We develop a tractable method to estimate multiple prior models of decisionmaking under ambiguity. Using a custom-designed module in a representative survey of the U.S. population, we find that choices made under ambiguity are best explained by a two-parameter version of the α-MaxMin model: one parameter measures ambiguity aversion (preferences toward ambiguity), and the second parameter quantifies the perceived degree of ambiguity relative to a reference distribution (perceptions about the level of ambiguity). We conclude that most people are ambiguity averse for uncertain events of moderate to high likelihood, yet they are ambiguity seeking for low likelihood events. Furthermore, we find ambiguity-seeking towards losses, and evidence of reference dependence and reflection. These patterns may help predict behavior outside the laboratory.