T use your true random generator. The universe could be deterministic insofar as your actions can be determined, but not the outcome of your truly random number generator. You would have to prove that your actions are truly and fundamentally unpredictable, which is not an easy job.

(Actually, you'd have to prove that this specific action was unpredictable. There's lots of actions that I can predict fairly successfully... Maybe this is one that Omega can predict?)

You are missing where I'm going with my generator.

Omega is supposed to be amazing at predicting human behaviour.. not so amazing at predicting the roll of dice...

That's what this entire thing is about: Omega's amazing personality prediction powers. He's so amazing at it that he'll know what choices we are going to make!

Nowhere did it say that he could predict what number a random number generator would yield.

Are we changing the parameters of the paradox?

 

[warpus]

Okay, this is a neat way to give yourself a 50% chance of choosing the right box, but why do that when you can guarantee yourself a 100% chance of getting $1,000,000?

Yeah, but everyone here is saying that the coin could only yield 1 result.. ie. only heads or only tails.

That is the issue I am bringing up. It doesn't make sense.

Or could I beat Omega's system (even if I lost) by flipping a coin?

 

[LightFang]

The probability of anything happening is 50% because either it happens or it doesn't.

 

[warpus]

The probability of anything happening is 50% because either it happens or it doesn't.

That sounds very insightful until you realize that it's wrong.

 

[Mise]

You are missing where I'm going with my generator.

Omega is supposed to be amazing at predicting human behaviour.. not so amazing at predicting the roll of dice...

That's what this entire thing is about: Omega's amazing personality prediction powers. He's so amazing at it that he'll know what choices we are going to make!

Nowhere did it say that he could predict what number a random number generator would yield.

Are we changing the parameters of the paradox?

What parameter of the paradox states the Omega can only predict personal choices?

Anyway, yeah, if Omega can predict something as complicated as human choice, but not something as simple as a dice roll, then you're right...

 

[Gogf]

Yeah, but everyone here is saying that the coin could only yield 1 result.. ie. only heads or only tails.

That is the issue I am bringing up. It doesn't make sense.

Or could I beat Omega's system (even if I lost) by flipping a coin?

Well presumably Omega would predict that you would use a coin. We don't know how he would react to you introducing randomness, though.