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Your problem setup contains a contradiction. You said that X and X*_i are identical copies, and then you said that they have different utility functions. This happened because you defined the utility function over the wrong domain; you specified it as (world-history, identity)=>R when it should be (world-history)=>R.
In response to
Simulation argument meets decision theory
Thanks for mentioning this. I know this wasn't put very nicely.
Imagine you were a very selfish person X only caring about yourself. If I make a really good copy of X which is then placed 100 meters next to X, then this copy X* only cares about the spatiotemporal dots of what we define X. Both agents, X and X, are identical if we formalize their algorithms incorporating indexical information. If we don't do that then a disparity remains, namely that X is different to X* in that, intrinsically, X only cares about the set of spatiotemporal dots constituting X. The same goes for X* accordingly. But this semantical issue doesn't seem to be relevant for the decision problem itself. The kind of similarity that is of interest here seems to be the one that determines similiar behavior in such games. (Probably you could set up games where the non-indexical formalization of the agents X and X* are relevantly different, I merely claim that this game is not one of them)
Simulation argument meets decision theory
Person X stands in front of a sophisticated computer playing the decision game Y which allows for the following options: either press the button "sim" or "not sim". If she presses "sim", the computer will simulate X*_1, X*_2, ..., X*_1000 which are a thousand identical copies of X. All of them will face the game Y* which - from the standpoint of each X* - is indistinguishable from Y. But the simulated computers in the games Y* don't run simulations. Additionally, we know that if X presses "sim" she receives a utility of 1, but "not sim" would only lead to 0.9. If X*_i (for i=1,2,3..1000) presses "sim" she receives 0.2, with "not sim" 0.1. For each agent it is true that she does not gain anything from the utility of another agent despite the fact she and the other agents are identical! Since all the agents are identical egoists facing the apparently same situation, all of them will take the same action.
Now the game starts. We face a computer and know all the above. We don't know whether we are X or any of the X*'s, should we now press "sim" or "not sim"?
EDIT: It seems to me that "identical" agents with "independent" utility functions were a clumsy set up for the above question, especially since one can interpret it as a contradiction. Hence, it might be better to switch to identical egoists whereas each agent only cares about her receiving money (linear monetary value function). If X presses "sim" she will be given 10$ (else 9$) in the end of the game; each X* who presses "sim" receives 2$ (else 1$), respectively. Each agent in the game wants to maximize the expected monetary value they themselves will hold in their own hand after the game. So, intrinsically, they don't care how much money the other copies make.
To spice things up: What if the simulation will only happen a year later? Are we then able to "choose" which year it is?
This quote seems to be endorsing the Mind Projection Fallacy; learning about the past doesn't seem to me to be the same thing as determining it...
It goes the other way round. An excerpt of my post (section Newcomb's Problem's problem of free will):
Perceiving time without an inherent “arrow” is not new to science and philosophy, but still, readers of this post will probably need a compelling reason why this view would be more goal-tracking. Considering the Newcomb’s Problem a reason can be given: Intuitively, the past seems much more “settled” to us than the future. But it seems to me that this notion is confounded as we often know more about the past than we know about the future. This could tempt us to project this disbalance of knowledge onto the universe such that we perceive the past as settled and unswayable in contrast to a shapeable future. However, such a conventional set of intuitions conflicts strongly with us picking only one box. These intuitions would tell us that we cannot affect the content of the box; it is already filled or empty since it has been prepared in the now inaccessible past.
Look, this is all too theoretical for me. Can you please go and actually read my example and tell me what your decision rule is for giving the drug?
There is more to this than d-separation. D-separation is just a visual rule for the way in which conditional independence works in certain kinds of graphical models. There is not enough conceptual weight in the d-separation idea alone to handle decision theory.
Look, HIV patients who get HAART die more often (because people who get HAART are already very sick). We don't get to see the health status confounder because we don't get to observe everything we want. Given this, is HAART in fact killing people, or not?
