Then I guess I will try to leave it to you to come up with a satisfactory example. The challenge is to include Newcomblike predictive power for Omega, but not without substantiating how Omega achieves this, while still passing your own standards of subject makes choice from own point of view. It is very easy to accidentally create paradoxes in mathematics, by assuming mutually exclusive properties for an object, and the best way to discover these is generally to see if it is possible construct or find an instance of the object described.
I don’t think it is, actually. It just seems so because it presupposes that your own choice is predetermined, which is kind of hard to reason with when you’re right in the process of making the choice. But that’s a problem with your reasoning, not with the scenario. In particular, the CDT agent has a problem with conceiving of his own choice as predetermined, and therefore has trouble formulating Newcomb’s problem in a way that he can use—he has to choose between getting two-boxing as the solution or assuming backward causation, neither of which is attractive.
This is not a failure of CDT, but one of your imagination. Here is a simple, five minute model which has no problems conceiving Newcomb’s problem without any backwards causation:
T=0: Subject is initiated in a deterministic state which can be predicted by Omega.
T=1: Omega makes an accurate prediction for the subject’s decision in Newcomb’s problem by magic / simulation / reading code / infallible heuristics. Denote the possible predictions P1 (one-box) and P2.
T=2: Omega sets up Newcomb’s problem with appropriate box contents.
T=3: Omega explains the setup to the subject and disappears.
T=4: Subject deliberates.
T=5: Subject chooses either C1 (one-box) or C2.
T=6: Subject opens box(es) and receives payoff dependent on P and C.
You can pretend to enter this situation at T=4 as suggested by the standard Newcomb’s problem. Then you can use the dominance principle and you will lose. But this just using a terrible model. You entered at T=0, because you were needed at T=1 for Omega’s inspection. If you did not enter the situation at T=0, then you can freely make a choice C at T=5 without any correlation to P, but that is not Newcomb’s problem.
Instead, at T=4 you become aware of the situation, and your decision making algorithm must return a value for C. If you consider this only from T=4 and onward, this is completely uninteresting, because C is already determined. At T=1, P was determined to either P1 or P2, and the value of C follow directly from this. Obviously, healthy one-boxing code wins and unhealthy two-boxing code loses, but there is no choice being made here, just different code with different return values being rewarded differently, and that is not Newcomb’s problem either.
Finally, we will work under illusion of choice with Omega as a perfect predictor. We realize that T=0 is the critical moment, seeing as all subsequent T follows directly from this. We work backwards as follows:
T=6: My preferences are P1C2 > P1C1 > P2C2 > P2C1.
T=5: I should choose either C2 or C1 depending on the current value of P.
T=4: this is when all this introspection is happening
T=3: this is why
T=2: I would really like there to be a million dollars present.
T=1: I want Omega to make prediction P1.
T=0: Whew, I’m glad I could do all this introspection which made me realize that I want P1 and the way to achieve this is C1. It would have been terrible if my decision making just worked by the dominance principle. Luckily, the epiphany I just had, C1, was already predetermined at T=0, Omega would have been aware of this at T=1 and made the prediction P1, so (...) and P1 C1 = a million dollars is mine.
Shorthand version of all the above; if the decision is necessarily predetermined before T=4, then you should not pretend you make the decision at T=4. Insert a decision making step at T=0.5, which causally determines the value of P and C. Apply your CDT to this step.
This is the only way of doing CDT honestly, and it is the slightest bit messy, but that is exactly what happens when you create a reference to the decision the decision theory is going to make in the future in the problem itself with perfect correlation to the decision before the decision has overtly been made. This sort of self reference creates impossibilities out of the thin air every day of week, such as when Pinocchio says my nose will grow now. The good news is that this way of doing it is a lot less messy than inventing a new, superfluous decision theory, and it also allows you to deal with problems like the psychopath button without any trouble whatsoever.
But isn’t this precisely the basic idea behind TDT?
The algorithm you are suggesting goes something like this: Chose that action which, if it had been predetermined at T=0 that you would take it, would lead to the maximal-utility outcome. You can call that CDT, but it isn’t. Sure, it’ll use causal reasoning for evaluating the counterfactual, but not everything that uses causal reasoning is CDT. CDT is surgically altering the action node (and not some precommitment node) and seeing what happens.
