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Nornagest comments on Decision Theories: A Less Wrong Primer - Less Wrong
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Comments (172)
There are a couple of things I find odd about this. First, it seems to be taken for granted that one-boxing is obviously better than two boxing, but I'm not sure that's right. J.M. Joyce has an argument (in his foundations of causal decision theory) that is supposed to convince you that two-boxing is the right solution. Importantly, he accepts that you might still wish you weren't a CDT (so that Omega predicted you would one-box). But, he says, in either case, once the boxes are in front of you, whether you are a CDT or a EDT, you should two-box! The dominance reasoning works in either case, once the prediction has been made and the boxes are in front of you.
But this leads me on to my second point. I'm not sure how much of a flaw Newcomb's problem is in a decision theory, given that it relies on the intervention of an alien that can accurately predict what you will do. Let's leave aside the general problem of predicting real agents' actions with that degree of accuracy. If you know that the prediction of your choice affects the success of your choices, I think that reflexivity or self reference simply makes the prediction meaningless. We're all used to self-reference being tricky, and I think in this case it just undermines the whole set up. That is, I don't see the force of the objection from Newcomb's problem, because I don't think it's a problem we could ever possibly face.
Here's an example of a related kind of "reflexivity makes prediction meaningless". Let's say Omega bets you $100 that she can predict what you will eat for breakfast. Once you accept this bet, you now try to think of something that you would never otherwise think to eat for breakfast, in order to win the bet. The fact that your actions and the prediction of your actions have been connected in this way by the bet makes your actions unpredictable.
Going on to the prisoner's dilemma. Again, I don't think that it's the job of decision theory to get "the right" result in PD. Again, the dominance reasoning seems impeccable to me. In fact, I'm tempted to say that I would want any future advanced decision theory to satisfy some form of this dominance principle: it's crazy to ever choice an act that is guaranteed to be worse. All you need to do to "fix" PD is to have the agent attach enough weight to the welfare of others. That's not a modification of the decision theory, that's a modification of the utility function.
Your actions have been determined in part by the bet that Omega has made with you - I do not see how that is supposed to make them unpredictable any more than adding any other variable would do so. Remember: You only appear to have free will from within the algorithm, you may decide to think of something you'd never otherwise think about but Omega is advanced enough to model you down to the most basic level - it can predict your more complex behaviours based upon the combination of far simpler rules. You cannot necessarily just decide to think of something random which would be required in order to be unpredictable.
Similarly, the whole question of whether you should choose to two box or one box is a bit iffy. Strictly speaking there's no SHOULD about it. You will one box or you will two box. The question phrased as a should question - as a choice - is meaningless unless you're treating choice as a high-level abstraction of lower level rules; and if you do that, then the difficult disappears - just as you don't ask a rock whether it should or shouldn't crush someone when it falls down a hill.
Meaningfully, we might ask whether it is preferable to be the type of person who two boxes or the type of person who one boxes. As it turns out it seems to be more preferable to one-box and make stinking great piles of dosh. And as it turns out I'm the sort of person who, holding a desire for filthy lucre, will do so.
It's really difficult to side step your intuitions - your illusion that you actually get a free choice here. And I think the phrasing of the problem and its answers themselves have a lot to do with that. I think if you think that people get a choice - and the mechanisms of Omega's prediction hinge upon you being strongly determined - then the question just ceases to make sense. And you've got to jettison one of the two; either Omega's prediction ability or your ability to make a choice in the sense conventionally meant.
Presented with this scenario, I'd come up with a scheme describing a table of as many different options as I could manage -- ideally a very large number, but the combinatorics would probably get unwieldy after a while -- and pull numbers from http://www.fourmilab.ch/hotbits/ to make a selection. I might still lose, but knowing (to some small p-value) that it's possible to predict radioactive decay would easily be worth $100.
Of course, that's the smartassed answer.
Well the smartarse response is that Omega's just plugged himself in on the other end of your hotbits request =p