FAWS comments on Raising the forecasting waterline (part 1) - Less Wrong

33 Post author: Morendil 09 October 2012 03:49PM

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Comment author: FAWS 10 October 2012 10:56:54AM 1 point [-]

I disagree with this. The reason you shouldn't assign 50% to the proposition "I will win the lottery" is because you have some understanding of the odds behind the lottery. If a yes/no question which I have no idea about is asked, I am 50% confident that the answer is yes. The reason for this is point 2: provided I think a question and its negation are equally likely to have been asked, there is a 50% chance that the answer to the question you have asked is yes.

That's only reasonable if some agent is trying to maximize the information content of your answer. The vast majority of possible statements of a given length are false.

Comment author: ArisKatsaris 10 October 2012 11:25:04AM 0 points [-]

The vast majority of possible statements of a given length are false.

That's surely an artifice of human languages and even so it would depend on whether the statement is mostly structured using "or" or using "and".

There's a 1-to-1 mapping between true and false statements (just add 'the following is false:' in front of each statement to get the opposite). In a language where 'the following is false' is assumed, the reverse would be actual.

Comment author: FAWS 10 October 2012 12:45:19PM *  -1 points [-]

That's surely an artifice of human languages and even so it would depend on whether the statement is mostly structured using "or" or using "and".

It's true of any language optimized for conveying information. The information content of a statement is reciprocal to it's prior probability, and therefore more or less proportional to how many other statements of the same form would be false.

In your counter example the information content of a statement in the basic form decreases with length.

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