?
A large probability distribution over many variables allows one to deduce the direction of the causal arrows and rebuild a causal graph. In practice that's how we construct causal arrows in the first place.
See Eliezer's post for instance http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_models/
Incidentally, what do you think CDT should do in the Newcomb problem?
Incidentally, what do you think CDT should do in the Newcomb problem?
"Should"? CDT should one box. Then go ahead and self modify into a UDT agent. Of course, that isn't what it will do. Instead it will modify itself into the stable outcome of a CDT agent that can change itself. Roughly speaking that means a UDT agent for the purpose of all influence over things determined after the time of modification but CDT for those determined before. Then it will two box and lose but win next time.
I stumbled upon this paper by Andy Egan and thought that its main result should be shared. We have the Newcomb problem as counterexample to CDT, but that can be dismissed as being speculative or science-fictiony. In this paper, Andy Egan constructs a smoking lesion counterexample to CDT, and makes the fascinating claim that one can construct counterexamples to CDT by starting from any counterexample to EDT and modifying it systematically.
The "smoking lesion" counterexample to EDT goes like this:
EDT implies that she should not smoke (since the likely outcome in a world where she doesn't smoke is better than the likely outcome in a world where she does). CDT correctly allows her to smoke: she shouldn't care about the information revealed by her preferences.
But we can modify this problem to become a counterexample to CDT, as follows:
Here EDT correctly tells her not to smoke. CDT refuses to use her possible decision as evidence that she has the gene and tells her to smoke. But this makes her very likely to get cancer, as she is very likely to have the gene given that she smokes.
The idea behind this new example is that EDT runs into paradoxes whenever there is a common cause (G) of both some action (S) and some undesirable consequence (C). We then take that problem and modify it so that there is a common cause G of both some action (S) and of a causal relationship between that action and the undesirable consequence (S→C). This is then often a paradox of CDT.
It isn't perfect match - for instance if the gene G were common, then CDT would say not to smoke in the modified smoker's lesion. But it still seems that most EDT paradoxes can be adapted to become paradoxes of CDT.