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Lee Corbin wrote:

*>
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*> Eliezer Yudkowsky wrote:
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*>
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*> > Out of all the parents who *could* say "At least one of my children is a
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*> > girl", 2/3 of them have a boy. Out of all the parents who *do* say "At
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*> > least one of my children is a girl", 1/2 of them have a boy.
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*>
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*> I am sufficiently innocent of Bayesian statistics that I have to
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*> admit that anything is possible; if you're right, then there is
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*> a demarcation between what mathematicians would or should say,
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*> and what statisticians could or do say. :-)
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(Vorlon voice:) "We are all Bayesian statisticians."

*> But why are the parents who *do* say "At least..." different than
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*> the parents who *could* say it?
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For the same reason that the set of people who can jump off buildings is

different from the set of people who do jump off buildings. I deny that

the distinction between "mathematician" and "statistician" is the right

one to make here. The mathematician is not being confronted with the fact

that a person *could* say something but the fact that the person *did* say

something. Now, if the mathematician were to ask the father "Is at least

one of your children a girl?" and the father answered "Yes", that would be

an *entirely different* matter. In fact, I bet that if you presented the

riddle this way, a much larger percentage of the reasoners would get it

right the first time.

Hey, I just made a testable prediction! Anyone want to try it? Robin?

*> The earlier idea, who *could* truthfully
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*> say what, seems much easier to grasp. As for what people do say, this
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*> would seem to me to depend a great deal upon the particular situation.
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*> One easily contrives a situation where even under *do* I'm right: King
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*> Harod orders everybody who could say it to go to a mathematician and
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*> actually say it, etc.
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Yes, that's why I said that the riddle does not adequately specify the

priors.

*> What situations do you have in mind where
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*>
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*> > Out of all the parents who *do* say "At least one of
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*> > my children is a girl", 1/2 of them have a boy.
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Situations where those parents who have both a boy and a girl will choose

at random whether to say "At least one of my children is a boy" or "at

least one of my children is a girl".

-- -- -- -- --

Eliezer S. Yudkowsky http://singinst.org/

Research Fellow, Singularity Institute for Artificial Intelligence

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