 The question then arises: Is there a conservative generalisation of the EU decision rule that can handle sets of probability and utility pairs? Contender decision rules are standardly framed in terms of choice functions that take as input some set of feasible options and return as output a non-empty set of admissible choices that is a subset of the feasible options. A basic constraint on these choice functions is that they respect the agent’s preferences in cases where options are in fact comparable. That is, if all pairs of probability and utility functions characterising the agent’s attitudes agree on the ranking of two options, then these particular options should be ranked accordingly. The relevant constraint on choice functions is that “EU-dominated options” are not admissible choices, i.e., if an option has lower expected utility than another option according to all pairs of probability and utility functions, then the former dominated option is not an admissible choice. Note that Levi (1986) has a slightly more restrictive condition on admissibility: if an option does not have maximum EU for at least one pair of probability and utility functions, then it is not admissible. In ordinary cases where sets of probability and utility functions are closed convex sets, however, Levi’s condition is equivalent to the aforementioned one that rules out EU-dominated options (Schervish et al. 2003).