 One prominent weakening of SEU that is capable of accommodating the Ellsberg cases is Choquet Expected Utility (CEU), initially proposed by Schmeidler (1989). The key concept in its representation of preferences is that of a capacity: a function \(v : \mathcal{E}\mapsto [0,1]\), such that \(v(\varnothing)=0\), \(v(\mathcal{S})=1\) and, for all \(A, B\in \mathcal{E}\), \(A\subseteq B\) implies \(v(A)\leq v(B)\). One can think of this as a kind of non-additive “probability” function, since the additivity property, according to which \(v(A\cup B)=v(A)+v(B)\) for disjoint events \(A\) and \(B\), does not hold. As with the presentation of RDU, the convention here is that the indices associated with the outcomes indicate increasing preference, so that, again, \(\bigcup\limits_{j=i}^{n} E^{f}_{j}\) is the event given which \(f\) yields an outcome at least as preferable as \(x_i\). CEU proposes: 