Choquet expected utility and never best choice

Given a set of capacities describing uncertainty over a set of states, and a set of acts, the question is considered when an act is never a best choice, i.e., when for every capacity there is another act with higher Choquet expected utility. This question is answered for several sets of capacities, distinguished by their supports, where the focus is on four different definitions of a support. One consequence of the analysis is that an act is never a best choice against the set of all capacities if and only if it is strictly dominated by a convex combination of the comonotonized versions of the other acts. This result can be seen as the counterpart of the analogous result for additive capacities, such as mixed strategies in games.