Re: Fun With Bayes' Theorem

From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sun May 13 2001 - 18:27:30 MDT

Lee Corbin wrote:
>
> But aren't we talking about the entire set of parents who could
> truthfully say all this? Isn't it true that of all those parents,
> two out of three of them in reality have a boy too?

This is the fundamental fallacy.

What matters, from a Bayesian perspective, is not how many parents *could*
say this, but how many of them *do* say it. If half the parents have a
50% chance of saying this and half have a 100% chance of saying it, that's
different than if all the parents have a 100% chance of saying so - even
though, in both cases, all the parents "could" say it.

Out of all the parents who *could* say "At least one of my children is a
girl", 2/3 of them have a boy. Out of all the parents who *do* say "At
least one of my children is a girl", 1/2 of them have a boy.

-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence

This archive was generated by hypermail 2b30 : Mon May 28 2001 - 10:00:05 MDT