It is not that clear to me what we know about HAART in this game. For instance, in case we know nothing about it and we only observe logical equivalences (in fact rather probabilistic tendencies) in the form "HAART" <--> "Patient dies (within a specified time interval)" and "no HAART" <--> "Patient survives" it wouldn't be irrational to reject the treatment.
Once we know more about HAART, for instance, that the probabilistic tendencies were due to unknowingly comparing sick people to healthy people, we then can figure out that P( patient survives | sick, HAART) > P (patient survives | sick, no HAART) and that P( patient survives | healthy, HAART)< P(patient survives | healthy, no HAART). Knowing that much, choosing not to give the drug would be a foolish thing to do.
If we come to know that a particular reasoning R leads to not prescribing the drug (even after the update above) is very strongly correlated with having patients that are completely healthy but show false-positive clinical test results, then not prescribing the drug would be the better thing to do. This, of course, would require that this new piece of information brings about true predictions about future cases (which makes the scenario quite unlikely, though considering the theoretical debate it might be relevant).
Generally, I think that drawing causal diagrams is a very useful heuristic in "everyday science", since replacing the term causality with all the conditionals involved might be confusing. Maybe this is a reason why some people tend to think that evidential reasoning is defined to only consider plain conditionals (in this example P(survival| HAART)) but not more background data. Because otherwise, in effortful ways you could receive the same answer as causal reasoners do but what would be the point of imitating CDT?
I think it is exactly the other way round. It's all about conditionals. It seems to me that a bayesian writes down "causal connection" in his/her map after updating on sophisticated sets of correlations. It seems impossible to completely rule out confounding at any place. Since evidential reasoning would suggest not to prescribe the drug in the false-positive scenario above its output is not similiar to the one conventional CDT produces. Differences between CDT and the non-naive evidential approach are described here as well: http://lesswrong.com/lw/j5j/chocolate_ice_cream_after_all/a6lh
It seems that CDT-supporters only do A if there is a causal mechanism connecting it with the desirable outcome B. An evidential reasoner would also do A if he knew that there would be no causal mechanism connecting it to B, but a true (but purely correlative) prediction stating the logical equivalences A<-->B and ~A <--> ~B.
We believe in the forecasting power, but we are uncertain as to what mechanism that forecasting power is taking advantage of to predict the world.
analogously, I know Omega will defeat me at Chess, but I do not know which opening move he will play.
In this case, the TDT decision depends critically on which causal mechanism underlies that forecasting power. Since we do not know, we will have to apply some principles for decision under uncertainty, which will depend on the payoffs, and on other features of the situation. The EDT decision does not. My intuitions and, I believe, the intuitions of many other commenters here, are much closer to the TDT approach than the EDT approach. Thus your examples are not very helpful to us - they lump things we would rather split, because our decisions in the sort of situation you described would depend in a fine-grained way on what causal explanations we found most plausible.
Suppose it is well-known that the wealthy in your country are more likely to adopt a certain distinctive manner of speaking due to the mysterious HavingRichParents gene. If you desire money, could you choose to have this gene by training yourself to speak in this way?
I agree that it is challenging to assign forecasting power to a study, as we're uncertain about lots of background conditions. There is forecasting power to the degree that the set A of all variables involved with previous subjects allow for predictions about the set A' of variables involved in our case. Though when we deal with Omega who is defined to make true predictions, then we need to take this forecasting power into account, no matter what the underlying mechanism is. I mean, what if Omega in Newcomb's Problem was defined to make true predictions and you don't know anything about the underlying mechanism? Wouldn't you one-box after all? Let's call Omega's prediction P and the future event F. Once Omega's prediction are defined to be true, we can denote the following logical equivalences: P(1 boxing) <--> F(1 boxing) and P(2 boxing) <--> P(2 boxing). Given this conditions, it impossible to 2-box when box B is filled with a million dollars (you could also formulate it in terms of probabilities where such an impossible event would have the probability of 0). I admit that we have to be cautious when we deal with instances that are not defined to make true predictions.
Suppose it is well-known that the wealthy in your country are more likely to adopt a certain distinctive manner of speaking due to the mysterious HavingRichParents gene. If you desire money, could you choose to have this gene by training yourself to speak in this way?
