CDT acts to physically cause nice things to happen. CDT can't physically cause the contents of the boxes to change, and fails to recognize the non-physical dependence of the box contents on its decision, which is a result of the logical dependence between CDT and Omega's CDT simulation. Since CDT believes its decision can't affect the contents of the boxes, it takes both in order to get any money that's there. Taking both boxes is in fact the correct course of action for the problem CDT thinks its facing, in which a guy may have randomly decided to leave some money around for them. CDT doesn't think that it will always get the $1 million; it is capable of representing a background probability that Omega did or didn't do something. It just can't factor out a part of that uncertainty, the part that's the same as its uncertainty about what it will do, into a causal relation link that points from the present to the past (or from a timeless platonic computation node to both the present and the CDT sim in the past, as TDT does).
Or from a different light, people who talked about causal decision theories historically were pretty vague, but basically said that causality was that thing by which you can influence the future but not the past or events outside your light cone, so when we build more formal versions of CDT, we make sure that's how it reasons and we keep that sense of the word causality.
Omniscient Omega doesn't entail backwards causality, it only entails omniscience. If Omega can extrapolate how you would choose boxes from complete information about your present, you're not going to fool it no matter how many times you play the game.
Imagine a machine that sorts red balls from green balls. If you put in a red ball, it spits it out Terminal A, and if you put in a green ball it spits it out Terminal B. If you showed a completely colorblind person how you could predict in which terminal a ball would get spit out of before putting it into the machine, it might look to them like backwards causality, but only forwards causality is involved.
If you know that Omega can predict your actions, you should condition your decisions on the knowledge that Omega will have predicted you correctly.
Humans are predictable enough in real life to make this sort of reasoning salient. For instance, I have a friend who, when I ask her questions such as "you know what happened to me?" or "You know what I think is pretty cool?" or any similarly open ended question, will answer "Monkeys?" as a complete non sequitur, more often than not (it's functionally her way ...
This is a simple question that is in need of a simple answer.
Because $1,000 is greater than $0, $1,001,000 is greater than $1,000,000 and those are the kind of comparisons that CDT cares about.
Please don't link to pages and pages of theorycrafting. Thank you.
You haven't seemed to respond to the 'simple' thus far and have instead defied it aggressively. That leaves you either reading the theory or staying confused.
If you ask a mathematician to find 0x + 1 for x = 3, they will answer 1. If you then ask the mathematician to find the 10th root of the factorial of the eighth Mersenne prime, multiplied by zero, plus one, they will answer 1. You may protest they didn't actually calculate the eighth Mersenne prime, find its factorial, or calculate the tenth root of that, but you can't deny they gave the right answer.
If you put CDT in a room with a million dollars in Box A and a thousand dollars in Box B (no Omega, just the boxes), and give it the choice of either A or bo...
Newcomb's problem has sequential steps - that's the key difference between it and problems like Prisoner's Dilemma. By the time the decision-agent is faced with the problem, the first step (where Omega examines you and decides how to seed the box) is already done. Absent time travel, nothing the agent does now will affect the contents of the boxes.
Consider the idea of the hostage exchange - the inherent leverage is in favor of the person who receives what they want first. It takes fairly sophisticated analysis to decide that what happened before should aff...
CDT calculates it this way: At the point of decision, either the million-dollar box has a million or it doesn't, and your decision now can't change that. Therefore, if you two-box, you always come out ahead by $1,000 over one-boxing.
I am not sure what you mean by "substitute Newcomb with a problem that consists of little more than simple calculation of priors and payoffs". If you mean that the decision algorithm should chose the the option correlated with the highest payoffs, then that's Evidential Decision Theory, and it fails on other problems- eg the Smoking Lesion.
Here is my take on the whole thing, fwiw.
The issue is assigning probability to the outcome (Omega predicted player one-boxing whereas player two-boxed), as it is the only one where two-boxing wins. Obviously any decision theorists who assigns a non-zero probability to this outcome hasn't read the problem statement carefully enough, specifically the part that says that Omega is a perfect predictor.
EDT calculates the expected utility by adding, for all outcomes (probability of outcome given specific action)*payoff of the outcome. In the Newcomb case the con...
It seems like if you haven't understood what's going on in a problem until very recently, when people explained it to you, and then you've come up with an answer to the problem that most people familiar with the subject material are objecting to.
How high is the prior for your hypothesis, that your posterior is still high after so much evidence pointing the other way?
What, exactly, is your goal in this conservation? What could an explanation why CDT two-boxes look like in order to make you accept that explanation?
You don't need to perfectly simulate Omega to play Newcomb. I am not Omega, but I bet that if I had lots of money and decided to entertain my friends with a game of Newcomb's boxes, I would be able to predict their actions with better than 50.1% accuracy.
