Re: poly: What probabilities?

Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
> When I say "The probability of H is 40%." I could mean to:
>
> 1. Say something about my personal subjective probability.
>
> 2. Say something about the common subjective probability relative to
> the present knowledge basis of humankind
>
> 3. Say something about the objective probability of the event.

> Depending on which sense of probability we have in mind, we might
> give very different numerical estimates. Consider the question: "What
> is the probability that nanotechnology will cause the extinction of
> earth-descendent intelligent life?"
>
> In sense 1, I might answer: "25%".
>
> In sense 2, I might say: "I don't know, but I would guess somewhere
> between 2% and 70%."
>
> In sense 3, I might say: "I don't know but I think it more probable
> that it is somewhere between 99.9% and 100% than that it is between
> 50% and 60%.

I don't understand why you give different answers for these
interpretations. It seems to me that they are different ways of stating
the same basic concept.

The one possible exception is case 2, where it sounds like you might be
referring to the probability that other people would assign to the event,
rather than the probability that you would assign to it. I personally
might believe an event to have 25% probability while the common person
would give it a 50% probability. However I suspect that is not what
you mean.

Looking at your examples, in case 1 you have given a specific value,
in case 2 you give a range, and in case 3 you hint at a probability
distribution over probabilities. Is that meant to be a general
distinguishing characteristic of your three interpretations? Would you
expect that interpretation 1 would always lead to a specific value,
interpretation 2 to a range, and interpretation 3 to a distribution over
probabilty ranges?

Couldn't your personal subjective probability be *defined* based on
the case 3 interpretation, where you imagine a set of possible worlds
which are consistent with your present knowledge, and you guess at
what percentage of them lead to the specified outcome? That seems to
be a reasonable way to understand the notion of uncertainty.

And isn't case 2 really just identifying the kind of information you
take into consideration in generating the probabilities you describe in
cases 1 and 3? Of course you will attempt to take into consideration
all the information available to you in making a probability judgement.
That will be a subset of the present knowledge of humankind, of course,
but surely you didn't literally mean that case 2 probabilites are based
on all of the information available, since no person can hold that much
information in his mind.

If you were just being philosophical and identifying different aspects
or ways we might think of probability, I'd let it go. But the fact
that you get different answers for the different approaches suggests
that there is some objective difference. In that case it would be
important to understand what sense of probability is being used in order
to interpret a statement of uncertainty.

Hal
Received on Mon Apr 27 16:38:13 1998