This paper shows that a decision maker’s attitude to ambiguity can change with the act’s certainty-equivalent level — the sure amount that the person finds equally good as the uncertain act. After using the standard Anscombe–Aumann step to put all prizes on the same von Neumann–Morgenstern utility scale, the author proves that preferences can be represented by a continuous family of event-weighting objects called capacities, one capacity for each interior certainty-equivalent value. Each nonendpoint act is evaluated by the Choquet integral — a way to aggregate state utilities when weights may be nonadditive — using the capacity that corresponds to that act’s own certainty-equivalent. Acts that lie on the same indifference surface share the same capacity, while acts with different certainty-equivalents may be evaluated by different capacities {ν_v} indexed by v in (0,1).