Dmytry comments on Decision Theories: A Less Wrong Primer - Less Wrong
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See mine and orthonormal's comments on the PD on this post for my view of that.
The point I'm struggling to express is that I don't think we should worry about the thought experiment, because I have the feeling that Omega is somehow impossible. The suggestion is that Newcomb's problem makes a problem with CDT clearer. But I argue that Newcomb's problem makes the problem. The flaw is not with the decision theory, but with the concept of such a predictor. So you can't use CDT's "failure" in this circumstance as evidence that CDT is wrong.
Here's a related point: Omega will never put the money in the box. Smith act like a one-boxer. Omega predicts that Smith will one-box. So the million is put in the opaque box. Now Omega reasons as follows: "Wait though. Even if Smith is a one-boxer, now that I've fixed what will be in the boxes, Smith is better off two-boxing. Smith is smart enough to realise that two-boxing is dominant, once I can't causally affect the contents of the boxes." So Omega doesn't put the money in the box.
Would one-boxing ever be advantageous if Omega were reasoning like that? No. The point is Omega will always reason that two-boxing dominates once the contents are fixed. There seems to be something unstable about Omega's reasoning. I think this is related to why I feel Omega is impossible. (Though I'm not sure how the points interact exactly.)
Well, i can implement omega by scanning your brain and simulating you. The other 'non implementations' of omega, though, imo are best ignored entirely. You can't really blame a decision theory for failure if there's no sensible model of the world for it to use.
My decision theory, personally, allows me to ignore unknown and edit my expected utility formula in ad-hoc way if i'm sufficiently convinced that omega will work as described. I think that's practically useful because effective heuristics often have to be invented on spot without sufficient model of the world.
edit: albeit, if i was convinced that omega works as described, i'd be convinced that it has scanned my brain and is emulating my decision procedure, or is using time travel, or is deciding randomly then destroying the universes where it was wrong... with more time i can probably come up with other implementations, the common thing about the implementations though is that i should 1-box.
Provided my brain's choice isn't affected by quantum noise, otherwise I don't think you can. :-)
People with memory problems tend to repeat "spontaneous" interactions in essentially the same way, which is evidence that quantum noise doesn't usually sway choices.
Good point. Still, the brain's choice can be quite deterministic, if you give it enough thought - averaging out noise.