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perpetualpeace1 comments on A question about Eliezer - Less Wrong Discussion
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If his decision theory had a solid theoretical background, but turned out to be terrible when actually implemented, how would we know? Has there been any empirical testing of his theory?
Permit me to substitute your question: TDT seems pretty neat philosophically, but can it actually be made to work as computer code?
Answer: Yes. (Sorry for the self-promotion, but I'm proud of myself for writing this up.) The only limiting factor right now is that nobody can program an efficient theorem-prover (or other equivalently powerful general reasoner), but that's not an issue with decision theory per se. (In other words, if we could implement Causal Decision Theory well, then we could implement Timeless Decision Theory well.) But in any case, we can prove theorems about how TDT would do if equipped with a good theorem-prover.
What does a decision theory that "has a solid theoretical background but turns out to be terrible" look like when implemented?
You play a game that you could either win or lose. One person follows, so far as he or she is able, the tenets of timeless decision theory. Another person makes a decision by flipping a coin. The coin-flipper outperforms the TDTer.
I'm pretty confident that if we played an iterated prisoners dilemma, your flipping a coin each time and my running TDT, I would win. This is, however, quite a low bar.
I took it as a statement of what would prove the theory false, rather than a statement of something believed likely.
I think that would only be true if there were more than 2 players. Won't random coin flip and TDT be tied in the two player case?
No. TDT, once it figures out it's facing a coin flipper, defects 100% of the time and runs away with it.
Nope, TDT will defect every time.
I'm not sure such a poor theory would survive having a solid theoretical background.
Actually, I think the proper case is "Two players play a one-player game they can either win or lose. One person follows, so far as able, the tenets of TDT. The other decides by flipping a coin. The coin-flipper outperforms the TDTer."
I mention this because lots of decision theories struggle against a coin flipping opponent: tit-for-tat is a strong IPD strategy that does poorly against a coin-flipper.
Is there any decision strategy that can do well (let's define "well" as "better than always-defect") against a coin-flipper in IPD? Any decision strategy more complex than always-defect requires the assumption that your opponent's decisions can be at least predicted, if not influenced.
No, of course not. Against any opponent whose output has nothing to do with your previous plays (or expected plays, if they get a peak at your logic), one should clearly always defect.
Not if their probability of cooperation is so high that the expected value of cooperation remains higher than that of defecting. Or if their plays can be predicted, which satisfies your criterion (nothing to do with my previous plays) but not mine.
If someone defects every third time with no deviation, then I should defect whenever they defect. If they defect randomly one time in sixteen, I should always cooperate. (of course, always-cooperate is not more complex than always-defect.)
...I swear, this made sense when I did the numbers earlier today.