Summary: We propose a model of decision making that captures reluctance to bet when the decision maker (DM) perceives that she lacks adequate information or expertise about the underlying contingencies. On the other hand, the same DM can prefer to bet in situations where she feels specially knowledgeable or competent even if the underlying contingencies have vague likelihoods. This separation in terms of sources of uncertainty is motivated by the Heath and Tversky’s competence hypothesis as well as by the Fox and Tversky’s comparative ignorance effect. Formally, we characterize preference relations \(\succsim\) over Anscombe-Aumann acts represented by
\[ J(f) = \min_{p \in C} \int_A u(f) d p + \max_{p \in C} \int_{A^c} u(f) d p, \]
where \(u\) is an affine utility index on consequences, \(C\) is a nonempty, convex and (weak\({}^\ast\)) compact subset of probabilities measures, and \(A\) is a referential chance event. In this model there is a clear separation of ambiguity attitudes. The case \(E \subset A\) captures possible familiar target events while the case \(E \subset A^c\) might refer to the case of relative ignorance concerning related contingencies. This model captures a special case of event dependence of ambiguity attitudes in which the well known maxmin model is a special case. We also characterize the case where we have a Choquet expected utility representation.