If you take a careful look at the model, you will realize that the agent has to be precommited, in the sense that what he is going to do is already fixed. Otherwise, the step at T=1 is impossible. I do not mean that he has precommited himself consciously to win at Newcomb’s problem, but trivially, a deterministic agent must be precommited.
It is meaningless to apply any sort of decision theory to a deterministic system. You might as well try to apply decision theory to the balls in a game of billiards, which assign high utility to remaining on the table but have no free choices to make. For decision theory to have a function, there needs to be a choice to be made between multiple, legal options.
As far as I have understood, your problem is that, if you apply CDT with an action node at T=4, it gives the wrong answer. At T=4, there is only one option to choose, so the choice of decision theory is not exactly critical. If you want to analyse Newcomb’s problem, you have to insert an action node at T<1, while there is still a choice to be made, and CDT will do this admirably.
As far as I have understood, your problem is that, if you apply CDT with an action node at T=4, it gives the wrong answer. At T=4, there is only one option to choose, so the choice of decision theory is not exactly critical.
Yes, it is. The point is that you run your algorithm at T=4, even if it is deterministic and therefore its output is already predetermined. Therefore, you want an algorithm that, executed at T=4, returns one-boxing. CDT does simply not do that.
Ultimately, it seems that we’re disagreeing about terminology. You’re apparently calling something CDT even though it does not work by surgically altering the node for the action under consideration (that action being the choice of box, not the precommitment at T<1) and then looking at the resulting expected utilities.
If you apply CDT at T=4 with a model which builds in the knowledge that the choice C and the prediction P are perfectly correlated, it will one-box. The model is exceedingly simple:
T’=0: Choose either C1 or C2
T’=1: If C1, then gain 1000. If C2, then gain 1.
This excludes the two other impossibilities, C1P2 and C2P1, since these violate the correlation constraint. CDT makes a wrong choice when these two are included, because then you have removed the information of the correlation constraint from the model, changing the problem to one in which Omega is not a predictor.
Okay, so I take it to be the defining characteristic of CDT that it uses of counterfactuals. So far, I have been arguing on the basis of a Pearlean conception of counterfactuals, and then this is what happens:
Your causal network has three variables, A (the algorithm used), P (Omega’s prediction), C (the choice). The causal connections are A → P and A → C. There is no causal connection between P and C.
Now the CDT algorithm looks at counterfactuals with the antecedent C1. In a Pearlean picture, this amounts to surgery on the C-node, so no inference contrary to the direction of causality is possible. Hence, whatever the value of the P-node, it will seem to the CDT algorithm not to depend on the choice.
Therefore, even if the CDT algorithm knows that its choice is predetermined, it cannot make use of that in its decision, because it cannot update contrary to the direction of causality.
Now it turns out that natural language counterfactuals work very much, but not quite like Pearl’s counterfactuals: they allow a limited amount of backtracking contrary to the direction of causality, depending on a variety of psychological factors. So if you had a theory of counterfactuals that allowed backtracking in a case like Newcomb’s problem, then a CDT-algorithm employing that conception of counterfactuals would one-box. The trouble would of course be to correctly state the necessary conditions for backtracking. The messy and diverse psychological and contextual factors that seem to be at play in natural language won’t do.
Could you try to maybe give a straight answer to, what is your problem with my model above? It accurately models the situation. It allows CDT to give a correct answer. It does not superficially resemble the word for word statement of Newcomb’s problem.
Therefore, even if the CDT algorithm knows that its choice is predetermined, it cannot make use of that in its decision, because it cannot update contrary to the direction of causality.
You are trying to use a decision theory to determine which choice an agent should make, after the agent has already had its algorithm fixed, which causally determines which choice the agent must make. Do you honestly blame that on CDT?
Could you try to maybe give a straight answer to, what is your problem with my model above? It accurately models the situation. It allows CDT to give a correct answer.
No, it does not, that’s what I was trying to explain. It’s what I’ve been trying to explain to you all along: CDT cannot make use of the correlation between C and P. CDT cannot reason backwards in time. You do know how surgery works, don’t you? In order for CDT to use the correlation, you need a causal arrow from C to P—that amounts to backward causation, which we don’t want. Simple as that.
