From: gts (gts_2000@yahoo.com)
Date: Wed Apr 30 2003 - 07:02:01 MDT
Ramez Naam wrote:
> As far as this example goes, I would guess that I was wearing
> a green hat if I had no other information whatsoever, but I
> would recognize that it was an extremely weak guess.
>
> Why? Because the distribution of hats is probably not
> random. It depends on the behavior of the person handing
> them out. That person may be giving yellow hats to all the
> bald men, and green hats to everyone else, or using any other
> criteria.
Actually, given that you have no knowledge of any such non-random rules the
hat-giver might be following, your best guess is still green and for the
same reasons I outlined in my last message. It is in your best interest to
assume the hats are distributed randomly, even if you suspect they are not.
Any deviation from the SSA would tend to weaken your guess.
For example if you are bald, and you have a hunch that bald guys tend to get
yellow hats, then you would weaken your guess by guessing yellow (unless of
course your hunch was based on solid evidence, but it isn't).
> If I knew that the person handing out the hats was
> really doing so randomly, then green would be a stronger
> guess. But until I know what the distribution pattern is,
> all of my guesses are weak.
Not at all. You know only that 90% of the hats are green. Given that you
must make a guess with your limited knowledge, your best guess is that you
are wearing a green hat. It's your strongest guess, regardless of the
distribution. To put this another way, any unknown non-random distribution
is as likely to favor green hats for you as it is to favor yellow hats for
you.
-gts
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