A note on justifiable preferences over opportunity sets

A ranking over opportunity sets is justifiable if there exists a binary relation on the set of alternatives, such that one opportunity set is at least as good as the second, if and only if there exists at least one alternative in the first set which is at least as good as any alternative of the two sets combined. This note characterizes (reflexive and complete) opportunity sets rankings which can be justified by acyclic binary relations – the broadest possible class of justifiable rankings.