You are trying to use a decision theory to determine which choice an agent should make, after the agent has already had its algorithm fixed, which causally determines which choice the agent must make.
I’m not sure what the meaning of this is. Of course the decision algorithm is fixed before it’s run, and therefore its output is predetermined. It just doesn’t know its own output before it has computed it. And I’m not trying to figure out what the agent should do—the agent is trying to figure that out. Our job is to figure out which algorithm the agent should be using.
PS: The downvote on your post above wasn’t from me.
You are applying a decision theory to the node C, which means you are implicitly stating: there are multiple possible choices to be made at this point, and this decision can be made independent of nodes not in front of this one. This means that your model does not model the Newcomb’s problem we have been discussing—it models another problem, where C can have values independent of P, which is indeed solved by two-boxing.
It is not the decision theory’s responsibility to know that the values of node C is somehow supposed to retrospectively alter the state of the branch the decision theory is working in. This is, however,a consequence of the modelling you do. You are on purpose applying CDT too late in your network, such that P and thus the cost of being a two-boxer has gone over the horizon and such that the node C must affect P backwards, not because the problem actually contains backwards causality, but because you want to fix the value of nodes in the wrong order.
If you do not want to make the assumption of free choice at C, then you can just not promote it to an action node. If the decision at C is casually determined from A, then you can apply a decision theory at node A and follow the causal inference. Then you will, once again, get a correct answer from CDT, this time for the version of Newcomb’s problem where A and C are fully correlated.
If you refuse to reevaluate your model, then we might as well leave it at this. I do agree that if you insist on applying CDT at C in your model, then it will two-box. I do not agree that this is a problem.
You don’t promote C to the action node, it is the action node. That’s the way the decision problem is specified: do you one-box or two-box? If you don’t accept that, then you’re talking about a different decision problem. But in Newcomb’s problem, the algorithm is trying to decide that. It’s not trying to decide which algorithm it should be (or should have been). Having the algorithm pretend—as a means of reaching a decision about C—that it’s deciding which algorithm to be is somewhat reminiscent of the idea behind TDT and has nothing to do with CDT as traditionally conceived of, despite the use of causal reasoning.
In AI, you do not discuss it in terms of anthropomorphic “trying to decide”. For example, there’s a “Model based utility based agent” . Computing what the world will be like if a decision is made in a specific way is part of the model of the world, i.e. part of the laws of physics as the agent knows them. If this physics implements the predictor at all, model-based utility-based agent will one-box.
I don’t see at all what’s wrong or confusing about saying that an agent is trying to decide something; or even, for that matter, that an algorithm is trying to decide something, even though that’s not a precise way of speaking.
More to the point, though, doesn’t what you describe fit EDT and CDT both, with each theory having a different way of computing “what the world will be like if the decision is made in a specific way”?
Decision theories do not compute what the world will be like. Decision theories select the best choice, given a model with this information included. How the world works is not something a decision theory figures out, it is not a physicist and it has no means to perform experiments outside of its current model. You need take care of that yourself, and build it into your model.
If a decision theory had the weakness that certain, possible scenarios could not be modeled, that would be a problem. Any decision theory will have the feature that they work with the model they are given, not with the model they should have been given.
Causality is under specified, whereas the laws of physics are fairly well defined, especially for a hypothetical where you can e.g. assume deterministic Newtonian mechanics for sake of simplifying the analysis. You have the hypothetical: sequence of commands to the robotic manipulator. You process the laws of physics to conclude that this sequence of commands picks up one box of unknown weight. You need to determine weight of the box to see if this sequence of commands will lead to the robot tipping over. Now, you see, to determine that sort of thing, models of physical world tend to walk backwards and forwards in time: for example if your window shatters and a rock flies in, you can conclude that there’s a rock thrower in the direction that the rock came from, and you do it by walking backwards in time.
In a way, albeit it does not resemble how EDT tends to be presented.
On the CDT, formally speaking, what do you think P(A if B) even is? Keep in mind that given some deterministic, computable laws of physics, given that you ultimately decide an option B, in the hypothetical that you decide an option C where C!=B , it will be provable that C=B , i.e. you have a contradiction in the hypothetical.
