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You can say the same thing about Newcomb's problem. It doesn't mean you can choose whether or not there will be a million in one of the boxes. It means that if there is a million in one of the boxes, then "some combination of logic, rationalisation or impulse will make you decide" to choose only one of the boxes (and if there's no million, then similarly you'll end up taking both boxes.) "You can then tell from your decision whether" you'll get the million or not, "but you couldn't have made the other decision, no matter what."
Either that, or you can be the first to outguess Omega and get the million as well as the thousand...
Nope, this reasoning doesn't work with Newcomb, and it doesn't work with the Smoking Lesion. If you want to win, you one-box, and you don't smoke.
One potentially-significant difference: in Newcomb, it is precisely the fact that you're disposed to two-box that causes you to lose out. (Omega is detecting and responding to this very disposition.) In Smoking Lesion, the disposition to smoke is intrinsically harmless; it merely happens to be correlated (due to a common cause) with a disposition to get cancer.
(But if you're right that the two cases are on a par, then that would significant increase my confidence that two-boxing is rational. The smoking lesion case is by far the more obvious of the two.)
Responding to the supposed difference between the cases:
Omega puts the million in the box or not before the game has begun, depending on your former disposition to one-box or two-box.
Then the game begins. You are considering whether to one-box or two-box. Then the choice to one-box or two-box is intrinsically harmless; it merely happens to be correlated with your previous disposition and with Omega's choice. Likewise, your present disposition to one-box or two-box is also intrinsically harmless. It is merely correlated with your previous disposition and with Omega's choice.
You can no more change your previous disposition than you can change whether you have the lesion, so the two cases are equivalent.
And if people's actions are deterministic, then in theory there could be an Omega that is 100% accurate. Nor would there be a need for simulation; as cousin_it has pointed out, it could "analyze your source code" and come up with a proof that you will one-box or two-box. In this case the 100% correlated smoking lesion and Newcomb would be precisely equivalent. The same is true if each has a 90% correlation, and so on.
If some subset of the information contained within you is sufficient to prove what you will do, simulating that subset is a relevant simulation of you.
I'm not sure what kind of proof you could do without going through the steps such that you essentially produced a simulation.
Could you give an example of the type of proof you're proposing, so I can judge for myself whether it seems to involve running through the relevant steps?
See cousin_it's post: http://lesswrong.com/lw/2ip/ai_cooperation_in_practice/
Many programs can be proven to have a certain result without any simulation, not even of a subset of the information. For example, think of a program that discovers the first 10,000 primes, increasing a counter by one for each prime it finds, and then stops. You can prove that the counter will equal 10,000 when it stops, without simulating this program.
See, to me that is a mental simulation of the relevant part of the program.
The counter will increase, point by point, it will remain an integer at each point and pass through every integer, and upon reaching 10,000 this will happen.
The fact that the relevant part of the program is as ridiculously simple as a counter just means that the simulation is easy.
So would you smoke even if the previous correlation were 100%, and included those who knew about the Lesion?
This could happen in reality, if everyone who smoked, smoked because he wanted to, and if everyone who sufficiently desired it did so, and if the sufficient desire for smoking was completely caused by the lesion. In other words, by choosing to smoke, you would be showing that you had sufficient desire, and therefore the lesion, and by choosing not to smoke, you would be showing that you did not have sufficient desire, and therefore not the lesion.
Under these circumstances, if you chose not to smoke, would you expect to get cancer, since you knew that you had some desire for smoking? (Presumably whether the desire was sufficient or not would not be evident to introspection, but only from whether or not you ended up smoking.) Or choosing to smoke, would you expect not to get cancer, since you say it doesn't make any difference to whether you have the lesion?
For the correlation to be 100%, smoking would have to be ABSOLUTELY IRRESISTIBLE to people with the lesion.
Hence, if I had the lesion, I would smoke. I wouldn't be able to resist doing so.
And of course smoking would have to be ABSOLUTELY UNTHINKABLE for people without the lesion.
Hence, if I didn't have the lesion, I wouldn't smoke, I wouldn't be able to even try it.
