Subjective probability, confidence, and Bayesian updating

I define subjective probabilities for an ambiguity averse agent who is given an exogenous information set $$\varDelta $$ Δ containing the true probability law on the state space S. The agent in my model evaluates every uncertain prospect via a mixture of the least favorable scenario in $$\varDelta $$ Δ and her unique subjective belief p. This parametric utility structure is characterized by four standard axioms—order, continuity, monotonicity, and Independence—where the last two conditions are modified via the information set $$\varDelta $$ Δ . Any pair of preferences $$\succeq _1$$ ⪰ 1 and $$\succeq _2$$ ⪰ 2 in my model can be compared in terms of confidence—the weights attached to the subjective beliefs $$p_1$$ p 1 and $$p_2$$ p 2 , respectively. The corresponding behavioral condition extends Epstein’s comparative ambiguity aversion that leaves some rankings $$\succeq _1$$ ⪰ 1 and $$\succeq _2$$ ⪰ 2 unrelated. Moreover, I relax the well-known dynamic consistency principle and characterize the Bayesian updating rule for the belief p conditional on any non-null event in S.