In a way, albeit it does not resemble how EDT tends to be presented.
So then how does it not fall prey to the problems of EDT? It depends on the precise formalization of “computing what the world will be like if the action is taken, according to the laws of physics”, of course, but I’m having trouble imagining how that would not end up basically equivalent to EDT.
On the CDT, formally speaking, what do you think P(A if B) even is?
That is not the problem at all, it’s perfectly well-defined. I think if anything, the question would be what CDT’s P(A if B) is intuitively.
So then how does it not fall prey to the problems of EDT?
What are those, exactly? The “smoking lesion”? It specifies that output of decision theory correlates with lesion. Who knows how, but for it to actually correlate with decision of that decision theory other than via the inputs to decision theory, it got to be our good old friend Omega doing some intelligent design and adding or removing that lesion. (And if it does through the inputs, then it’ll smoke).
That is not the problem at all, it’s perfectly well-defined.
Given world state A which evolves into world state B (computable, deterministic universe), the hypothetical “what if world state A evolved into C where C!=B” will lead, among other absurdities, to a proof that B=C contradicting that B!=C (of course you can ensure that this particular proof won’t be reached with various silly hacks but you’re still making false assumptions and arriving at false conclusions). Maybe what you call ‘causal’ decision theory should be called ‘acausal’ because it in fact ignores causes of the decision, and goes as far as to break down it’s world model to do so. If you don’t do contradictory assumptions, then you have a world state A that evolves into world state B, and world state A’ that evolves into world state C, and in the hypothetical that the state becomes C!=B, the prior state got to be A’!=A . Yeah, it looks weird to westerners with their philosophy of free will and your decisions having the potential to send the same world down a different path. I am guessing it is much much less problematic if you were more culturally exposed to determinism/fatalism. This may be a very interesting topic, within comparative anthropology.
The main distinction between philosophy and mathematics (or philosophy done by mathematicians) seem to be that in the latter, if you get yourself a set of assumptions leading to contradictory conclusions (example: in Newcomb’s on one hand it can be concluded that agents which 1 box walk out with more money, on the other hand , agents that choose to two-box get strictly more money than those that 1-box), it is generally concluded that something is wrong with the assumptions, rather than argued which of the conclusions is truly correct given the assumptions.
The values of A, C and P are all equivalent. You insist on making CDT determine C in a model where it does not know these are correlated. This is a problem with your model.
You are applying a decision theory to the node C, which means you are implicitly stating: there are multiple possible choices to be made at this point, and this decision can be made independent of nodes not in front of this one.
Yes. That’s basically the definition of CDT. That’s also why CDT is no good. You can quibble about the word but in “the literature”, ‘CDT’ means just that.
Well, a practically important example is a deterministic agent which is copied and then copies play prisoner’s dilemma against each other.
There you have agents that use physics. Those, when evaluating hypothetical choices, use some model of physics, where an agent can model itself as a copyable deterministic process which it can’t directly simulate (i.e. it knows that the matter inside it’s head obeys known laws of physics). In the hypothetical that it cooperates, after processing the physics, it is found that copy cooperates, in the hypothetical that it defects, it is found that copy defects.
And then there’s philosophers. The worse ones don’t know much about causality. They presumably have some sort of ill specified oracle that we don’t know how to construct, which will tell them what is a ‘consequence’ and what is a ‘cause’ , and they’ll only process the ‘consequences’ of the choice as the ‘cause’. This weird oracle tells us that other agent’s choice is not a ‘consequence’ of the decision, so it can not be processed. It’s very silly and not worth spending brain cells on.
Playing prisoner’s dilemma against a copy of yourself is mostly the same problem as Newcomb’s. Instead of Omega’s prediction being perfectly correlated with your choice, you have an identical agent whose choice will be perfectly correlated with yours—or, possibly, randomly distributed in the same manner. If you can also assume that both copies know this with certainty, then you can do the exact same analysis as for Newcomb’s problem.
Whether you have a prediction made by an Omega or a decision made by a copy really does not matter, as long as they both are automatically going to be the same as your own choice, by assumption in the problem statement.
