Smooth aggregation of Bayesian experts

I study the ex-ante aggregation of preferences of Bayesian agents in a purely subjective framework. I relax the assumption of a Bayesian social preference while keeping the Pareto condition. Under a simple axiom that relates society's preference to those of the agents, I obtain an additively separable representation of society's preference. Adding an ambiguity aversion axiom I obtain a representation that resembles the Smooth Ambiguity Criterion of Klibanoff et al. (2005). I then briefly consider applications of this framework to inequality and treatment choice under ambiguity.