From: David McFadzean (david@lucifer.com)
Date: Wed Nov 26 2003 - 18:27:59 MST
rhinoceros wrote:
> [Lucifer]
> I would estimate a probability distribution for the balance in the
> account given whatever information I have available (like how this
> person is dressed, how they speak, where we are, etc). Then I would
> find the amount that maximizes the expected return (amount *
> probability). Finding out the balance after I wrote the check would
> not change my answer.
>
>
> [rhinoceros]
> This is a good approach if you can really translate these things into
> a numerical probability distribution. What does the last sentence
> mean? Wouldn't the exact sum be the best answer if you knew it?
[Lucifer]
The more time and information I have to make a good estimate of the
probability curve, the better my answer will be (in terms of decision,
not necessarily in terms of outcome, the distinction is subtle but
all important for decision theory). I made a couple clarifications
for Raven after I posted this. First, the estimated curve represents
the probability that any given value is less than the balance of the
bank account. This means the curve is monotonically decreasing and
a bit easier to estimate. The second point Raven brought up is that
I should take into account the utility of the money, rather than the
face value of the money. For example 1 billion dollars is not (necessarily)
worth 1000 times as much as 1 million dollars to me at this time.
Yes, if I knew the exact sum in advance that would make it easy but
the question was different: would knowing that I would find out the
exact sum after I choose change my choice? I wouldn't want to know
(it would always be bad news unless I lucked out and guessed the exact
amount) but it wouldn't change my answer in any case.
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