 Now a common, but not mandatory, interpretation of \(\Gamma\) is that it corresponds to the set of objective probability assignments that the decision maker takes to be consistent with his or her evidence. In view of the result just flagged out, this in turn invites an interpretation of capacities as lower estimates of objective probabilities. More specifically, a CEU maximiser whose capacity is convex can be interpreted as considering possible all and only those assignments of objective probabilities that are consistent with the lower estimates given by that capacity. This interpretation of the capacity in the particular example at hand is obviously particularly tempting, as \(\nicefrac{1}{3}\) and \(\nicefrac{2}{3}\) constitute plausible lower bounds on the decision maker’s estimates of the probabilities of \(\{r\}\) and \(\{b,y\}\), respectively.