Re: poly: What probabilities?

Hal F. writes:
>> Note that none of this requires any revision of the standard
>> probability picture.
>
>In the standard mathematical theory of probability, probability is defined
>as a measure function over a set of disjoint outcomes, such that the sum
>of the measures of all the outcomes is 1. Can the idea of "probability
>of probability" be formalized? Do all probabilities have a probability?
>... I am still not completely comfortable with these second order
>probabilities. It makes me wonder why we stop there.

You're assuming you have to add some structure over regular probabilities (P)
to get probabilities over probabilities (P on P). You don't. Any probability
distribution over states that describe other agents already implicitly includes
such P on P, as well as P on P on P on P ... to any order you like. Yourself
ten minutes from now counts as another agent. Game theorists have formally
described the infinite heirarchy of my P of your P of my P ,etc. and it's
all equivalent to a single standard P.

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 Mon Apr 27 16:14:51 1998