A smooth model of decision making under ambiguity

We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if E_μφ(E_π(u ◦ f) ≥ E_μφ(E_π(u ◦ g), where E is the expectation operator, u is a von Neumann–Morgenstern utility function, φ is an increasing transformation, and μ is a subjective probability over the set Π of probability measures π that the decision maker thinks are relevant given his subjective information