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

68 31 January 2008 07:36PM

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Comment author: 12 August 2010 09:30:16PM 0 points [-]

From what I understand, to be a "Rational Agent" in game theory means someone who maximises their utility function (and not the one you ascribe to them). To say Omega is rewarding irrational agents isn't necessarily fair, since payoffs aren't always about the money. Lottery tickets are a good example this.

What if my utility function says the worst outcome is living the rest of my life with regrets that I didn't one box? Then I can one box and still be a completely rational agent.

Comment author: 12 August 2010 09:36:35PM 9 points [-]

You're complicating the problem too much by bringing in issues like regret. Assume for sake of argument that Newcomb's problem is to maximize the amount of money you receive. Don't think about extraneous utility issues.

Comment author: 12 August 2010 09:56:12PM 2 points [-]

Fair point. There are too many hidden variables already without me explicitly adding more. If Newcomb's problem is to maximise money recieved (with no regard for what it seen as reasonable), the "Why ain't you rich argument seems like a fairly compelling one doesn't it? Winning the money is all that matters.

I just realised that all I've really done is paraphrase the original post. Curse you source monitoring error!

Comment author: 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.