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Jiro comments on Conceptual Analysis and Moral Theory - Less Wrong
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Comments (456)
Clearly thats two boxing. Omega already made his choice, so if he thought I'd two box, I'll get;
-One box: nothing -two boxing: the small reward
if Omega thought I'd one box: -One box:big reward -two box: big reward + small reward
Two boxing results in more money no matter how Omega thought I'd chose.
What if I try to predict what Omega does, and do the opposite?
That would mean that either 1) there are some strategies I am incapable of executing, or 2) Omega can't in principle predict what I do, since it is indirectly predicting itself.
Alternatively, what if instead of me trying to predict Omega, we run this with transparent boxes and I base my decision on what I see in the boxes, doing the opposite of what Omega predicted? Again, Omega is indirectly predicting itself.
I don't see how this is relevant, but yes, in principle it's impossible to predict the universe perfectly. On account of the universe + your brain is bigger than your brain. Although, if you live in a bubble universe that is bigger than the rest of the universe, whose interaction with the rest of the universe is limited precisely to your chosen manipulation of the connecting bridge; basically, if you are AIXI, then you may be able to perfectly predict the universe conditional on your actions.
This has pretty much no impact on actual newcomb's though, since we can just define such problems away by making omega do the obvious thing to prevent such shenanigans ("trolls get no money"). For the purpose of the thought experiment, action-conditional predictions are fine.
IOW, this is not a problem with Newcomb's. By the way, this has been discussed previously.
You've now destroyed the usefulness of Newcomb as a potentially interesting analogy to the real world. In real world games, my opponent is trying to infer my strategy and I'm trying to infer theirs.
If Newcomb is only about a weird world where omega can try and predict the player's actions, but the player is not allowed to predict omega's, then its sort of a silly problem. Its lost most of its generality because you've explicitly disallowed the majority of strategies.
If you allow the player to pursue his own strategy, then its still a silly problem, because the question ends up being inconsistent (because if omega plays omega, nothing can happen).
In real world games, we spend most our time trying to make action-conditional predictions. "If I play Foo, then my opponent will play Bar". There's no attempting to circularly predict yourself with unconditional predictions. The sensible formulation of Newcomb's matches that.
(For example, transparent boxes: Omega predicts "if I fill both boxes, then player will _" and fills the boxes based on that prediction. Or a few other variations on that.)
In many (probably most?) games we consider the opponents strategy, not simply their next move. Making moves in an attempt to confuse your opponent's estimation of your own strategy is a common tactic in many games.
Your "modified Newcomb" doesn't allow the chooser to have a strategy- they aren't allowed to say "if I predict Omega did X, I'll do Y." Its a weird sort of game where my opponent takes my strategy into account, but something keeps me from considering my opponents.
Can't Omega follow the strategy of 'Trolls get no money,' which by assumption is worse for you? I feel like this would result in some false positives, but perhaps not - and the scenario says nothing about the people who don't get to play in any case.
No, because that's fighting the hypothetical. Assume that he doesn't do that.
It is actually approximately the opposite of fighting the hypothetical. It is managing the people who are trying to fight the hypothetical. Precise wording of the details of the specification can be used to preempt such replies but for casual defininitions that assume good faith sometimes explicit clauses for the distracting edge cases need to be added.
It is fighting the hypothetical because you are not the only one providing hypotheticals. I am too; I'm providing a hypothetical where the player's strategy makes this the least convenient possible world for people who claim that having such an Omega is a self-consistent concept. Saying "no, you can't use that strategy" is fighting the hypothetical.
Moreover, the strategy "pick the opposite of what I predict Omega does" is a member of a class of strategies that have the same problem; it's just an example of such a strategy that is particularly clear-cut, and the fact that it is clear-cut and blatantly demonstrates the problem with the scenario is the very aspect that leads you to call it trolling Omega. "You can't troll Omega" becomes equivalent to "you can't pick a strategy that makes the flaw in the scenario too obvious".
If your goal is to show that Omega is "impossible" or "inconsistent", then having Omega adopt the strategy "leave both boxes empty for people who try to predict me / do any other funny stuff" is a perfectly legitimate counterargument. It shows that Omega is in fact consistent if he adopts such strategy. You have no right to just ignore that counterargument.
Indeed, Omega requires a strategy for when he finds that you are too hard to predict. The only reason such a strategy is not provided beforehand in the default problem description is because we are not (in the context of developing decision theory) talking about situations where you are powerful enough to predict Omega, so such a specification would be redundant. The assumption, for the purpose of illuminating problems with classical decision theory, is that Omega has vastly more computational resources than you do, so that the difficult decision tree that presents the problem will obtain.
By the way, it is extremely normal for there to be strategies you are "incapable of executing". For example, I am currently unable to execute the strategy "predict what you will say next, and counter it first", because I can't predict you. Computation is a resource like any other.
If you are suggesting that Omega read my mind and think "does this human intend to outsmart me, Omega", then sure he can do that. But that only takes care of the specific version of the strategy where the player has conscious intent.
If you're suggesting "Omega figures out whether my strategy is functionally equivalent to trying to outsmart me", you're basically claiming that Omega can solve the halting problem by analyzing the situation to determine if it's an instance of the halting problem, and outputting an appropriate answer if that is the case. That doesn't work.
That still requires that he determine that I am too hard to predict, which either means solving the halting problem or running on a timer. Running on a timer is a legitimate answer, except again it means that there are some strategies I cannot execute.
I thought the assumption is that I am a perfect reasoner and can execute any strategy.
There's your answer.
I don't see how omega running his simulation on a timer makes any difference for this, but either way this is normal and expected. Problem resolved.