My answer depends on the specific set-up. What exactly do we mean with "It is well-known"? It doesn't seem to be a study that would describe the set A of all factors involved which we then could use to derive A' that applied to our own case. Unless we define "It is well-known" as a instance that allows for predictions in the direction A --> A', I see little reason to assume a forecasting power. Without forecasting power, screening off applies and it would be foolish to train the distinctive manner of speaking. If we specified the game in a way that there is forecasting power at work (or at least we had reason to believe so), depending on your definition of choice (I prefer one that is devoid of free will) you can or cannot choose the gene. These kind of thoughts are listed here or in the section "Newcomb’s Problem’s Problem of Free Will" in the post.
In response to
Chocolate Ice Cream After All?
My thoughts: 1) The failure of CDT is its modeling of the decision process as ineffable 'free will' upon which things in the past cannot depend. Deviation from CDT is justified only when such dependencies exist. 2) The assumption that your decision is predictable requires the existence of such a dependency. 3) If we postulate that no such dependency exists, either CDT wins or our postulates are contradictory.
In particular, in Newcomb's Soda, the assumptions that the soda flavor predicts the ice-cream flavor with high probability and that the assignment of soda (and the choice of subjects) is uncorrelated with subjects' decision theory require that we are exceptional in employing decision theory. If lots of subjects were using CDT or EDT, they would all be choosing ice cream independently of their soda, and we wouldn't see that correlation (except maybe by coincidence). So it doesn't have to be stated in the problem that other subjects aren't using evidential reasoning--it can be seen plainly from the axioms! To assume that they are reasoning as you are is to assume a contradiction.
The AB game is confusing because it flirts with contradiction. You act as if you're free to choose A or B according to your decision theory while simultaneously assuming that Omega can predict your choice perfectly. But in fact, the only way Omega can predict perfectly is by somehow interacting with your decision theory. He can either administer the game only to people whose decision theory matches their genes, or manipulate people's answers, or manipulate their genes. In the first case, EDTers will get a free gene test if they have GA, but will not be miraculously healed if they have GB. In the second case, you'll find yourself pressing 'B' if you have G_B no matter what you try to precommit to. In the third case only, you have legitimate reason to commit to 'A', because your predetermined decision has causal influence on your genes.
You might try to counter with the case where Omega ensures that all children who are born will answer in a way consistent with their genes, and both things are determined at conception. But if this is the case, then if you have G_B, you can't commit yourself to EDT no matter how hard you think about decision theory. This follows from the assumptions, and the only reason to think otherwise is if you still count free will among your premises.
If lots of subjects were using CDT or EDT, they would all be choosing ice cream independently of their soda, and we wouldn't see that correlation (except maybe by coincidence). So it doesn't have to be stated in the problem that other subjects aren't using evidential reasoning--it can be seen plainly from the axioms! To assume that they are reasoning as you are is to assume a contradiction.
If lots of subjects were using CDT or EDT, they would be choosing ice cream independently of their soda iff the soda has no influence on whether they argue according to CDT or EDT. It is no logical contradiction to say that the sodas might affect which decision theoretic intuitions a subject is going to have. As long as we don't specify what this subconscious desire for ice cream exactly means, it is thinkable that the sodas imperceptibly affect our decision algorithm. In such a case, most of the V-I people (the fraction originating from V-S) would be attracted to causal reasoning, whereas most of the Ch-I people (the fraction originating from Ch-S) would find the evidential approach compelling. One can say now that the sodas "obviously" do not affect one's decision theory, but this clearly had to be pointed out when introducing a "subconscious desire."
I agree that once it is specified that we are the only agents using decision theory, screening off applies. But the game is defined in a way that we are subjects of a study where all the subjects are rewarded with money:
(an excerpt of the definition in Yudkowsky (2010))
It so happens that all participants in the study who test the Chocolate Soda are rewarded with a million dollars after the study is over, while participants in the study who test the Vanilla Soda receive nothing. But subjects who actually eat vanilla ice cream receive an additional thousand dollars, while subjects who actually eat chocolate ice cream receive no additional payment.
