But if this is the case, then the problem looks underspecified. The correct decision depends on exact nature of the noise.
This is always so, there are details absent from any incomplete model, whose state can decide the outcome as easily as your decision. Gaining knowledge about those details allows to improve the decision, but absent that knowledge the only thing to do is to figure out what the facts you do know suggest.
If Omega makes the decision by analyzing the agent’s psychological tests taken in childhood, then the agent should two-box.
If people use this consideration to consistently beat Omega, its accuracy can’t be 90%. Therefore, in that case, they can’t beat Omega with this argument, proof by contradiction.
(If they don’t use this consideration, then you could win, but this hypothetical is of little use if you don’t know that. For example, it seems like a natural correction to specify that you only know the figure 90% and not correlation between the correctness of guesses and the test subjects’ properties, and that the people sampled for this figure were not different from you in any way that you consider relevant for this problem.)
This is always so, there are details absent from any incomplete model, whose state can decide the outcome as easily as your decision. Gaining knowledge about those details allows to improve the decision, but absent that knowledge the only thing to do is to figure out what the facts you do know suggest.
If no facts about the nature of the “noise” is specified, then the phrase “probability of correct decision by Omega is 0.9″ does not make sense. It does not add any knowledge beyond “sometimes Omega makes mistakes”.
If people use this consideration to consistently beat Omega, its accuracy can’t be 90%.
If only 10% of the people use this consideration, then why not?
(AFAIU, the point in parentheses basically amounts to the idea that in the absence of any known causal links I should use EDT (=Bayesian reasoning))
AFAIU, the point in parentheses basically amounts to the idea that in the absence of any known causal links I should use EDT (=Bayesian reasoning)
You use all that is known about how events, including your own decision, depend on each other. Some of these dependencies can’t withstand your interventions, which are often themselves coming out of the error terms. In this way, EDT is the same as TDT, its errors originating from failure to recognize this effect of breaking correlations and (a flaw shared with CDT) from unwillingness in include abstract computations in the models. CDT, on the other hand, severs too many dependencies by using its causal graph surgery heuristic.
My correction of the problem statement makes sure that the dependence of Omega’s prediction on your decision is not something that can be broken by your decision, so graph surgery should spare it. (In CDT terms, both your decision and Omega’s prediction depend on your original state, and CDT mistakenly severs this dependence by thinking its decision uncaused.)
My correction of the problem statement makes sure that the dependence of Omega’s prediction on your decision is not something that can be broken by your decision, so graph surgery should spare it.
But when you make this correction, and then compare agents performance based on it, you should place the agents in the same situation, if the comparison is to be fair. In particular, the situation must be the same regarding the knowledge of this correction—knowledge that “the dependence of Omega’s prediction on your decision is not something that can be broken by your decision”. In a regular analysis here on LW of Newcomb’s problem, TDT receives an unfair advantage, in that it is given this knowledge while CDT is not, presumably because CDT cannot represent it.
But in fact it can—why not? If it means drawing causal arrows backwards in time, so what?
And in case of “pure” Newcomb’s problem, where the agent knows that Omega is 100% correct, even the backward causal arrows are not needed. I think. That was what my original comment was about, and so far no one answered...
In a regular analysis here on LW of Newcomb’s problem, TDT receives an unfair advantage, in that it is given this knowledge while CDT is not, presumably because CDT cannot represent it.
The comparison doesn’t necessarily have to be fair, it only needs to accurately discern the fittest. A cat, for example, won’t even notice that an IQ test is presented before it, but that doesn’t mean that we have to make adjustments, that the conclusion is incorrect.
If it means drawing causal arrows backwards in time, so what?
Updates are propagated in both directions, so you draw causal arrows only forwards in time, just don’t sever this particular arrow during standard graph surgery on a standard-ish causal graph, so that knowledge about your decision tells you something about its origins in the past, and then about the other effects of those origins on the present. But CDT is too stubborn to do that, and a re-educated CDT is not a CDT anymore, it’s half-way towards becoming a TDT.
The comparison doesn’t necessarily have to be fair, it only needs to accurately discern the fittest. A cat, for example, won’t even notice that an IQ test is presented before it, but that doesn’t mean that we have to make adjustments, that the conclusion is incorrect.
Good point.
But CDT is too stubborn to do that, and a re-educated CDT is not a CDT anymore, it’s half-way towards becoming a TDT.
Perhaps. Although it’s not clear to me why CDT is allowed to notice that its mirror image does whatever it does, but not that its perfect copy does whatever it does.
And what about the “simulation uncertainty” argument? Is it valid or there’s a mistake somewhere?
If no facts about the nature of the “noise” is specified, then the phrase “probability of correct decision by Omega is 0.9″ does not make sense.
That is just what “probability” means: it quantifies possibilities that can’t be ruled out, where it’s not possible to distinguish those that do take place from those that don’t.
On me having chicken for supper. Unless you can unpack “being conditional” to more than a bureaucratic hoop that’s easily jumped through, it’s of no use.
On reflection, my previous comment was off the mark. Knowing that Omega always predicts “two-box” is an obvious correlation between a property of agents and the quality of prediction. So, your correction basically states that the second view is the “natural” one: Omega always predicts correctly and then modifies the answer in 10% cases.
