Can anyone explain to me why CDT two-boxes?
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?
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Comments (136)
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 of saying "no, go on.") However, sometimes she will not say this, and instead say something like "No, what?" A number of times, I have contrived situations where the correct answer is "monkeys," but only asked the question when I predicted that she would not say "monkeys." So far, I have predicted correctly every time; she has never correctly guessed "monkeys."
I agree if you say that a more accurate statement would have been "omniscient Omega entails either backwards causality or the absence of free will."
I actually assign a rather high probability to free will not existing; however discussing decision theory under that assumption is not interesting at all.
Regardless of the issue of free will (which I don't want to discuss because it is obviously getting us nowhere), if Omega makes its prediction solely based on your past, then your past suddenly becomes an inherent part of the problem. This means that two-boxing-You either has a different past than one-boxing-You and therefore plays a different game, or that Omega makes the same prediction for both versions of you, in which case two-boxing-You wins.
Two-boxing-you is a different you than one-boxing-you. They make different decisions in the same scenario, so something about them must not be the same.
Omega doesn't make its decision solely based on your past, it makes the decision based on all information salient to the question. Omega is an omniscient perfect reasoner. If there's anything that will affect your decision, Omega knows about it.
If you know that Omega will correctly predict your actions, then you can draw a decision tree which crosses off the outcomes "I choose to two box and both boxes contain money," and "I choose to one box and the other box contains no money," because you can rule out any outcome that entails Omega having mispredicted you.
Probability is in the mind. The reality is that either one or both boxes already contain money, and you are already going to choose one box or both, in accordance with Omega's prediction. Your role is to run through the algorithm to determine what is the best choice given what you know. And given what you know, one boxing has higher expected returns than two boxing.
Omega cannot have the future as an input; any knowledge Omega has about the future is a result of logical reasoning based upon its knowledge of the past.
You cannot know this, unless you (a) consider backwards causality, which is wrong, or (b) consider absence of free will, which is uninteresting.
You can also not know that Omega will correctly predict your choice with p≠0.5. At best, you can only know that Omega predicts you to one-box/two-box with p=whatever.
So apparently you have not followed my advice to consider free will. I really recommend that you read up on this because it seems to cause a significant part of our misunderstanding here.
You can have "free will" in the sense of being able to do what you want within the realm of possibility, while your wants are set deterministically.
If I offer most people a choice between receiving a hundred dollars, or being shot in the head, I can predict with near certainty that they will choose the hundred dollars, because I know enough about what kind of agents they are. Any formulation of "free will" which says I should not be able to do this is simply wrong. If I were making the same offer to Queebles (a species which hates money and loves being shot in the head,) I would predict the reverse. Omega, having very complete information and perfect reasoning, can predict in advance whether you will one-box or two-box.
You can predict that Kasparov will beat you in a chess match without knowing the specific moves he'll make. If you could predict all the moves he'd make, you could beat him in a chess match, but you can't. Similarly, if you could assign nonequal probabilities to how Omega would fill the boxes irrespective of your own choice, then you could act on those probabilities and beat Omega more than half the time, so that would entail a p≠0.5. probability of Omega predicting your choice.
If you play chess against a perfect chess playing machine, which has solved the game of chess, then you can predict in advance that if you decide to play black, black will lose,and if you decide to play white, white will lose, because you know that the machine is playing on a higher level than you. And if you play through Newcomb's problem with Omega, you can predict that if you one box, both boxes will contain money, and if you two box, only one will. Omega is on a higher level than you, the game has been played, and you already lost.
The reason why you lose in chess is because you will make the wrong moves, and the reason why you will make the wrong moves is because there are much too many of them to make it likely enough that you will find the right ones by chance. This is not the case in a game that consists of only two different moves.
What if you also tell them that you've made a prediction about them, and if your prediction is correct, they will get the money and not be shot even if their decision was to get shot? (If your prediction was wrong, the same happens as in your original game.)
What if you were in that very situation, with Omega, whose predictions are always right, holding the money and the gun? Could you make a distinction between the choices offered to you?
In a game with two moves, you want to model the other person, and play one level higher than that. So if I take the role of Omega and put you in Newcomb's problem, and you think I'll expect you to two box because you've argued in favor of two boxing, then you expect me to put money in only one box, so you want to one box, thereby beating your model of me. But if I expect you to have thought that far, then I want to put money in both boxes, making two boxing the winning move, thereby beating my model of you. And you expect me to have thought that far, you want to play a level above your model of me and one box again.