I think that the "ABSOLUTELY IRRESISTIBLE" and "ABSOLUTELY UNTHINKABLE" language can be a bit misleading here. Yes, someone with the lesion is compelled to smoke, but his experience of this may be experience of spending days deliberating about whether to smoke - even though, all along, he was just running along preprepared rails and the end-result was inevitable.
If we assume determinism, however, we might say this about any decision. If someone makes a decision, it is because his brain was in such a state that it was compelled to make that decision, and any other decision was "UNTHINKABLE". We don't normally use language like that, even if we subscribe to such a view of decisions, because "UNTHINKABLE" implies a lot about the experience itself rather than just implying something about the certainty of particular action or compulsion towards it.
I could walk to the nearest bridge to jump off, and tell myself all along that, to someone whose brain was predisposed to jumping off the bridge, not doing it was unthinkable, so any attempt on my part to decide otherwise is meaningless. Acknowledging some kind of fatalism is one thing, but injecting it into the middle of our decision processes seems to me to be asking for trouble.
For the correlation with Omega to be 100%, one-boxing would have to be ABSOLUTELY IRRESISTABLE when there was a million in the box...
Hence, if there was a million, the person would one-box. He wouldn't be able to resist doing so...
And of course taking only one box would have to be ABSOLUTELY UNTHINKABLE for people when the million wasn't there.
And so on.
Nope. In the Newcombian situation the lines of causality are different.
What's in the box is explicitly caused by what you will choose, whereas in the smoking lesion example they simply share a cause.
Different lines of causality, different scenario.
No. What is in the box is not caused by what you will choose. It is caused by Omega after analyzing your original disposition, before the game begins. After you start the game, your choice and the million share a cause, namely your original disposition. So the cases are the same-- same lines of causality, same scenario.
You can no more change your original disposition (which causes the million), than you can change the lesion that causes cancer.
You can control your original disposition in exactly the same way you usually control your decisions. Even normally when you consider a decision the outcome is already settled and the measure of all Everett branches involved already determined. Just because you consider the counterfactual of local miracles that result in a different decision when evaluating your preferences doesn't mean any such local miracles actually happen. Your original disposition is caused by your preferences between the two "possible" actions, just like with any other decision. The lesion example is different because your preferences are at no point involved in the causal history of the cancer.
Even going on that basis, which I disagree with (I disagree with the "lack of simulation" hypothesis; see the other thread of comments in a second)
Right now, I could precommit myself to winning in all newcomb-like problems I encounter in future, and thus, right now, I can change my disposition.
I can't precommit to not finding something irresistable due to brain damage/lesions/whatever.
That's a pretty significant difference.
You can precommit to not smoking in the same way you can precommit to taking only one box. If you might later find smoking irresistable, you might later find taking both boxes irresistable.
Precommitting changes my disposition, making me not find two-boxing irresistable.
Precommitting CAN'T change whether I get the lesion or not.
In Newcombs scenario, precommitting changes the outcome. In the smoking lesion, it doesn't.
I find that the term "cause" or "causality" can be very misleading in this situation.
As a matter of terminology, I actually agree with you: in lay speech, I see nothing wrong with saying that "One-boxing causes the sealed box to be filled", because this is exactly how we perceive causality in the world.
However, when speaking of these problems, theorists nail down their terminology as best they can. And in such problems, standard usage is such that the concept of causality only applies to cases where an event changes things solely in the future[1], not merely where it reveals you to be in a situation in which a past event has happened.
When speaking of decision-theoretic problems, it is important to stick to this definition of causality, counter-intuitive though it may be.
Another example of the distinction is in Drescher's Good and Real. Consider this: if you raise your hand (in a deterministic universe), you are setting the universe's state 1 billion years ago to be such that a chain of events will unfold in a way that, 1 billion years later, you will raise your hand. In a (lay) sense, raising your hand "caused" that state.
However, because that state is in the past, it violates decision-theoretic usage to say that you caused that state; instead, you should simply say that either:
a) there is an acausal relationship between your choice to raise your hand and that state of the universe, or
b) by choosing to raise your hand, you have learned about a past state of universe. (Just as deciding whether to exit in the Absent-Minded Driver problem tells you something about which exit you are at.)
[1] or, in timeless formalisms, where the cause screens off that which it causes.
