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Manfred comments on Is causal decision theory plus self-modification enough? - Less Wrong
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I agree - at least if this CDT agent has the foresight to self-modify before getting "scanned" by Omega (or put through a lie detector test, which is a statistically significant implementation of the same idea).
The question is then, if our self-modifying agent foresees running into a variety of problems where other agents will be able to predict its actions, what decision theory should it self-modify to?
Could you have a CDT agent that's never thought about Newcomb problems, out for a stroll, then Omega appears and explains the situation, and then the CDT agent reasons its way to one-boxing anyway? Maybe, AIXI-style, it does an exhaustive investigation of the payoffs resulting from various actions, it notices that changing itself into a one-boxer is correlated with a higher payoff, and so it performs the act!
It wouldn't work as you've stated it. The action of changing itself to a one-boxer would, according to its current decision theory, increase payoffs for every Newcomb's Problem it would encounter from that moment forward, but not for any in which the Predictor had already made its decision.
Seriously, you can work this out for yourself.
What confuses me here is that a causal model of reality would still tell it that being a one-boxer now will maximize the payoff now, if it examines possible worlds in the right way. It seems to come down to cognitive contingencies - whether its heuristics manage to generate this observation, without it then being countered by a "can't-change-the-past" heuristic.
I may need to examine the decision-theory literature to see what I can reasonably call a "CDT agent", especially Gibbard & Harper, where the distinction with evidential decision theory is apparently defined.
That's the main difference between decision theories like CDT, TDT and UDT.
I think it's the only difference between CDT and TDT: TDT gets a semi-correct causal graph, CDT doesn't. (Only semi-correct because the way Eliezer deals with Platonic nodes, i.e. straightforward Bayesian updating, doesn't seem likely to work in general. This is where UDT seems better than TDT.)
What is this "correlated" you speak of? :P I think if Omega pops up with already-filled boxes, the standard argument for two-boxing goes through whether the CDT agent is self-modifying or not.