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Nornagest comments on Newcomb's Problem and Regret of Rationality - Less Wrong

68 Post author: Eliezer_Yudkowsky 31 January 2008 07:36PM

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Comment author: Nornagest 19 November 2010 01:32:15AM *  3 points [-]

Lottery tickets exploit a completely different failure of rationality, that being our difficulties with small probabilities and big numbers, and our problems dealing with scale more generally. (ETA: The fantasies commonly cited in the context of lotteries' "true value" are a symptom of this failure.) It's not hard to come up with a game-theoretic agent that maximizes its payoffs against that kind of math. Second-guessing other agents' models is considerably harder.

I haven't given much thought to this particular problem for a while, but my impression is that Newcomb exposes an exploit in simpler decision theories that's related to that kind of recursive modeling: naively, if you trust Omega's judgment of your psychology, you pick the one-box option, and if you don't, you pick up both boxes. Omega's track record gives us an excellent reason to trust its judgment from a probabilistic perspective, but it's trickier to come up with an algorithm that stabilizes on that solution without immediately trying to outdo itself.