I think you've misunderstood me. "What you will choose" is a fact that exists before omega fills the boxes.
This fact determines how the boxes are filled.
"What you will choose" (some people seem to refer to this, or something similar, as your "disposition", but I find my terminology more immediately apparent) causes the future event "how the boxes are filled"
Oh, sorry. Some of this stuff is just tough to parse, but your points are correct.
I'll leave up the previous post because it's an important thing to keep in mind.
Indeed. I'll try to be clearer in future.
That isn't relevant. For all you know, Omega also created the universe, and so set it in the situation that disposed you to choose the way you did.
When the game actually begins, you cannot change your disposition, and you cannot change the million dollars.
Someone should wrap it up with a problem where what you choose is determined by what's in the box. Any ideas, anyone?
Actually, this is excellent. We could rewrite Newcomb's problem like this:
Omega places in the box together with the million or non-million, a device that influences your brain, programming the device so that you are caused to take both if it does not place the million, and programming the device so that you are caused to one-box if it places the million. In other words, Omega decides in advance whether you are going to get the million or not, then sets up the situation so you will make the choice that gets you what it wanted you to get.
However, the influence on your brain is quite subtle; to you, it still feels like you are deciding in the normal way, using some decision theory or other.
Now, do you one-box or two-box? This is certainly exactly the same as the smoking lesion. Nor can you answer "I don't have to decide because my actions are determined" because your actions might well be determined in real life anyway, and you still have to decide.
If you one-box here, you should not smoke in the lesion problem. If you don't one-box here... well, too bad for you.
The obvious answer is ‘whatever Omega decided’. But I hope that I one-box.
You might as well say in general that you do "whatever the laws of physics determine."
But you still have to decide, anyway. Hoping doesn't help.
I do whatever I'm being influenced into doing.
This is a fact.
You can argue all you like about what I should do, but what I will do is already decided, and isn't influenced by my thoughts, my rationality, or anything else.
All the information needed to determine what I will do is in the lesion/machine.
Applying rationality to a scenario where the agent is by definition incapable of rationality is just plain silly.
Do you think that in real life you are exempt from the laws of physics?
If not, does that mean that "what you will do is already decided"? That you don't have to make a decision? That you are "incapable of rationality"?
Every event has multiple causes, and what causes you point out is not such important as you seem to think. In Newcomb, Omega's decision and your one-or-two-boxing are both ultimately consequences of the state of the world before the scenario has started.
The only difference between Newcomb and the lesion is that in case of 100% effective lesion, there will be no correlation between having read about EDT and smoking. And in a world where there was such a correlation, one should start believing in fate.
Well, yeah, which is why people resist the story about Omega, think it must be nonsense, and decide to two-box (although it would be better to explicitly reject the story). Or interpret it to imply backwards causality (in which case even CDT makes you one-box) or something else that violates the laws of physics as I know them.
This is one reason to stick with probabilistic versions of Newcomb's Paradox.
In both cases (Newcomb's Paradox and the Smoking Lesion), this seems to another example of the difficulty with 0 and 1 as probabilities.
Yes I can, right now.
I think the difference is that your disposition to one-box or two-box is something you can decide to change. Whether you were born with a lesion is not.
When you are standing there, and there is either a million in the box or there isn't, can you change whether or not there is a million in the box?
No, no more than whether you were born with a lesion or not. The argument, "I should smoke, because if I have the lesion I have it whether or not I smoke" is exactly the same as the argument "I should take two boxes, because if the million is there, it is there whether or not I take two boxes."
I agree, insofar as I think "I should not smoke" is true as long as I'm also allowed to say "I should not have the lesion".
The problem is I think running into the proper use of 'should'. We'd need to draw very sharp lines around the things we pretend that we can or cannot control for purposes of that word.
Basically, you end up with a black-box concept containing some but not all of the machinery that led up to your decision such that words like 'should' and 'control' apply to the workings of the black box and not to anything else. And then we can decide whether it's sensible to ask 'should I smoke' in Smoking Lesion and 'should I one-box' in Newcomb.
Right now I don't have a good enough handle on this model to draw those lines, and so don't have an answer to this puzzle.