However, my initial thought is that it may require/assume logical omnicience.

Probably. Bayes is also easier to work with if you assume logical omniscience (i.e. knowledge of P(evidence|X) and P(E|~X)).

Also, I'm unclear, could you clarify what it is you'd be using a multiset for? Do you mean "increase measure only by increasing number of copies of this in the multiset, and no other means allowed" or did you intend something else?

Yes, using multisets of worlds with identical measure is equivalent to (for rational measures only) but 'more frequentist' than sets of worlds with variable measure.

incidentally, I think I do prefer coherence/dutch book/vulnerability style constructions of epistemic probability. Especially the ones that build up decision theory along the way, so one ends up starting with utilities almost. Such have very much of a "mathematical karma" flavor, as I've expressed elsewhere.

Yeah, my idea was only meant as an existence proof and is probably an inferior formal construction, although it is how I tend to personally think about subjective probability. I guess at heart I'm still a frequentist.

(You could think about Rolf's problem this way; if the vast majority of the measure of possible worlds given Bob's knowledge is in worlds where he loses, he's objectively wrong.)

## Comments (190)

OldHowever, my initial thought is that it may require/assume logical omnicience.Probably. Bayes is also easier to work with if you assume logical omniscience (i.e. knowledge of P(evidence|X) and P(E|~X)).

Also, I'm unclear, could you clarify what it is you'd be using a multiset for? Do you mean "increase measure only by increasing number of copies of this in the multiset, and no other means allowed" or did you intend something else?Yes, using multisets of worlds with identical measure is equivalent to (for rational measures only) but 'more frequentist' than sets of worlds with variable measure.

incidentally, I think I do prefer coherence/dutch book/vulnerability style constructions of epistemic probability. Especially the ones that build up decision theory along the way, so one ends up starting with utilities almost. Such have very much of a "mathematical karma" flavor, as I've expressed elsewhere.Yeah, my idea was only meant as an existence proof and is probably an inferior formal construction, although it is how I tend to personally think about subjective probability. I guess at heart I'm still a frequentist.

(You could think about Rolf's problem this way; if the vast majority of the measure of possible worlds given Bob's knowledge is in worlds where he loses, he's objectively wrong.)