After reading this, it is not a priori clear to me that I would be the only subject who knows about the money at stake. To the contrary, as one of many subjects I assume that I know as much as other subjects know about the setting. Once other subjects know about the money they probably also think about whether choosing Ch-I or V-I produces the better outcome. It seems to me that all the agents base their decision on some sort of intuition about which would be the correct decisional algorithm.
To sum up, I tend to assume that other agents play a decision theoretic game as well and that the soda might affect their decision theoretic intuitions. Even if we assigned a low prior to the event that the sodas affect the subject's decision algorithms, the derived reasoning would not be invalid but it's power would shrink in proportion to the prior. Finally, it is definetly not a contradictory statement to say that the soda affects how the subject's decide and that the subject's use CDT or EDT.
In response to
Chocolate Ice Cream After All?
Presumably, if you use E to decide in Newcomb's soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E. If we assume E does in fact recommend to eat the chocolate ice cream, 50% of E agents will drink chocolate soda, 50% will drink the vanilla soda (assuming reasonable experimental design), and 100% will eat the chocolate ice cream. Therefore, given that you use E, there is no correlation between your decision and receiving the $1,000,000, so you might as well eat the vanilla and get the $1000. Therefore E does not actually recommend eating the chocolate ice cream.
Note that this reasoning does not generalize to Newcomb's problem. If E agents take one box, Omega will predict that they will all take one box, so they all get the payoff and the correlation survives.
Presumably, if you use E to decide in Newcomb's soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E.
Can you show where the screening off would apply (like A screens off B from C)?
I am just saying, fix CDT, not EDT. I claim EDT is irrepairably broken on far less exotic problems than Parfit's hitchhiker. Problems like "should I give drugs to patients based on the results of this observational study?" The reason I think this is I can construct arbitrarily complicated causal graphs where getting the right answer entails having a procedure that is "causal inference"-complete, and I don't think anyone who uses EDT is anywhere near there (and if they are .. they are just reinventing CDT with a different language, which seems silly).
I am not strawmanning EDT, I am happy to be proven wrong by any EDT adherent and update accordingly (hence my challenge). For example, I spent some time with Paul Christiano et al back at the workshop trying to get a satisfactory answer out of EDT, and we didn't really succeed (although to be fair, that was a tangent to the main thrust of that workshop, so we didn't really spend too much time on this).
I claim EDT is irrepairably broken on far less exotic problems than Parfit's hitchhiker. Problems like "should I give drugs to patients based on the results of this observational study?"
This seems to be a matter of screening off. Once we don't prescribe drugs because of evidential reasoning we don't learn anything new about the health of the patient. I would only not prescripe the drug if a credible instance with forecasting power (for instance Omega) shows to me that generally healthy patients (who show suspicious symptoms) go to doctors who endorse evidential reasoning and unhealthy patients go to conventional causal doctors. This sounds counterintuitive, but structurally it is equal to Newcomb's Problem: The patient corresponds to the box, we know it already "has" a specific value, but we don't know it yet. Choosing only box B (or not to give the drug) would be the option that is only compatible with the more desirable past where Omega has put the million into the box (or where the patient has been healthy all along).
I am just saying, fix CDT, not EDT. I claim EDT is irrepairably broken on far less exotic problems than Parfit's hitchhiker. Problems like "should I give drugs to patients based on the results of this observational study?" The reason I think this is I can construct arbitrarily complicated causal graphs where getting the right answer entails having a procedure that is "causal inference"-complete, and I don't think anyone who uses EDT is anywhere near there (and if they are .. they are just reinventing CDT with a different language, which seems silly).
I am not strawmanning EDT, I am happy to be proven wrong by any EDT adherent and update accordingly (hence my challenge). For example, I spent some time with Paul Christiano et al back at the workshop trying to get a satisfactory answer out of EDT, and we didn't really succeed (although to be fair, that was a tangent to the main thrust of that workshop, so we didn't really spend too much time on this).
