Re: poly: What probabilities?

Hal asks:
>When dealing with an uncertain event, is there any more information to
>give once you have specified your best guess at the probability?

Yes, of course. For example, there are also your conditional
probabilities of the event given various other events.

>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%.
>
>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%?

It seems to me that the difference is just that in the first case you
can't imagine many conditions that would change your estimate, and in
the second case you can. If you find your estimate to be very senstive
conditioning on each new peice of information you consider when trying
to construct your estimate, you might want to guess at a distribution
over what your estimate will be if your thought about it for another
ten minutes. That is a legit probability over probabilities. Or you
might want to ask for bounds, for example, the 5% and 95% percentiles.

Similarly, you can ask what your estimate would be if you know what
other people's estimates would be, or something about what action
they're taking based on their estimate. This is the natural source
of the bid ask spreads in markets; one price is a market maker's estimate
conditional on someone offering to sell, and the other on someone offering
to buy.

Note that none of this requires any revision of the standard
probability picture.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Sun Apr 26 22:10:34 1998