Not at all. Though it may be convenient to postulate arbitrarily large computing power (as long as Omega's power is increased to match) so that we can consider brute force algorithms instead of having to also worry about how to make it efficient.
(Actually, if you look at the decision tree for Newcomb's, the intended options for your strategy are clearly supposed to be "unconditionally one-box" and "unconditionally two-box", with potentially a mixed strategy allowed. Which is why you are provided wth no information whatsoever that would allow you to predict omega. And indeed the decision tree explicitly states that your state of knowledge is identical whether omega fills or doesn't fill the box.)
It's me who has to run on a timer. If I am only permitted to execute 1000 instructions to decide what my answer is, I may not be able to simulate Omega.
Yes, I am assuming that I am capable of executing arbitrarily many instructions when computing my strategy.
I know what problem Omega is trying to solve. If I am a perfect reasoner, and I know that Omega is, I should be able to predict Omega without actually having knowledge of Omega's internals.
Deciding which branch of the decision tree to pick is something I do using a process that has, as a step, simulating Omega. It is tempting to say "it doesn't matter what process you use to choose a branch of the decision tree, each branch has a value that can be compared independently of why you chose the branch", but that's not correct. In the original problem, if I just compare the branches without considering Omega's predictions, I should always two-box. If I consider Omega's predictions, that cuts off some branches in a way which changes the relative ranking of the choices. If I consider my predictions of Omega's predictions, that cuts off more branches, in a way which prevents the choices from even having a ranking.
Why would this be the assumption?
This contradicts the accuracy stated at the beginning. Omega can't leave both boxes empty for people who try to adopt a mixed strategy AND also maintain his 99.whatever accuracy on one-boxers.
And even if Omega has way more computational than I do, I can still generate a random number. I can flip a coin thats 60/40 one-box, two-box. The most accurate Omega can be, then, is to assume I one box.
He can maintain his 99% accuracy on deterministic one-boxers, which is all that matters for the hypothetical.
Alternatively, if we want to explicitly include mixed strategies as an available option, the general answer is that Omega fills the box with probability = the probability that your mixed strategy one-boxes.
All of this is very true, and I agree with it wholeheartedly. However, I think Jiro's second scenario is more interesting, because then predicting Omega is not needed; you can see what Omega's prediction was just by looking in (the now transparent) Box B.
As I argued in this comment, however, the scenario as it currently is is not well-specified; we need some idea of what sort of rule Omega is using to fill the boxes based on his prediction. I have not yet come up with a rule that would allow Omega to be consistent in such a scenario, though, and I'm not sure if consistency in this situation would even be possible for Omega. Any comments?
Previous discussions of Transparent Newcomb's problem have been well specified. I seem to recall doing so in footnotes so as to avoid distraction.
The problem (such as it is) is that there is ambiguity between the possible coherent specifications, not a complete lack. As your comment points out there are (merely) two possible situations for the player to be in and Omega is able to counter-factually predict the response to either of them, with said responses limited to a boolean. That's not a lot of permutations. You could specify all 4 exhaustively if you are lazy.
IF (Two box when empty AND One box when full) THEN X
IF ...
Any difficulty here is in choosing the set of rewards that most usefully illustrate the interesting aspects of the problem.
I'd say that about hits the nail on the head. The permutations certainly are exhaustively specifiable. The problem is that I'm not sure how to specify some of the branches. Here's all four possibilities (written in pseudo-code following your example):
The rewards for 1 and 2 seem obvious; I'm having trouble, however, imagining what the rewards for 3 and 4 should be. The original Newcomb's Problem had a simple point to demonstrate, namely that logical connections should be respected along with causal connections. This point was made simple by the fact that there's two choices, but only one situation. When discussing transparent Newcomb, though, it's hard to see how this point maps to the latter two situations in a useful and/or interesting way.
It may be the least convenient possible world. More specifically it is the minor inconvenience of being careful to specify the problem correctly so as not to be distracted. Nshepperd gives some of the reason typically used in such cases.
What happens when you try to pick the the opposite of what you predict Omega does is something like what happens when you try to beat Deep Fritz 14 at chess while outrunning a sports car. You just fail. Your brain is a few of pounds of fat approximately optimised for out-competing other primates for mating opportunities. Omega is a super-intelligence. The assumption that Omega is smarter than the player isn't an unreasonable one and is fundamental to the problem. Defying it is a particularly futile attempt to fight the hypothetical by basically ignoring it.
Generalising your proposed class to executing maximally inconvenient behaviours in response to, for example, the transparent Newcomb's problem is where it gets actually gets (tangentially) interesting. In that case you can be inconvenient without out-predicting the superintelligence and so the transparent Newcomb's problem requires more care with the if clause.
In the first scenario, I doubt you would be able to predict Omega with sufficient accuracy to be able to do what you're suggesting. Transparent boxes, though, are interesting. The problem is, the original Newcomb's Problem had a single situation with two possible choices involved; tranparent Newcomb, however, involves two situations:
It's unclear from this what Omega is even trying to predict; is he predicting your response to the first situation? The second one? Both? Is he following the rule: "If the player two-boxes in either situation, fill Box B with nothing"? Is he following the rule: "If the player one-boxes in either situation, fill Box B with $1000000"? The problem isn't well-specified; you'll have to give a better description of the situation before a response can be given.
That falls under 1) there are some strategies I am incapable of executing.
The transparent scenario is just a restatement of the opaque scenario with transparent boxes instead of "I predict what Omega does". If you think the transparent scenario involves two situations, then the opaque scenario involves two situations as well. (1=opaque box B contains $1000000, and I predict that Omega put in $1000000 and 2=opaque box B contains nothing, and I predict that Omega puts in nothing.) If you object that we have no reason to think both of those opaque situations are possible, I can make a similar objection to the transparent situations.