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Eliezer_Yudkowsky comments on Harry Potter and the Methods of Rationality discussion thread, part 25, chapter 96 - Less Wrong Discussion

6 Post author: NancyLebovitz 25 July 2013 04:36AM

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Comment author: BT_Uytya 25 July 2013 05:41:59PM *  2 points [-]

You are talking about prior probability. P(Dark Lord is Death|no specific background information) roughly equals to P(Eliezer changes things from canon), which isn't very large; so after updating both with a equally favorable piece of evidence "Death is Dark Lord" is still behind "Voldemort is Dark Lord".

You can assign prior probabilities in various ways, and one of them is giving every hypothesis an appropriate complexity penalty (or you can just judge everything as equally likely, or give everything a simplicity penalty, or penalize every hypothesis according to how many people it affects, or...). Some ways are better than others, but:

1) Why "complexity penalty" should work in fiction, even in a rationalist fiction?

2) Why hypothesis "Voldemort is Dark Lord" is simpler than "Death is Dark Lord" in the sense of program length? One can argue that the former hypothesis points to the specific human from a pool of a 6 billion people (or 100 billion, if you want to consider every human ever lived) while the latter talks about some entity likely to be very basic from the Magic viewpoint.

Hope that clears some of confusion!

Comment author: Eliezer_Yudkowsky 25 July 2013 06:50:04PM 12 points [-]

1) Why "complexity penalty" should work in fiction, even in a rationalist fiction?

Because there will still be an infinite (countable) number of finite hypotheses which could be considered and only a finite amount of probability to divide among them, which necessarily implies that in the limit more complicated hypotheses will have individual probability approaching zero. This will be true in the limit even if you define 'complexity' differently than the person who constructed the distribution.

Comment author: ThisSpaceAvailable 27 July 2013 09:59:06PM *  2 points [-]

Is "A or B" more "complex" than "A"? It seems to me that it generally takes more bits to say "A or B", but the prior for "A" should be smaller than for "A or B". Is there something in the "assign prior according to complexity" heuristic that accounts for that?