Facing several decisions, people may consider each one in isolation or integrate them into a single optimization problem. Isolation and integration may yield different choices, for instance, if uncertainty is involved, and only one randomly selected decision is implemented. We investigate whether the random incentive system in experiments that measure ambiguity aversion provides a hedge against ambiguity, making ambiguity‐averse subjects who integrate behave as if they were ambiguity neutral. Our results suggest that about half of the ambiguity averse subjects integrated their choices in the experiment into a single problem, whereas the other half isolated. Our design further enables us to disentangle properties of the integrating subjects' preferences over compound objects induced by the random incentive system and the choice problems in the experiment.