The copy problem is well specified, though. Unlike the “predictor”. I clarified more in private. The worst part about Newcomb’s is that all the ex religious folks seem to substitute something they formerly knew as ‘god’ for predictor. The agent can also be further specified; e.g. as a finite Turing machine made of cogs and levers and tape with holes in it. The agent can’t simulate itself directly, of course, but it knows some properties of itself without simulation. E.g. it knows that in the alternative that it chooses to cooperate, it’s initial state was in set A—the states that result in cooperation, in the alternative that it chooses to defect, it’s initial state was in set B—the states that result in defection, and that no state is in both sets.
Then I guess I will try to leave it to you to come up with a satisfactory example. The challenge is to include Newcomblike predictive power for Omega, but not without substantiating how Omega achieves this, while still passing your own standards of subject makes choice from own point of view. It is very easy to accidentally create paradoxes in mathematics, by assuming mutually exclusive properties for an object, and the best way to discover these is generally to see if it is possible construct or find an instance of the object described.
This is not a failure of CDT, but one of your imagination. Here is a simple, five minute model which has no problems conceiving Newcomb’s problem without any backwards causation:
T=0: Subject is initiated in a deterministic state which can be predicted by Omega.
T=1: Omega makes an accurate prediction for the subject’s decision in Newcomb’s problem by magic / simulation / reading code / infallible heuristics. Denote the possible predictions P1 (one-box) and P2.
T=2: Omega sets up Newcomb’s problem with appropriate box contents.
T=3: Omega explains the setup to the subject and disappears.
T=4: Subject deliberates.
T=5: Subject chooses either C1 (one-box) or C2.
T=6: Subject opens box(es) and receives payoff dependent on P and C.
You can pretend to enter this situation at T=4 as suggested by the standard Newcomb’s problem. Then you can use the dominance principle and you will lose. But this just using a terrible model. You entered at T=0, because you were needed at T=1 for Omega’s inspection. If you did not enter the situation at T=0, then you can freely make a choice C at T=5 without any correlation to P, but that is not Newcomb’s problem.
Instead, at T=4 you become aware of the situation, and your decision making algorithm must return a value for C. If you consider this only from T=4 and onward, this is completely uninteresting, because C is already determined. At T=1, P was determined to either P1 or P2, and the value of C follow directly from this. Obviously, healthy one-boxing code wins and unhealthy two-boxing code loses, but there is no choice being made here, just different code with different return values being rewarded differently, and that is not Newcomb’s problem either.
Finally, we will work under illusion of choice with Omega as a perfect predictor. We realize that T=0 is the critical moment, seeing as all subsequent T follows directly from this. We work backwards as follows:
T=6: My preferences are P1C2 > P1C1 > P2C2 > P2C1.
T=5: I should choose either C2 or C1 depending on the current value of P.
T=4: this is when all this introspection is happening
T=3: this is why
T=2: I would really like there to be a million dollars present.
T=1: I want Omega to make prediction P1.
T=0: Whew, I’m glad I could do all this introspection which made me realize that I want P1 and the way to achieve this is C1. It would have been terrible if my decision making just worked by the dominance principle. Luckily, the epiphany I just had, C1, was already predetermined at T=0, Omega would have been aware of this at T=1 and made the prediction P1, so (...) and P1 C1 = a million dollars is mine.
Shorthand version of all the above; if the decision is necessarily predetermined before T=4, then you should not pretend you make the decision at T=4. Insert a decision making step at T=0.5, which causally determines the value of P and C. Apply your CDT to this step.
This is the only way of doing CDT honestly, and it is the slightest bit messy, but that is exactly what happens when you create a reference to the decision the decision theory is going to make in the future in the problem itself with perfect correlation to the decision before the decision has overtly been made. This sort of self reference creates impossibilities out of the thin air every day of week, such as when Pinocchio says my nose will grow now. The good news is that this way of doing it is a lot less messy than inventing a new, superfluous decision theory, and it also allows you to deal with problems like the psychopath button without any trouble whatsoever.
But isn’t this precisely the basic idea behind TDT?
