Joe Halpern wrote:
Judea's probability of provability is one, but only one
among several. Another one is Philippe's TBM. Yet another is belief
functions as lower envelopes of families of probability ..
Joe,
I will be the first to buy your "thousand-flower" model
as soon as I find two flowers blooming. So far, I have found only one.
1. TBM is still waiting for canonical example
to convince us that one need to quantify the 'strength
of ones opinion", and in a TBM-specific way.
2. The "lower envelop" picture does not work --
and I believe you and Fagin showed it -- as soon
as we start conditioning on some evidence, the
envelop ceases to be a belief-function.
3. Belief as evidence ? same as TBM; waiting for canonical example
(and I read your paper) where it is clear that what we
need to quantify is the "evidence for a proposition",
rather than the strength of one's belief in a proposition.
So far we have one flower and two contending linguistic expressions:
"strength of opinion" and "belief as evidence",
and with this ammunition we need to convince Kathy that
sometimes it is important
to compute BF rather than probabilities.
Recall, Kathy does not fall for just fancy expressions,
she requested a SITUATION with compelling REASON why it is
CORRECT to compute one quantity and INCORRECT to compute
another.
Give me two, and I will buy the thousand.
=========Judea