In such case, the “simulation uncertainty” argument should work the same way as in the “pure” Newcomb’s problem, with the correction for the 10% noise (which does not change the answer).
Oh, come on. According to Janes, the marginal probability P(Omega is correct | Omega predicts something) is supposed to be additionally conditioned on everything you know about the situation. If you know that Omega always predicts “two-box”, then P(Omega is correct | Omega predicts something) is equal to the relative frequency of two-boxers in the population. If you know that Omega first always predicts correctly and then modifies its answer in 10% cases, then it’s something completely different. If you have no knowledge about whether the first or the second is true, then what can you do? Presumably, try Solomonoff induction, too bad it’s incomputable.
This is always so, there are details absent from any incomplete model, whose state can decide the outcome as easily as your decision. Gaining knowledge about those details allows to improve the decision, but absent that knowledge the only thing to do is to figure out what the facts you do know suggest.
If people use this consideration to consistently beat Omega, its accuracy can’t be 90%. Therefore, in that case, they can’t beat Omega with this argument, proof by contradiction.
(If they don’t use this consideration, then you could win, but this hypothetical is of little use if you don’t know that. For example, it seems like a natural correction to specify that you only know the figure 90% and not correlation between the correctness of guesses and the test subjects’ properties, and that the people sampled for this figure were not different from you in any way that you consider relevant for this problem.)
If no facts about the nature of the “noise” is specified, then the phrase “probability of correct decision by Omega is 0.9″ does not make sense. It does not add any knowledge beyond “sometimes Omega makes mistakes”.
If only 10% of the people use this consideration, then why not?
(AFAIU, the point in parentheses basically amounts to the idea that in the absence of any known causal links I should use EDT (=Bayesian reasoning))
You use all that is known about how events, including your own decision, depend on each other. Some of these dependencies can’t withstand your interventions, which are often themselves coming out of the error terms. In this way, EDT is the same as TDT, its errors originating from failure to recognize this effect of breaking correlations and (a flaw shared with CDT) from unwillingness in include abstract computations in the models. CDT, on the other hand, severs too many dependencies by using its causal graph surgery heuristic.
My correction of the problem statement makes sure that the dependence of Omega’s prediction on your decision is not something that can be broken by your decision, so graph surgery should spare it. (In CDT terms, both your decision and Omega’s prediction depend on your original state, and CDT mistakenly severs this dependence by thinking its decision uncaused.)
But when you make this correction, and then compare agents performance based on it, you should place the agents in the same situation, if the comparison is to be fair. In particular, the situation must be the same regarding the knowledge of this correction—knowledge that “the dependence of Omega’s prediction on your decision is not something that can be broken by your decision”. In a regular analysis here on LW of Newcomb’s problem, TDT receives an unfair advantage, in that it is given this knowledge while CDT is not, presumably because CDT cannot represent it.
But in fact it can—why not? If it means drawing causal arrows backwards in time, so what?
And in case of “pure” Newcomb’s problem, where the agent knows that Omega is 100% correct, even the backward causal arrows are not needed. I think. That was what my original comment was about, and so far no one answered...
The comparison doesn’t necessarily have to be fair, it only needs to accurately discern the fittest. A cat, for example, won’t even notice that an IQ test is presented before it, but that doesn’t mean that we have to make adjustments, that the conclusion is incorrect.
Updates are propagated in both directions, so you draw causal arrows only forwards in time, just don’t sever this particular arrow during standard graph surgery on a standard-ish causal graph, so that knowledge about your decision tells you something about its origins in the past, and then about the other effects of those origins on the present. But CDT is too stubborn to do that, and a re-educated CDT is not a CDT anymore, it’s half-way towards becoming a TDT.
Good point.
Perhaps. Although it’s not clear to me why CDT is allowed to notice that its mirror image does whatever it does, but not that its perfect copy does whatever it does.
And what about the “simulation uncertainty” argument? Is it valid or there’s a mistake somewhere?
That is just what “probability” means: it quantifies possibilities that can’t be ruled out, where it’s not possible to distinguish those that do take place from those that don’t.
Bayesians say all probabilities are conditional. The question here is on what this “0.9” probability is conditioned.
On me having chicken for supper. Unless you can unpack “being conditional” to more than a bureaucratic hoop that’s easily jumped through, it’s of no use.
On reflection, my previous comment was off the mark. Knowing that Omega always predicts “two-box” is an obvious correlation between a property of agents and the quality of prediction. So, your correction basically states that the second view is the “natural” one: Omega always predicts correctly and then modifies the answer in 10% cases.
In such case, the “simulation uncertainty” argument should work the same way as in the “pure” Newcomb’s problem, with the correction for the 10% noise (which does not change the answer).
Oh, come on. According to Janes, the marginal probability P(Omega is correct | Omega predicts something) is supposed to be additionally conditioned on everything you know about the situation. If you know that Omega always predicts “two-box”, then P(Omega is correct | Omega predicts something) is equal to the relative frequency of two-boxers in the population. If you know that Omega first always predicts correctly and then modifies its answer in 10% cases, then it’s something completely different. If you have no knowledge about whether the first or the second is true, then what can you do? Presumably, try Solomonoff induction, too bad it’s incomputable.
(See the parenthetical in the current updated version of the comment.)
I added a parenthetical to my comment as well :)