If humans followed this kind of recursion infinitely, it would never resolve and you couldn't do better than maximum entropy in predicting the other person's decision. But people don't do that, humans tend to follow very few levels of recursion when modeling others (example here, you can look at the comments for the results.) So if one person is significantly better at modeling the other, they'll have an edge and be able to do considerably better than maximum entropy in guessing the other person's choice.
Omega is a hypothetical entity who models the universe perfectly. If you decide to one box, his model of you decides to one box, so he plays a level above that and puts money in both boxes. If you decide to two box, his model of you decides to two box, so he plays a level above that and only puts money in one box. Any method of resolving the dilemma that you apply, his model of you also applies; if you decide to flip a coin, his model of you also decides to flip a coin, and because Omega models the whole universe perfectly, not just you, the coin in his model shows the same face as the coin you actually flip. This does essentially require Omega to be able to fold up the territory and put it in his pocket, but it doesn't require any backwards causality. Real life Newcomblike dilemmas involve predictors who are very reliable, but not completely infallible.
I could choose either, knowing that the results would be the same either way. Either I choose the money, in which case Omega has predicted that I will choose the money, and I get the money and don't get shot, or I choose the bullet, in which case, Omega has predicted that I choose the bullet, and I will get the money and not get shot. In this case, you don't need Omega's perfect prediction to avoid shooting the other person, you can just predict that they'll choose to get shot every time, because whether you're right or wrong they won't get shot, and if you want to shoot them, you should always predict that they'll choose the money, because predicting that they'll choose the money and having them choose the bullet is the only branch that results in shooting them. Similarly, if you're offered the dilemma, you should always pick the money if you don't want to get shot, and the bullet if you do want to get shot. It's a game with a very simple dominant strategy on each side.
I don't see why you think this would apply to Newcomb. Omega is not an "other person"; it has no motivation, no payoff matrix.
Really? If your decision theory allows you to choose either option, then how could Omega possibly predict your decision?
Whatever its reasons, Omega wants to set up the boxes so that if you one box, both boxes have money, and if you two box, only one box has money. It can be said to have preferences insofar as they lead to it using its predictive powers to try to do that.
I can't play at a higher level than Omega's model of me. Like playing against a stronger chess player, I can only predict that they will win. Any step where I say "It will stop here, so I'll do this instead," it won't stop there, and Omega will turn out to be playing at a higher level than me.
Because on some level my choice is going to be nonrandom (I am made of physical particles following physical rules,) and if Omega is an omniscient perfect reasoner, it can determine my choice in advance even if I can't.
But as it happens, I would choose the money, because choosing the money is a dominant strategy for anything up to absolute certainty in the other party's predictive abilities, and I'm not inclined to start behaving differently as soon as I theoretically have absolute certainty.
What you actually choose is one particular option (you may even strongly suspect in advance which one; and someone else might know it even better). "Choice" doesn't imply lack of determinism. If what you choose is something definite, it could as well be engraved on a stone tablet in advance, if it was possible to figure out what the future choice turns out to be. See Free will (and solution).
Yes you can. Something existing that can predict your actions in no way precludes free will. (I suppose definitions of "free will" could be constructed such that predicting negates it, in which case you can still be predicted, don't have free will and the situation is exactly as interesting as it was before.)
Let us assume a repeated game where an agent is presented with a decision between A and B, and Omega observes that the agent chooses A in 80% and B in 20% of the cases.
If Omega now predicts the agent to choose A in the next instance of the game, then the probability of the prediction being correct is 80% - from Omega's perspective as long as the roll hasn't been made, and from the agent's perspective as long as no decision has been made. However, once the decision has been made, the probability of the prediction being correct from the perspective of the agent is either 100% (A) or 0% (B).
If, instead, Omega is a ten-sided die with 8 A-sides and 2 B-sides, then the probability of the prediction being correct is 68% - from Omega's perspective, and from the agent's perspective as long as no decision has been made. However, once the decision has been made, the probability of the prediction being correct from the perspective of the agent is either 80% (A) or 20% (B).
