Subjective probability, confidence, and Bayesian updating

I derive a unique subjective probabilistic belief p and Bayesian updating for this belief from ambiguity averse preferences. To do so, I assume an exogenous information set ∆ of possible probabilistic scenarios on the state space S. Every uncertain prospect f is evaluated via a mixture of the unique subjective belief p with the least favorable scenario for f in the set ∆. The weight of p in this mixture is also unique and reflects a degree of subjective confidence in p. I use the well-known axioms—order, continuity, monotonicity, and Independence—with the last two conditions adjusted for the exogenous ambiguity in the set ∆. Bayesian updating for the belief p contingent on any non-null event E is derived from a weak version of dynamic consistency.