My comment above strongly called into question whether CDT gives the right answers. Therefore I wouldn't try to reinvent CDT with a different language. For instance, in the post I suggest that we should care about "all" the outcomes, not only the one happening in the future. I've first read about this idea in Paul Almond's paper on decision theory. An excerpt that might be of interest:
Suppose the universe is deterministic, so that the state of the universe at any time completely determines its state at some later time. Suppose at the present time, just before time tnow, you have a choice to make. There is a cup of coffee on a table in front of you and have to decide whether to drink it. Before you decide, let us consider the state of the universe at some time, tsooner, which is earlier than the present. The state of the universe at tsooner should have been one from which your later decision, whatever it is going to be, can be determined: If you eventually end up drinking the coffee at tnow, this should be implied by the universe at tsooner. Assume we do not know whether you are going to drink the coffee. We do not know whether the state of the universe at tsooner was one that led to you drinking the coffee. Suppose that there were a number of conceivable states of the universe at tsooner, each consistent with what you know in the present, which implied futures in which you drink the coffee at tnow. Let us call these states D1,D2,D3,…Dn. Suppose also that there were a number of conceivable states of the universe at tsooner, each consistent with what you know in the present, which implied futures in which you do not drink the coffee at tnow. Let us call these states N1,N2,N3,…Nn. Suppose that you just drunk the coffee at tnow. You would now know that the state of the universe at tsooner was one of the states D1,D2,D3,…Dn. Suppose now that you did not drink the coffee at tnow. You would now know that the state of the universe at tsooner was one of the states N1,N2,N3,…Nn. Consider now the situation in the present, just before tnow, when you are faced with deciding whether to drink the coffee. If you choose to drink the coffee then at tsooner the universe will have been in one of the states D1, D2, D3,…Dn and if you choose not to drink the coffee then at tsooner the universe will have been in one of the states N1,N2,N3,…Nn. From your perspective, your choice is determining the previous state of the universe, as if backward causality were operating. From your perspective, when you are faced with choosing whether or not to drink the coffee, you are able to choose whether you want to live in a universe which was in one of the states D1,D2,D3,…Dn or one of the states N1,N2,N3,…Nn in the past. Of course, there is no magical backward causality effect operating here: The reality is that it is your decision which is being determined by the earlier state of the universe. However, this does nothing to change how things appear from your perspective. Why is it that Newcomb’s paradox worries people so much, while the same issue arising with everyday decisions does not seem to cause the same concern? The main reason is probably that the issue is less obvious outside the scope of contrived situations like that in Newcomb’s paradox. With the example I have been discussing here, you get to choose the state of the universe in the past, but only in very general terms: You know that you can choose to live in a universe that, in the past, was in one of the states D1,D2,D3,…Dn, but you are not confronted with specific details about one of these states, such as knowing that the universe had a specific state in which some money was placed in a certain box (which is how the backward causality seems to operate in Newcomb’s paradox). It may make it seem more like an abstract, philosophical issue than a real problem. In reality, the lack of specific knowledge should not make us feel any better: In both situations you seem to be choosing the past as well as the future. You might say that you do not really get to choose the previous state of the universe, because it was in fact your decision that was determined by the previous state, but you could as well say the same about your decision to drink or not drink the coffee: You could say that whether you drink the coffee was determined by some earlier state of the universe, so you have only the appearance of a choice. When making choices we act as if we can decide, and this issue of the past being apparently dependent on our choices is no different from the normal consequences of our future being apparently dependent on our choices, even though our choices are themselves dependent on other things: We can act as if we choose it.
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The question is whether this is analogous to Newcomb's problem. After all, one can make the same argument you make that "no matter what the contents of the box, taking both boxes is the dominant strategy,"
I agree. It seems to me that the speciality of the Necomb Problem is that actions "influence" states and that this is the reason why the dominance principle alone isn't giving the right answer. The same applies to this game. Your action (sim or not sim) determines the probability of which agent you have been all along and therefore "influences" the states of the game, whether you are X or X*. Many people dislike this use of the word "influence" but I think there are some good reasons in favour of a broader use of it (eg. quantum entanglement).