If the agent knows that Omega makes the prediction before the agent makes the decision, then the agent cannot make different decisions without affecting the probability of the prediction being correct, unless Omega's prediction is a coin toss (p=0.5).
The only case where the probability of Omega being correct is unchangeable with p≠0.5 is the case where the agent cannot make different decisions, which I call "no free will".
You are using the wrong sense of "can" in "cannot make different decisions". The every day subjective experience of "free will" isn't caused by your decisions being indeterminate in an objective sense, that's the incoherent concept of libertarian free will. Instead it seems to be based on our decisions being dependent on some sort of internal preference calculation, and the correct sense of "can make different decisions" to use is something like "if the preference calculation had a different outcome that would result in a different decision".
Otherwise results that are entirely random would feel more free than results that are based on your values, habits, likes, memories and other character traits, i. e. the things that make you you. Not at all coincidentally this is also the criterion whether it makes sense to bother thinking about the decision.
You yourself don't know the result of the preference calculation before you run it, otherwise it wouldn't feel like a free decision. But whether Omega knows the result in advance has no impact on that at all.
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.
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.
... which means that CDT doesn't play Newcomb, because there are no $1,001,000 or $0 in Newcomb.
I have never said that CDT one-boxes in Newcomb, and I don't feel very confused right now. In fact the very first reply I got fully answered my question. I have edited my top level post, please refer to that if you feel the need to discuss this further.
We can see that. That's why neither simple explanations nor theorycrafting have all that much chance of being understood.
If it seemed like the top level post wasn't going to be downvoted below visibility I would have to respond to it in order to prevent muddled thinking from spreading.
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 affect what happens after because it appears that there is no penalty for ignoring what happened before. (ie the hostage taker should release the hostage after being paid - but they already have the money).
But Omega figuring out your decision is time travel. That's the whole point of Newcomb, and why you need a "timeless" decision theory to one-box.
As soon as you're talking about reality (hostages, empirical evidence, no time travel, ...) you're talking about weak Newcomb, which is not an issue here. Also, Newcomb becomes a very different problem if you repeat it, similar to PD.
Newcomb's problem is not particularly interesting if one assumes the mechanism is time travel. If Omega really (1) wants to reduce the amount it spends and (2) can send information backward in time (ie time travel). no decision theory can do well. The fact that Eliezar's proposed decision theory is called "timeless" doesn't actually mean anything - and it hasn't really been formalized anyway.
In short, try thinking about the problem with time travel excluded. What insights there are to gain from the problem are most accessible from that perspective.
This statement is clearly false. Any decision theory that gives time-travelling Omega enough incentive to believe that you will one-box will do well. I don't think this is possible without actually one-boxing, though.
You can substitute "timeless" with "considering violation of causality, for example time travel". "Timeless" is just shorter.
Without time travel, this problem either ceases to exist, or becomes simple calculus.
No; Timeless Decision Theory does not violate causality. It is not a physical theory, which postulates new timetravelling particles or whatever; almost all of its advocates believe in full determinism, in fact. (Counterfactual mugging is an equivalent problem.)
Newcomb's Problem has never included time travel. Every standard issue was created for the standard, non-time travel version. In particular, if one allows for backward causation (ie for one's decision to causally affect what's in the box) then the problem becomes trivial.
I didn't say (or mean) that it violated causality. I meant it assigned a probability p>0 to violation of causality being possible. I may be wrong on this, since I only read enough about TDT to infer that it isn't interesting or relevant to me.
Actual Newcomb includes an omniscient being, and omniscience is impossible without time travel / violation of causality.
If you say that Omega makes its prediction purely based on the past, Newcomb becomes trivial as well.
It intrinsically says nothing about causality violation. All zero is not a probability and lack of infinite certainty issues are independent of the decision theory. The decision theory just works with whatever your map contains.
Actual Newcomb doesn't include an omniscient being; I quote from Wikipedia:
Except that this is false, so nevermind.
Also, actual knowledge of everything aside from the Predictor is possible without time travel. It's impossible in practice, but this is a thought experiment. You "just" need to specify the starting position of the system, and the laws operating on it.
Well, the German Wikipedia says something entirely different, so may I suggest you actually read Nozick? I have posted a paragraph from the paper in question here.
Translation from German Wiki: "An omniscient being..."
What does this tell us? Exactly, that we shouldn't use Wikipedia as a source.
Oops, my apologies.