The algorithm you are suggesting goes something like this: Chose that action which, if it had been predetermined at T=0 that you would take it, would lead to the maximal-utility outcome. You can call that CDT, but it isn’t. Sure, it’ll use causal reasoning for evaluating the counterfactual, but not everything that uses causal reasoning is CDT. CDT is surgically altering the action node (and not some precommitment node) and seeing what happens.
If you take a careful look at the model, you will realize that the agent has to be precommited, in the sense that what he is going to do is already fixed. Otherwise, the step at T=1 is impossible. I do not mean that he has precommited himself consciously to win at Newcomb’s problem, but trivially, a deterministic agent must be precommited.
It is meaningless to apply any sort of decision theory to a deterministic system. You might as well try to apply decision theory to the balls in a game of billiards, which assign high utility to remaining on the table but have no free choices to make. For decision theory to have a function, there needs to be a choice to be made between multiple, legal options.
As far as I have understood, your problem is that, if you apply CDT with an action node at T=4, it gives the wrong answer. At T=4, there is only one option to choose, so the choice of decision theory is not exactly critical. If you want to analyse Newcomb’s problem, you have to insert an action node at T<1, while there is still a choice to be made, and CDT will do this admirably.
Yes, it is. The point is that you run your algorithm at T=4, even if it is deterministic and therefore its output is already predetermined. Therefore, you want an algorithm that, executed at T=4, returns one-boxing. CDT does simply not do that.
Ultimately, it seems that we’re disagreeing about terminology. You’re apparently calling something CDT even though it does not work by surgically altering the node for the action under consideration (that action being the choice of box, not the precommitment at T<1) and then looking at the resulting expected utilities.
If you apply CDT at T=4 with a model which builds in the knowledge that the choice C and the prediction P are perfectly correlated, it will one-box. The model is exceedingly simple:
T’=0: Choose either C1 or C2
T’=1: If C1, then gain 1000. If C2, then gain 1.
This excludes the two other impossibilities, C1P2 and C2P1, since these violate the correlation constraint. CDT makes a wrong choice when these two are included, because then you have removed the information of the correlation constraint from the model, changing the problem to one in which Omega is not a predictor.
What is your problem with this model?
Okay, so I take it to be the defining characteristic of CDT that it uses of counterfactuals. So far, I have been arguing on the basis of a Pearlean conception of counterfactuals, and then this is what happens:
Your causal network has three variables, A (the algorithm used), P (Omega’s prediction), C (the choice). The causal connections are A → P and A → C. There is no causal connection between P and C.
Now the CDT algorithm looks at counterfactuals with the antecedent C1. In a Pearlean picture, this amounts to surgery on the C-node, so no inference contrary to the direction of causality is possible. Hence, whatever the value of the P-node, it will seem to the CDT algorithm not to depend on the choice.
Therefore, even if the CDT algorithm knows that its choice is predetermined, it cannot make use of that in its decision, because it cannot update contrary to the direction of causality.
Now it turns out that natural language counterfactuals work very much, but not quite like Pearl’s counterfactuals: they allow a limited amount of backtracking contrary to the direction of causality, depending on a variety of psychological factors. So if you had a theory of counterfactuals that allowed backtracking in a case like Newcomb’s problem, then a CDT-algorithm employing that conception of counterfactuals would one-box. The trouble would of course be to correctly state the necessary conditions for backtracking. The messy and diverse psychological and contextual factors that seem to be at play in natural language won’t do.
Could you try to maybe give a straight answer to, what is your problem with my model above? It accurately models the situation. It allows CDT to give a correct answer. It does not superficially resemble the word for word statement of Newcomb’s problem.
You are trying to use a decision theory to determine which choice an agent should make, after the agent has already had its algorithm fixed, which causally determines which choice the agent must make. Do you honestly blame that on CDT?
No, it does not, that’s what I was trying to explain. It’s what I’ve been trying to explain to you all along: CDT cannot make use of the correlation between C and P. CDT cannot reason backwards in time. You do know how surgery works, don’t you? In order for CDT to use the correlation, you need a causal arrow from C to P—that amounts to backward causation, which we don’t want. Simple as that.
