**Next message:**Lee Corbin: "Re: Reversible Computation and Experience"**Previous message:**Lee Corbin: "Re: I disagree with Lee's answer"**In reply to:**Lee Corbin: "Re: I disagree with Lee's answer"**Next in thread:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Emlyn \(onetel\): "Re: I strongly disagree with Lee's answer"**Reply:**Lee Corbin: "Re: Fun with Bayes' Theorem"**Maybe reply:**Amara Graps: "Re: I strongly disagree with Lee's answer"**Maybe reply:**Jeff Davis: "Re: I strongly disagree with Lee's answer"**Maybe reply:**KPJ: "Re: I strongly disagree with Lee's answer"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Lee,

I don't think your word problems provide the necessary priors. To

estimate the probabilities, I would need to know the algorithms used by

each of the people making statements, and that information is not

provided.

For example, suppose that you're on a game show called "ExtroQuiz" and

there are three doors: A, B, and C. One door has a prize behind it. You

pick door C. The game show host opens up door A, and shows you that it's

empty. What is the probability that the prize is behind door B? Answer:

0%. Why? Because the game show host *knows* the standard answer to this

riddle, *knows* that most Extropians will switch to B, and he opens A *if

and only if* the prize is actually behind C.

The "mathematician's daughters" is a much worse instance of the problem.

If you know that the mathematician will say "At least one of my children

is a girl" for BG, GB, and GG, but say "At least one of my children is a

boy" only for BB, and the mathematician says "At least one of my children

is a girl", then the probability that the other child is a boy is 2/3. If

you know that the mathematician will say "At least one is a girl" for GG,

"At least one is a boy" for BB, and pick a statement at random for BG and

GB, then the probability that the other child is a boy is 1/2. I think

that most people unconsciously assume this kind of symmetry by default -

it seems, a priori, a more likely visualization of the underlying causes -

which is why most people return the allegedly "wrong" answer 1/2. To

assume otherwise requires that one assume the mathematician has an

inherent bias towards naming girls, which is an odd thing to assume about

someone. The above mixture of probabilities is exactly what results from

the mathematician picking one child at random and saying "At least one of

my children is an X", in which case the statement provides no information

about the second child. Most people unconsciously assume that's what the

mathematician did, in which case the given answer, 1/2, is exactly

correct.

I've *always* felt that riddle had a problem; now, twelve years later, I

finally get to articulate it.

(In Lee Corbin's question as stated, I expect that the mathematician

hypothesizes the father to be symmetrical, rather than hypothesizing that

the father exhibits a feminine bias, and answers 1/2.)

-- -- -- -- --

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

Research Fellow, Singularity Institute for Artificial Intelligence

**Next message:**Lee Corbin: "Re: Reversible Computation and Experience"**Previous message:**Lee Corbin: "Re: I disagree with Lee's answer"**In reply to:**Lee Corbin: "Re: I disagree with Lee's answer"**Next in thread:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Spike Jones: "Re: I strongly disagree with Lee's answer"**Reply:**Emlyn \(onetel\): "Re: I strongly disagree with Lee's answer"**Reply:**Lee Corbin: "Re: Fun with Bayes' Theorem"**Maybe reply:**Amara Graps: "Re: I strongly disagree with Lee's answer"**Maybe reply:**Jeff Davis: "Re: I strongly disagree with Lee's answer"**Maybe reply:**KPJ: "Re: I strongly disagree with Lee's answer"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b30
: Mon May 28 2001 - 10:00:04 MDT
*