Omega makes its prediction purely based on the past (and present).
That being the case which decision would you say is trivially correct? Based on what you have said so far I can't predict which way your decision would go.
Ruling out backwards causality, I would two-box, and I would get $1000 unless Omega made a mistake.
No, I wouldn't rather be someone who two-boxes in Newcomb, because if Omega makes its predictions based on the past, this would only lead to me losing $1000, because Newcomb is a one-time problem. I would have to choose differently in other decisions for Omega to change its prediction, and that is something I'm not willing to do.
Of course if I'm allowed to communicate with Omega, I would try to convince it that I'll be one-boxing (while still two-boxing), and if I can increase the probability of Omega predicting me to one-box enough to justify actually precommiting to one-boxing (by use of a lie detector or whatever), then I would do that.
However, in reality I would probably get some satisfaction out of proving Omega wrong, so the payoff matrix may not be that simple. I don't think this is in any way relevant to the theoretical problem, though.
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 both, it will take both, and walk away with one million and one thousand dollars. If you explain this whole Omega thing to CDT, then put it in the room, it will notice that it doesn't actually need to calculate the eighth Mersenne prime, etc, because when Omega leaves you are effectively multiplying by zero - all the fancy simulating is irrelevant because the room is just two boxes that may contain money, and you can take both.
Yes, CDT doesn't think it's playing Newcomb's Puzzle, it thinks it's playing "enter a room with money".
You're completely right, except that (assuming I understand you correctly) you're implying CDT only thinks it's playing "room with money", while in reality it would be playing Newcomb.
And that's the issue; in reality Newcomb cannot exist, and if in theory you think you're playing something, you are playing it.
Does that make sense?
Perfect sense. Theorising that CDT would lose because it's playing a different game is uninteresting as a thought experiment; if I theorise that any decision theory is playing a different game it will also lose; this is not a property of CDT but of the hypothetical.
Let's turn to the case of playing in reality, as it's the interesting one.
If you grant that Newcomb paradoxes might exist in reality, then there is a real problem: CDT can't distinguish between free money boxes and Newcomb paradoxes, so so when it encounters a Newcomb situation it underperforms.
If you claim Newcomb cannot exist in reality, then this is not a problem with CDT. I (and hopefully others, though I shan't speak for them) would accept that this is not a problem with CDT if it is shown that Newcomb's is not possible in real life - but we are arguing against you here because we think Newcomb is possible. (Okay, I did speak for them).
I disagree on two points: one, I think a simulator is possible (that is, Omega 's impossibility comes from other powers we've given it, we can remove those powers and weaken Omega to a fits-in-reality definition without losing prediction), and two, I don't think the priors-and-payoffs approach to an empirical predictor is correct (for game-theoretic reasons which I can explicate if you'd like, but if it's not the point of contention it would only distract).
No, CDT can in fact distinguish very well. It always concludes that the money is there, and it is always right, because it never encounters Newcomb.
To clarify: You are talking about actual Newcomb with an omniscient being, yes? Because in that case, I think several posters have already stated they deem this impossible, and Nozick agrees.
If you're talking about empirical Newcomb, that certainly is possible, but it is impossible to do better than CDT without choosing differently in other situations, because if you've acted like CDT in the past, Omega is going to assume you are CDT, even if you're not.
I agree on the "we can remove those powers and weaken Omega to a fits-in-reality definition without losing prediction" part, but this will change what the "correct" answer is. For example, you could substitute Omega with a coin toss and repeat the game if Omega is wrong. This is still a one-time problem, because Omega is a coin and therefore has no memory, but CDT, which would two-box in empirical Newcomb, one-boxes in this case and takes the $1,000,000.
I don't think this is the point of contention, but after we've settled that, I would be interested in hearing your line of thought on this.
How about the version where agents are computer programs, and Omega runs a simulation of the agent facing the choice, observes it's behavior, and fills the boxes accordingly?
I see no violation of causality in that version.
If you are a computer program that can be simulated, then the problem also becomes trivial, because either the simulation can be incorrect, in which case Omega is not omniscient, or the simulation cannot be incorrect, in which case you don't have a choice.
If the simulation is correct, a program that chooses to one-box will get $1,000,000, and a program that chooses to two-box will get $1,000. I wouldn't call that "not having a choice".
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.
