In elaborationg upon the recent thought-provoking paper\Subjective probability in behavioral economics and _nance: A radical reformulation" by H. Joel Jeffrey and Anthony O. Putman [5], we proceed to specify the calculus of their \probability (uncertainty) appraisals" as possiblity measures, i.e., the \radical" reformulation of the usual calculus of subjective probabilities is that of idempotent uncertainty. With possibility measures as quantitative uncertainty for subjective probabilities, we discuss the necessary mariage of possibility measures and Kolmogorov probability measures in a new Bayesian analysis for economic applications.