gjm comments on Rationality is Systematized Winning - Less Wrong

48 Post author: Eliezer_Yudkowsky 03 April 2009 02:41PM

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Comment author: gjm 03 April 2009 11:45:01PM 3 points [-]

What is it, pray tell, that Omega cannot do?

Well, for instance, he cannot make 1+1=3. And, if one defines rationality as actually winning then he cannot act in such a way that rational people lose. This is perfectly obvious; and, in case you have misunderstood what I wrote (as it looks like you have), that is the only thing I said that Omega cannot do.

In the discussion of strategy S, my claim was not about what Omega can do but about what you (a person attempting to implement such a strategy) can consistently include in your model of the universe. If you are an S-rational agent, then Omega may decide to screw you over, in which case you lose; that's OK (as far as the notion of rationality goes; it's too bad for you) because S doesn't purport to guarantee that you don't lose.

What S does purport to do is to arrange that, in so far as the universe obeys your (incomplete, probabilistic, ...) model of it, you win on average. Omega's malfeasance is only a problem for this if it's included in your model. Which it can't be. Hence:

what your example shows [...] is that you can't consistently expect Omega to act in a way that falsifies your beliefs and/or invalidates your strategies for acting.

(Actually, I think that's not quite right. You could probably consistently expect that, provided your expectations about how he's going to to it were vague enough.)

I did not claim, nor do I believe, that a regular person can compute a perfectly rational strategy in the sense I described. Nor do I believe that a regular person can play chess without making any mistakes. None the less, there is such a thing as playing chess well; and there is such a thing as being (imperfectly, but better than one might be) rational. Even with a definition of the sort Eliezer likes.