So what you're saying is that CDT refuses the whole setup and then proceeds to solve a completely different problem, correct?
Well, Nozick's formulation in 1969, which popularized the problem in philosophy, went ahead and specified that "what you actually decide to do is not part of the explanation of why he made the prediction he made".
Which means smuggling in a theory of unidirectional causality into the very setup itself, which explains how it winds up called "Newcomb's Paradox" instead of Newcomb's Problem.
No.
No, it's just not aware that it could be running inside Omega's head.
Another way of putting it is that CDT doesn't model entities as modeling it.
And this is an Open Thread, which exists precisely for this kind of questions.
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.
Only in the "No True Scottsman" sense. What Will calls CDT is an interesting decision theory and from what little I've seen of Will talking about it it may also be a superior decision theory, but it doesn't correspond to the decision theory called CDT. The version of Causal Decision Theory that is in academics' heads is CDT, the one that is in Will's head needs a new name.
(Fair enough. My only real problem with causal decision theory being called causal decision theory is that at best it's a strange use of the word "causal", breaking with thousands of years of reasonable philosophical tradition. That's my impression anyway—but there's like a billion papers on Newcomb's problem, and maybe one of them gives a perfectly valid explanation of the terminology.)
I'm not familiar with the philosophical tradition that would be incompatible with the way CDT uses 'causality'. It quite possibly exists and my lack of respect for philosophical tradition leaves me ignorant of such.
From my perspective, it's a shame that you have little regard for philosophical tradition. But as someone who is intimately familiar with the philosophical literature on causation, it seems to me that the sense of "causal" in causal decision theory, while imprecise, is perfectly compatible with most traditional approaches. I don't see any reason to think the "causal" in "causal decision theory" is incompatible with regularity theories, probabilistic theories, counterfactual theories, conserved quantity theories, agency/manipulation/intervention theories, primitivism, power theories, or mechanism theories. It might be a tense relation between CDT and projectivist theories, but I suspect that even there, you will not find outright incompatibility.
For a nice paper in the overlap between decision theory and the philosophy of causation and causal inference, you might take a look at the paper Conditioning and Intervening (pdf) by Meek and Glymour if you haven't seen it already. Of course, Glymour's account of causation is not very different from Pearl's, so maybe you don't think of this as philosophy.
That was my impression (without sufficient confidence that I wished to outright contradict on facts.)
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 contentious outcome has zero probability because "perfect predictor" means that a player never two-boxes unless Omega predicted so.
CDT does not calculate (probability of a certain outcome given specific action), but rather (probability that, if the action were performed, the outcome happens). In the Newcomb case this (probability of $1,001,000 payout were the player to two-box) can be (mis-)interpreted as certainty because "boxes already contain the prizes". This statement is in contradiction with the the "perfect predictor" clause.
In other words, the argument "Because your choice of one or two boxes can't causally affect the Predictor's guess, causal decision theory recommends the two-boxing strategy." is not really a CDT argument, but a misunderstanding of the problem statement. The suggested option ($M+$T) in SEP is actually never an option.
No, because two-boxing also wins if Omega predicts you to two-box, and therefore always wins if your decision doesn't alter Omega's prediction of that very decision. CDT would two-box because n+1000 > n for both n = 0 and n = 1000000.
But, because Newcomb can't exist, CDT can never choose anything in Newcomb.
Other than that, your post seems pretty accurate.
I'm still not at all sure what you mean when you say that Newcomb can't exist. Could you say a bit more about what exactly you think cannot exist?
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.
No, it doesn't. Newcomb's problem assumes that Omega has enough accuracy to make the expected value of one boxing greater than the expected value of two boxing. That is all that is required in order to give the problem the air of paradox.
I don't see a problem with the perfect predictor existing, I see the statement like "one can choose something other than what Omega predicted" as a contradiction in the problem's framework. I suppose the trick is to have an imperfect predictor and see if it makes sense to take a limit (prediction accuracy -> 100%).
It's not a matter of accuracy, it's a matter of considering backwards causality or not. Please read this post of mine.
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?
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.
If Omega makes its prediction based on the past instead of the future, CDT two-boxes and gets $1,000. However, that is a result not of the decision CDT is making, but of the decisions it has made in the past. If Omega plays this game with e.g. TDT, and you substitute TDT with CDT without Omega noticing, CDT two-boxes and takes $1,001,000. Vice versa, if you substitute CDT with TDT, it gets nothing.
