These misperceptions were strongly associated with perceived personal probability
of becoming infected while using public transportation.
On one meaning, logical omniscience requires that the personal probability function of the ideally rational Bayesian agent assign a probability to all of the propositions that can be formulated within her language.
However, the ideally rational Bayesian agent cannot add any hypotheses to the set of hypotheses covered by her personal probability function.
In order to be coherent with the axioms of the probability calculus the personal probability functions of ideally rational Bayesian agents must understand completely the logical structure of the propositions over which they are defined.
The conclusion seems inescapable that statements about chances reduce to being merely statements of personal probability
Given this H and thi E, the prior personal probability of H, given E, is one, since the randomizatio ensures that the probability of E is zero on any hypothesis other than H.
When we infer probabilities from sample statistics, a non-random sample and a random sample can yield just the same conditional personal probability for statistic E given the H under investigation, and so can underpin just the same statistical inference.