I’m not sure what the meaning of this is. Of course the decision algorithm is fixed before it’s run, and therefore its output is predetermined. It just doesn’t know its own output before it has computed it. And I’m not trying to figure out what the agent should do—the agent is trying to figure that out. Our job is to figure out which algorithm the agent should be using.
PS: The downvote on your post above wasn’t from me.
You are applying a decision theory to the node C, which means you are implicitly stating: there are multiple possible choices to be made at this point, and this decision can be made independent of nodes not in front of this one. This means that your model does not model the Newcomb’s problem we have been discussing—it models another problem, where C can have values independent of P, which is indeed solved by two-boxing.
It is not the decision theory’s responsibility to know that the values of node C is somehow supposed to retrospectively alter the state of the branch the decision theory is working in. This is, however,a consequence of the modelling you do. You are on purpose applying CDT too late in your network, such that P and thus the cost of being a two-boxer has gone over the horizon and such that the node C must affect P backwards, not because the problem actually contains backwards causality, but because you want to fix the value of nodes in the wrong order.
If you do not want to make the assumption of free choice at C, then you can just not promote it to an action node. If the decision at C is casually determined from A, then you can apply a decision theory at node A and follow the causal inference. Then you will, once again, get a correct answer from CDT, this time for the version of Newcomb’s problem where A and C are fully correlated.
If you refuse to reevaluate your model, then we might as well leave it at this. I do agree that if you insist on applying CDT at C in your model, then it will two-box. I do not agree that this is a problem.
You don’t promote C to the action node, it is the action node. That’s the way the decision problem is specified: do you one-box or two-box? If you don’t accept that, then you’re talking about a different decision problem. But in Newcomb’s problem, the algorithm is trying to decide that. It’s not trying to decide which algorithm it should be (or should have been). Having the algorithm pretend—as a means of reaching a decision about C—that it’s deciding which algorithm to be is somewhat reminiscent of the idea behind TDT and has nothing to do with CDT as traditionally conceived of, despite the use of causal reasoning.
In AI, you do not discuss it in terms of anthropomorphic “trying to decide”. For example, there’s a “Model based utility based agent” . Computing what the world will be like if a decision is made in a specific way is part of the model of the world, i.e. part of the laws of physics as the agent knows them. If this physics implements the predictor at all, model-based utility-based agent will one-box.
I don’t see at all what’s wrong or confusing about saying that an agent is trying to decide something; or even, for that matter, that an algorithm is trying to decide something, even though that’s not a precise way of speaking.
More to the point, though, doesn’t what you describe fit EDT and CDT both, with each theory having a different way of computing “what the world will be like if the decision is made in a specific way”?
Decision theories do not compute what the world will be like. Decision theories select the best choice, given a model with this information included. How the world works is not something a decision theory figures out, it is not a physicist and it has no means to perform experiments outside of its current model. You need take care of that yourself, and build it into your model.
If a decision theory had the weakness that certain, possible scenarios could not be modeled, that would be a problem. Any decision theory will have the feature that they work with the model they are given, not with the model they should have been given.
Causality is under specified, whereas the laws of physics are fairly well defined, especially for a hypothetical where you can e.g. assume deterministic Newtonian mechanics for sake of simplifying the analysis. You have the hypothetical: sequence of commands to the robotic manipulator. You process the laws of physics to conclude that this sequence of commands picks up one box of unknown weight. You need to determine weight of the box to see if this sequence of commands will lead to the robot tipping over. Now, you see, to determine that sort of thing, models of physical world tend to walk backwards and forwards in time: for example if your window shatters and a rock flies in, you can conclude that there’s a rock thrower in the direction that the rock came from, and you do it by walking backwards in time.
So it’s basically EDT, where you just conditionalize on the action being performed?
In a way, albeit it does not resemble how EDT tends to be presented.
On the CDT, formally speaking, what do you think P(A if B) even is? Keep in mind that given some deterministic, computable laws of physics, given that you ultimately decide an option B, in the hypothetical that you decide an option C where C!=B , it will be provable that C=B , i.e. you have a contradiction in the hypothetical.
So then how does it not fall prey to the problems of EDT? It depends on the precise formalization of “computing what the world will be like if the action is taken, according to the laws of physics”, of course, but I’m having trouble imagining how that would not end up basically equivalent to EDT.