If Omega makes its prediction based on the future, CDT assigns a probability of 0 to being in that situation, which is correct, since this is purely theoretical.
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?
We've already established that some of the disagreement comes from whether Newcomb includes backwards causality or not, with most posters agreeing that Newcomb including backwards causality is not realistic or interesting (see the excerpt from Nozick that I edited into my top level post) and the focus instead shifting onto weak (empirical) Newcomb, where Omega makes its predictions without looking into the future.
Right now, most posters also seem to be of the opinion that the answer to Newcomb is not to just one-box, but to precommit to one-boxing before Omega can make its decision, for example by choosing a different decision theory before encountering Newcomb. I argued that this is a different problem ("meta-Newcomb") that is fundamentally different from both Newcomb and weak Newcomb. The question of whether a CDT agent should change strategies (precommit) in meta-Newcomb seems to be dependent on whether such a strategy can be proven to never perform worse than CDT in non-Newcomb problems.
The last sentence is my personal assessment; the rest should be general consensus by now.
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.
It's not a question of whether Omega is fallible or not, it's a question of whether Omega's prediction (no matter how incorrect) is dependent on the decision you are going to make (backwards causality), or only on decisions you have made in the past (no backwards causality). The first case is uninteresting since it cannot occur in reality, and in the second case it is always better to two-box, no matter the payouts or the probability of Omega being wrong.
What if Omega makes an identical copy of you, puts the copy in an identical situation, and uses the copy's decision to predict what you will do? Is "whatever I decide to do, my copy will have decided the same thing" a valid argument?
No, because if Omega tells you that, then you have information that your copy doesn't, which means that it's not an identical situation; and if Omega doesn't tell you, then you might just as well be the copy itself, meaning that either you can't be predicted or you're not playing Newcomb.
If Omega tells both of you the same thing, it lies to one of you; and in that case you're not playing Newcomb either.
Could you elaborate on this?
That's certainly the situation I have in mind (although certainly Omega can tell both of you "I have made a copy of the person that walked into this room to simulate; you are either the copy or the original" or something to that effect). But I don't see how either one of "you can't be predicted or you're not playing Newcomb" makes sense.
If you're the copy that Omega bases its prediction of the other copy on, how does Omega predict you?
Unless you like money, in which case you should one box.
If Omega is 100% sure you're one-boxing, you can one-box and get $1,000,000 or you can two-box and get $1,001,000. You cannot make the argument that one-boxing is better in this case unless you argue that your decision affects Omega's prediction, and that would be backwards causality. If you think backwards causality is a possibility, that's fine and you should one-box; but then you still have to agree that under the assumption that backwards causality cannot exist, two-boxing wins.
Backwards causality cannot exist. I still take one box. I get the money. You don't. Your reasoning fails.
On a related note: The universe is (as far as I know) entirely deterministic. I still have free will.
It's not completely clear what "backward causality" (or any causality, outside the typical contexts) means, so maybe it can exist. Better to either ignore the concept in this context (as it doesn't seem relevant) or taboo/clarify it.
The meaning of what Andreas was saying was sufficiently clear. He means "you know, stuff like flipping time travel and changing the goddamn past". Trying to taboo causality and sending everyone off to read Pearl would be a distraction. Possibly a more interesting distraction than another "CDT one boxes! Oh, um.... wait... No, Newcomb's doesn't exist. Err... I mean CDT two boxes and it is right to do so so there!" conversation but not an overwhelmingly relevant one.
We are in a certain sense talking about determining the past, the distinction is between shared structure (as in, the predictor has your source code) and time machines. The main problem seems to be unwillingness to carefully consider the meaning of implausible hypotheticals, and continued distraction by the object level dispute doesn't seem to help.
("Changing" vs. "determining" point should probably be discussed in the context of the future, where implausibility and fiction are less of a distraction.)
If backwards causality cannot exist, would you say that your decision can affect the prediction that Omega made before you made your decision?
No. Both the prediction and my decision came about due to past states of the universe (including my brain). They do not influence each other directly. I still take one box and get $1,000,000 and that is the best possible outcome.o. Both the prediction and my decision came about due to past states of the universe (including my brain). I still take one box and get $1,000,000 and that is the best possible outcome I can expect.