We investigate the classical Anscombe–Aumann model of decision‐making under uncertainty without the completeness axiom. We distinguish between the dual traits of “indecisiveness in beliefs” and “indecisiveness in tastes.” The former is captured by the Knightian uncertainty model, the latter by the single‐prior expected multi‐utility model. We characterize axiomatically the latter model. Then we show that, under independence and continuity, these two models can be jointly characterized by means of a partial completeness property.