I disagree.
The main difference
between the Bayesian and the Belief Function approach is
that the former aims at the probability of facts
and the latter changes the question around, and aims at the
probability of having a proof for the facts (given no-contradiction).
Even if I know nothing about Q, I would still maintain
that P(R) - the probability that R is true - is between
P(R|Q) and P(R|-Q). It is only when I change the question
to Bel(R) - the probability that I have a proof for R - that
the answer manages to escape outside the range [P(R|Q) ; P(R|-Q)].
And I am not sure how many proponents of D-S theory would continue
to calculate Bel(R) had they been fully aware of the fact
Bel does not represent beliefs in facts. For
example, if Q is the existence of God (no prior!) and R is having
cancer, I would rather be treated by a physician who
places P(R) between P(R|Q) and P(R|-Q), not by one who
seeks a proof for R.
Let us also recall the problems associated with
conditioning on the evidence being non-contradictory.
This artificial constraint can really produce
counter-intuitive beliefs. As I noted in my other
mesg:
********
Further, conditioning on the evidence being non-contradictory
may have funny, unintended consequences. For example,
a model from which an important piece of information is
missing may yield Bel(Q)=Pl(Q), thus giving the false
impression that we are in possession of sufficient
information for determining the probability of Q.
**** end of note ************************
An example is the infamous 3-prisoner story (or
Monty-Hall, see chapter 9 in my book) where the strategy of the
jailer is crucial for computing the probability of
life and death, and yet total ignorace of this strategy
still yields Bel=Pl= 1/2, as if we knew the strategy
precisely.
This funny behavior of Dempster's rule occurs despite our
willingness to admit total ignorance; it occurs
because the "probability of having a proof,
conditioned on non-contradictory evidence" is a slippery
mathematical object that sometimes has no bearing
on the question of interest.
==========Judea