cupholder comments on Outside the Laboratory - Less Wrong

63 Post author: Eliezer_Yudkowsky 21 January 2007 03:46AM

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Comment author: JoshuaZ 12 July 2010 03:15:18PM 0 points [-]

Perhaps I should bring up a point about probabilistic reasoning here. If you believe that a proposition is true with probability 1, then you cannot rationally change your belief away from probability 1. This is a consequence of Bayes' theorem. So really, nobody believes any empirical fact with a probability of 1 or 0.

The last sentence shouldn't be "nobody" but "no Bayesian rationalist."

Comment deleted 12 July 2010 04:00:42PM [-]
Comment author: cupholder 17 July 2010 07:07:51AM *  3 points [-]

what interpretation of the word "probability" does allow you to think that the probability of something is 1 and then change to something other than 1?

Any interpretation where you can fix a broken model. I can imagine a conversation like this...

Prankster: I'm holding a die behind my back. If I roll it, what probability would you assign to a 1 coming up?

cupholder: Is it loaded?

Prankster: No.

cupholder: Are you throwing it in a funny way, like in one of those machines that throws it so it's really likely to come up a 6 or something?

Prankster: No, no funny tricks here. Just rolling it normally.

cupholder: Then you've got a 1/6 probability of rolling a 1.

Prankster: And what about rolling a 2?

cupholder: Well, the same.

Prankster: And so on for all the other numbers, right?

cupholder: Sure.

Prankster: So you assign a probability of 1 to a number between 1 and 6 coming up?

cupholder: Yeah.

Prankster: Surprise! It's 20-sided!

cupholder: Huh. I'd better change my estimate from 1 to 6/20.

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