Clearly CDT (assuming for the sake of the argument that I'm friends with CDT) doesn't care about my prediction skills, and two-boxes anyway, earning a guaranteed $1000 and a 49.9% chance of a million, for a total of $500K in expectation.
On the other hand, if one of my friends one-boxes, then he gets a 50.1% chance of a million, for a total of $501K in expectation.
Not quite as dramatic a difference, but it's there.
Because academic decision theorists say that CDT two boxes. A real causal decision theorist would, of course, one box. But the causal decision theorists in academic decision theorists' heads two box, and when people talk about causal decision theory, they're generally talking about the version of causal decision theory that is in academics' heads. This needn't make any logical sense.
I have read lots of LW posts on this topic, and everyone seems to take this for granted without giving a proper explanation. So if anyone could explain this to me, I would appreciate that.
This is a simple question that is in need of a simple answer. Please don't link to pages and pages of theorycrafting. Thank you.
Edit: Since posting this, I have come to the conclusion that CDT doesn't actually play Newcomb. Here's a disagreement with that statement:
If you write up a CDT algorithm and then put it into a Newcomb's problem simulator, it will do something. It's playing the game; maybe not well, but it's playing.
And here's my response:
The thing is, an actual Newcomb simulator can't possibly exist because Omega doesn't exist. There are tons of workarounds, like using coin tosses as a substitution for Omega and ignoring the results whenever the coin was wrong, but that is something fundamentally different from Newcomb.
You can only simulate Newcomb in theory, and it is perfectly possible to just not play a theoretical game, if you reject the theory it is based on. In theoretical Newcomb, CDT doesn't care about the rule of Omega being right, so CDT does not play Newcomb.
If you're trying to simulate Newcomb in reality by substituting Omega with someone who has only empirically been proven right, you substitute Newcomb with a problem that consists of little more than simple calculation of priors and payoffs, and that's hardly the point here.
Edit 2: Clarification regarding backwards causality, which seems to confuse people:
Newcomb assumes that Omega is omniscient, which more importantly means that the decision you make right now determines whether Omega has put money in the box or not. Obviously this is backwards causality, and therefore not possible in real life, which is why Nozick doesn't spend too much ink on this.
But if you rule out the possibility of backwards causality, Omega can only make his prediction of your decision based on all your actions up to the point where it has to decide whether to put money in the box or not. In that case, if you take two people who have so far always acted (decided) identical, but one will one-box while the other one will two-box, Omega cannot make different predictions for them. And no matter what prediction Omega makes, you don't want to be the one who one-boxes.
Edit 3: Further clarification on the possible problems that could be considered Newcomb:
There's four types of Newcomb problems:
- Omniscient Omega (backwards causality) - CDT rejects this case, which cannot exist in reality.
- Fallible Omega, but still backwards causality - CDT rejects this case, which cannot exist in reality.
- Infallible Omega, no backwards causality - CDT correctly two-boxes. To improve payouts, CDT would have to have decided differently in the past, which is not decision theory anymore.
- Fallible Omega, no backwards causality - CDT correctly two-boxes. To improve payouts, CDT would have to have decided differently in the past, which is not decision theory anymore.
That's all there is to it.
Edit 4: Excerpt from Nozick's "Newcomb's Problem and Two Principles of Choice":
Now, at last, to return to Newcomb's example of the predictor. If one believes, for this case, that there is backwards causality, that your choice causes the money to be there or not, that it causes him to have made the prediction that he made, then there is no problem. One takes only what is in the second box. Or if one believes that the way the predictor works is by looking into the future; he, in some sense, sees what you are doing, and hence is no more likely to be wrong about what you do than someone else who is standing there at the time and watching you, and would normally see you, say, open only one box, then there is no problem. You take only what is in the second box. But suppose we establish or take as given that there is no backwards causality, that what you actually decide to do does not affect what he did in the past, that what you actually decide to do is not part of the explanation of why he made the prediction he made. So let us agree that the predictor works as follows: He observes you sometime before you are faced with the choice, examines you with complicated apparatus, etc., and then uses his theory to predict on the basis of this state you were in, what choice you would make later when faced with the choice. Your deciding to do as you do is not part of the explanation of why he makes the prediction he does, though your being in a certain state earlier, is part of the explanation of why he makes the prediction he does, and why you decide as you do.
I believe that one should take what is in both boxes. I fear that the considerations I have adduced thus far will not convince those proponents of taking only what is in the second box. Furthermore I suspect that an adequate solution to this problem will go much deeper than I have yet gone or shall go in this paper. So I want to pose one question. I assume that it is clear that in the vaccine example, the person should not be convinced by the probability argument, and should choose the dominant action. I assume also that it is clear that in the case of the two brothers, the brother should not be convinced by the probability argument offered. The question I should like to put to proponents of taking only what is in the second box in Newcomb's example (and hence not performing the dominant action) is: what is the difference between Newcomb's example and the other two examples which make the difference between not following the dominance principle, and following it?