> Probabilities may be *derived* from properties of the world, given a
> particular state of knowledge. But there is still a dependence on that
> state of knowledge. .....
Must be quick for reasons given yesterday. I'm not too sure if there is thatmuch disagreement between us - it is
certainly very useful _for_me_ having this
discussion.
The above is what I meant by an indirect measure.
The interesting thing (to me) is that given the same state of knowledge
about a situation, there can (often) be a high degree of consistency in
people's estimates of a probability/subjective measures of belief.
In situations where that is the case, the role of the subject becomes
less important - whichever subject you choose to ask for a probability,
their answers will be very similar.
This suggests to me that the representation condition for probability as
a measure of (call it for the moment) propensity is satisfied _provided_
you have agreement on the situation you are being asked about.
That is; give all the background information:
Rockwool is a man-made fibre and should be handled with care;
The bag of balls is shaken before sampling but otherwise the numbers are known
as per yesterday's mail;
Tossing a coin with two sides, checked to have evenly distributed density.
and so forth...
You should get empirical agreement on the relation (don't ask for numbers
at this stage, just ask if the probability of one situation is less than another):
p(Paul changes from potting in bark to potting in rockwool)
is lower than
p(Paul picks a red)
is lower than
p(Paul tosses a head)
This relation is mirrored by the numerical relations obtained when values are actually
assigned to these probabilities.
There then seems to be some coherence in using this thing called probability
as a measure of a (rather abstract) property (which I provisionally call) propensity.
_But_ I can't touch or feel propensity (although it can often impact on me!)
so it is rather difficult to say for sure where it resides (in my mind or as a property
of a carefully specified situation).
As mentioned, I have to drop out now for a couple of weeks. So lack of further
response is not thru' lack of interest from me. (Although I'm still not sure if it is
of interest to UAI mailist, I emphasise that these comments from you are
very helpful to me).
Best
Paul
-- ====================================================== Paul J. Krause Philips Research Laboratories Crossoak Lane Redhill, Surrey RH1 5HA United Kingdom Tel: +44 (0)1293 815298 Fax: +44 (0)1293 815500 mailto:krause@prl.research.philips.com =======================================================