Eliezer wrote:
>> But why are the parents who *do* say "At least..."
>> different than the parents who *could* say it?
>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.
But the people who do jump really are wildly different
from those who can. Don't confuse me with bad examples :-)
>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.
But problems that almost everyone gets right just aren't
much fun. As my topology professor used to say, "you
can't really learn anything until you get confused".
>> What situations do you have in mind where
>>
>> > Out of all the parents who *do* say "At least one
>> > of my children is a girl", 1/2 of them have a boy.
>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".
Choose at random? Here, I suspect, is where Bayesianism comes in.
The B statisticians are happy to assume certain priors when there
is no evidence for them. Now, I've always liked that, and feel
that in many cases it is justified, because it enables them to
give answers to questions that others shy away from (complaining
of insufficient data, etc.).
But in some cases, like this, they start reading into situations
protocols that aren't needed to answer the question. In this case,
as you say, they demand a "do" (and then have to conjure up what
could reasonably cause the "do"). Staying with *could*, on the
other hand---which mathematicians apparently are more prone to
do---obviates further assumptions. One simply considers sets
and subsets, and so on, and defines probability accordingly.
Lee
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