Does there exist uniqueness ( of representation) theorems for dempster schafer and or other weaker formalisms of which the probability measure is a subclass? (presumably it would have to be at least a dempster schafer function, or something stronger, not a mere plausibility measure)
. Ie, for example if there is one, could one build a better justification for probabilism . First by deriving something like Scotts axiom for a strong representation of your qualitative probability ordering, thus guaranteeing the existence of said canonical probability function (which is a also a belief function and representation theirof), and then derive a "strong?"dempter schafer uniqueness theorem, or some kind of plausibility measure uniqueness theorem, which would mean that given there is only one belief function it has to be a probability function (and unique), which means that one only needs to presume that the dempster schafer axioms holds, to get out probabilism.
One can always prove a representation theorem for probabilism, but this is just a necessary condition for probabilism, as there generally always exists (even given the first two probability axioms) a non additive (non probability function) that respect the same ordering; it just shows you that there exists one amongst those which does satisfy addivity (and so one is still presuming probabilism to some degree) in making that claim that these relations must satisfy the probability calculus; ie from going to 'possible' to 'must'). But if one can do the above, it would mean that given whatever your system is, whilst it still only a 'possibility result', one must be assumed to get the 'must' given the representation theorem is a lot weaker.
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