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orthonormal comments on Decision Theories: A Less Wrong Primer - Less Wrong
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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.
It's not always cooperating- that would be dumb. The claim is that there can be improvements on what a CDT algorithm can achieve: TDT or UDT still defects against an opponent that always defects or always cooperates, but achieves (C,C) in some situations where CDT gets (D,D). The dominance reasoning is only impeccable if agents' decisions really are independent, just like certain theorems in probability only hold when the random variables are independent. (And yes, this is a precisely analogous meaning of "independent".)
Aha. So when agents' actions are probabilistically independent, only then does the dominance reasoning kick in?
So the causal decision theorist will say that the dominance reasoning is applicable whenever the agents' actions are causally independent. So do these other decision theories deny this? That is, do they claim that the dominance reasoning can be unsound even when my choice doesn't causally impact the choice of the other?
That's one valid way of looking at the distinction.
CDT allows the causal link from its current move in chess to its opponent's next move, so it doesn't view the two as independent.
In Newcomb's Problem, traditional CDT doesn't allow a causal link from its decision now to Omega's action before, so it applies the independence assumption to conclude that two-boxing is the dominant strategy. Ditto with playing PD against its clone.
(Come to think of it, it's basically a Markov chain formalism.)
So these alternative decision theories have relations of dependence going back in time? Are they sort of couterfactual dependences like "If I were to one-box, Omega would have put the million in the box"? That just sounds like the Evidentialist "news value" account. So it must be some other kind of relation of dependence going backwards in time that rules out the dominance reasoning. I guess I need "Other Decision Theories: A Less Wrong Primer".