That is not the problem at all, it’s perfectly well-defined. I think if anything, the question would be what CDT’s P(A if B) is intuitively.
What are those, exactly? The “smoking lesion”? It specifies that output of decision theory correlates with lesion. Who knows how, but for it to actually correlate with decision of that decision theory other than via the inputs to decision theory, it got to be our good old friend Omega doing some intelligent design and adding or removing that lesion. (And if it does through the inputs, then it’ll smoke).
Given world state A which evolves into world state B (computable, deterministic universe), the hypothetical “what if world state A evolved into C where C!=B” will lead, among other absurdities, to a proof that B=C contradicting that B!=C (of course you can ensure that this particular proof won’t be reached with various silly hacks but you’re still making false assumptions and arriving at false conclusions). Maybe what you call ‘causal’ decision theory should be called ‘acausal’ because it in fact ignores causes of the decision, and goes as far as to break down it’s world model to do so. If you don’t do contradictory assumptions, then you have a world state A that evolves into world state B, and world state A’ that evolves into world state C, and in the hypothetical that the state becomes C!=B, the prior state got to be A’!=A . Yeah, it looks weird to westerners with their philosophy of free will and your decisions having the potential to send the same world down a different path. I am guessing it is much much less problematic if you were more culturally exposed to determinism/fatalism. This may be a very interesting topic, within comparative anthropology.
The main distinction between philosophy and mathematics (or philosophy done by mathematicians) seem to be that in the latter, if you get yourself a set of assumptions leading to contradictory conclusions (example: in Newcomb’s on one hand it can be concluded that agents which 1 box walk out with more money, on the other hand , agents that choose to two-box get strictly more money than those that 1-box), it is generally concluded that something is wrong with the assumptions, rather than argued which of the conclusions is truly correct given the assumptions.
The values of A, C and P are all equivalent. You insist on making CDT determine C in a model where it does not know these are correlated. This is a problem with your model.
Yes. That’s basically the definition of CDT. That’s also why CDT is no good. You can quibble about the word but in “the literature”, ‘CDT’ means just that.
This only shows that the model is no good, because the model does not respect the assumptions of the decision theory.
Well, a practically important example is a deterministic agent which is copied and then copies play prisoner’s dilemma against each other.
There you have agents that use physics. Those, when evaluating hypothetical choices, use some model of physics, where an agent can model itself as a copyable deterministic process which it can’t directly simulate (i.e. it knows that the matter inside it’s head obeys known laws of physics). In the hypothetical that it cooperates, after processing the physics, it is found that copy cooperates, in the hypothetical that it defects, it is found that copy defects.
And then there’s philosophers. The worse ones don’t know much about causality. They presumably have some sort of ill specified oracle that we don’t know how to construct, which will tell them what is a ‘consequence’ and what is a ‘cause’ , and they’ll only process the ‘consequences’ of the choice as the ‘cause’. This weird oracle tells us that other agent’s choice is not a ‘consequence’ of the decision, so it can not be processed. It’s very silly and not worth spending brain cells on.
Playing prisoner’s dilemma against a copy of yourself is mostly the same problem as Newcomb’s. Instead of Omega’s prediction being perfectly correlated with your choice, you have an identical agent whose choice will be perfectly correlated with yours—or, possibly, randomly distributed in the same manner. If you can also assume that both copies know this with certainty, then you can do the exact same analysis as for Newcomb’s problem.
Whether you have a prediction made by an Omega or a decision made by a copy really does not matter, as long as they both are automatically going to be the same as your own choice, by assumption in the problem statement.
The copy problem is well specified, though. Unlike the “predictor”. I clarified more in private. The worst part about Newcomb’s is that all the ex religious folks seem to substitute something they formerly knew as ‘god’ for predictor. The agent can also be further specified; e.g. as a finite Turing machine made of cogs and levers and tape with holes in it. The agent can’t simulate itself directly, of course, but it knows some properties of itself without simulation. E.g. it knows that in the alternative that it chooses to cooperate, it’s initial state was in set A—the states that result in cooperation, in the alternative that it chooses to defect, it’s initial state was in set B—the states that result in defection, and that no state is in both sets.