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linas comments on Decision Theory FAQ - Less Wrong
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I'm with incogn on this one: either there is predictability or there is choice; one cannot have both.
Incogn is right in saying that, from omega's point of view, the agent is purely deterministic, i.e. more or less equivalent to a computer program. Incogn is slightly off-the-mark in conflating determinism with predictability: a system can be deterministic, but still not predictable; this is the foundation of cryptography. Deterministic systems are either predictable or are not. Unless Newcombs problem explicitly allows the agent to be non-deterministic, but this is unclear.
The only way a deterministic system becomes unpredictable is if it incorporates a source of randomness that is stronger than the ability of a given intelligence to predict. There are good reasons to believe that there exist rather simple sources of entropy that are beyond the predictive power of any fixed super-intelligence -- this is not just the foundation of cryptography, but is generically studied under the rubric of 'chaotic dynamical systems'. I suppose you also have to believe that P is not NP. Or maybe I should just mutter 'Turing Halting Problem'. (unless omega is taken to be a mythical comp-sci "oracle", in which case you've pushed decision theory into that branch of set theory that deals with cardinal numbers larger than the continuum, and I'm pretty sure you are not ready for the dragons that lie there.)
If the agent incorporates such a source of non-determinism, then omega is unable to predict, and the whole paradox falls down. Either omega can predict, in which case EDT, else omega cannot predict, in which case CDT. Duhhh. I'm sort of flabbergasted, because these points seem obvious to me ... the Newcomb paradox, as given, seems poorly stated.
Think of real people making choices and you'll see it's the other way around. The carefully chosen paths are the predictable ones if you know the variables involved in the choice. To be unpredictable, you need think and choose less.
Hell, the archetypical imagery of someone giving up on choice is them flipping a coin or throwing a dart with closed eyes -- in short resorting to unpredictability in order to NOT choose by themselves.
Either your claim is false or you are using a definition of at least one of those two words that means something different to the standard usage.
I do not think the standard usage is well defined, and avoiding these terms altogether is not possible, seeing as they are in the definition of the problem we are discussing.
Interpretations of the words and arguments for the claim are the whole content of the ancestor post. Maybe you should start there instead of quoting snippets out of context and linking unrelated fallacies? Perhaps, by specifically stating the better and more standard interpretations?
Huh? Can you explain? Normally, one states that a mechanical device is "predicatable": given its current state and some effort, one can discover its future state. Machines don't have the ability to choose. Normally, "choice" is something that only a system possessing free will can have. Is that not the case? Is there some other "standard usage"? Sorry, I'm a newbie here, I honestly don't know more about this subject, other than what i can deduce by my own wits.
Machines don't have preferences, by which I mean they have no conscious self-awareness of a preferred state of the world -- they can nonetheless execute "if, then, else" instructions.
That such instructions do not follow their preferences (as they lack such) can perhaps be considered sufficient reason to say that machines don't have the ability to choose -- that they're deterministic doesn't... "Determining something" and "Choosing something" are synonyms, not opposites after all.
Newcomb's problem makes the stronger precondition that the agent is both predictable and that in fact one action has been predicted. In that specific situation, it would be hard to argue against that one action being determined and immutable, even if in general there is debate about the relationship between determinism and predictability.
Hmm, the FAQ, as currently worded, does not state this. It simply implies that the agent is human, that omega has made 1000 correct predictions, and that omega has billions of sensors and a computer the size of the moon. That's large, but finite. One may assign some finite complexity to Omega -- say 100 bits per atom times the number of atoms in the moon, whatever. I believe that one may devise pseudo-random number generators that can defy this kind of compute power. The relevant point here is that Omega, while powerful, is still not "God" (infinite, infallible, all-seeing), nor is it an "oracle" (in the computer-science definition of an "oracle": viz a machine that can decide undecidable computational problems).
I do not want to make estimates on how and with what accuracy Omega can predict. There is not nearly enough context available for this. Wikipedia's version has no detail whatsoever on the nature of Omega. There seems to be enough discussion to be had, even with the perhaps impossible assumption that Omega can predict perfectly, always, and that this can be known by the subject with absolute certainty.
I think I agree, by and large, despite the length of this post.
Whether choice and predictability are mutually exclusive depends on what choice is supposed to mean. The word is not exactly well defined in this context. In some sense, if variable > threshold then A, else B is a choice.
I am not sure where you think I am conflating. As far as I can see, perfect prediction is obviously impossible unless the system in question is deterministic. On the other hand, determinism does not guarantee that perfect prediction is practical or feasible. The computational complexity might be arbitrarily large, even if you have complete knowledge of an algorithm and its input. I can not really see the relevance to my above post.
Finally, I am myself confused as to why you want two different decision theories (CDT and EDT) instead of two different models for the two different problems conflated into the single identifier Newcomb's paradox. If you assume a perfect predictor, and thus full correlation between prediction and choice, then you have to make sure your model actually reflects that.
Let's start out with a simple matrix, P/C/1/2 are shorthands for prediction, choice, one-box, two-box.
If the value of P is unknown, but independent of C: Dominance principle, C=2, entirely straightforward CDT.
If, however, the value of P is completely correlated with C, then the matrix above is misleading, P and C can not be different and are really only a single variable, which should be wrapped in a single identifier. The matrix you are actually applying CDT to is the following one:
The best choice is (P&C)=1, again by straightforward CDT.
The only failure of CDT is that it gives different, correct solutions to different, problems with a properly defined correlation of prediction and choice. The only advantage of EDT is that it is easier to cheat in this information without noticing it - even when it would be incorrect to do so. It is entirely possible to have a situation where prediction and choice are correlated, but the decision theory is not allowed to know this and must assume that they are uncorrelated. The decision theory should give the wrong answer in this case.
Yes. I was confused, and perhaps added to the confusion.
If Omega cannot predict, TDT will two-box.