Re: poly: What probabilities?

Hal Finney wrote:

> Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
> > In sense 2, I might say: "I don't know, but I would guess somewhere
> > between 2% and 70%."
>
> When dealing with an uncertain event, is there any more information to
> give once you have specified your best guess at the probability? Given
> the question above, where you are uncertain between 2% and 70%, suppose
> 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
> chance is 25%, and situations where you are uncertain, but the best
> guess is 25%?
>
> To describe the chances of a future event, does probability need
> error bars? Should we have to draw a normal-shaped curve showing the
> probability that we think a certain probability is correct? (And if so,
> does it stop there, or do we need to further qualify the probability
> that we give to the probabilities?)

Depends on which sense of 'probability' you are talking about.

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