From: Nick Bostrom <bostrom@ndirect.co.uk>

Date: Sun Apr 26 1998 - 17:42:28 PDT

Date: Sun Apr 26 1998 - 17:42:28 PDT

Hal Finney wrote:

*> Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
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*> > In sense 2, I might say: "I don't know, but I would guess somewhere
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*> > between 2% and 70%."
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*>
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*> When dealing with an uncertain event, is there any more information to
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*> give once you have specified your best guess at the probability? Given
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*> the question above, where you are uncertain between 2% and 70%, suppose
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*> that if you were forced to pin it down you would say 25%.
*

Notice that I didn't give an interval estimate as an illustration of

probability in sense 1, my own subjective probability. It seems

unproblematic that I could be uncertain what the probability is in

sense 2, since that was the subjective probability relative the

totality of mankind's knowledge.

I think I can even imagine a natural interpretation of a probability

interval in sense 1 though. You have presumably experienced how

difficult it can be to give a number when somebody asks you how

probable you think a certain event is. Now, when you answer "Between

20% and 40%." you could mean: I now think that if I were to reflect

on the matter for a long time (but wouldn't get any new information),

I would settle on a probability somewhere between 20% and 40%.

*> Is there a difference between situations where you are "certain" the
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*> chance is 25%, and situations where you are uncertain, but the best
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*> guess is 25%?
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*>
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*> To describe the chances of a future event, does probability need
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*> error bars? Should we have to draw a normal-shaped curve showing the
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*> probability that we think a certain probability is correct? (And if so,
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*> does it stop there, or do we need to further qualify the probability
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*> that we give to the probabilities?)
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Depends on which sense of 'probability' you are talking about.

*> This question has come up on the FX (idea futures) game, where people
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*> are betting on the probability of future events. Is it significant
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*> whether there is a strong market consensus that a certain probability
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*> is about right, versus a claim where there is a broader range of
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*> values which have support?
*

I'm not sure exactly what you mean. Physicists believe in the

probabilities given by quantum mechanics. This is clearly different

from a situation where the weighted average of their beliefs would

give the same number, but each believed in a different theory.

_____________________________________________________

Nick Bostrom

Department of Philosophy, Logic and Scientific Method

London School of Economics

n.bostrom@lse.ac.uk

http://www.hedweb.com/nickb

Received on Sun Apr 26 23:48:19 1998

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