Is the objectivity of plausibility assignments assumed in the Jaynes-Cox formulation of probability theory?

This is what I mean by “the objectivity of plausibility assignments”:

and are propositions. is the plausibility of given that is true and is represented with a real number as a result of our desiderata. Is the quantity uniquely determined by and ?

If this is the case, is this one of the assumptions that we make (implicitly or explicitly) or can this be derived from our desiderata?

If not, then in what sense is the plausibility of given objective?

Thank you

Thanks!

Objective Bayesians say that “if two different people have the same information, B, then they will assign the same plausibility (A|B)”, right? If they didn’t say this, wouldn’t they just be subjective Bayesians?

So how is this possible without the plausibility (A|B) being uniquely determined by A and B?