 If one grants that the outcomes are adequately characterised in sole terms of associated changes in level of wealth, these “Ellsberg preferences” stand in direct contradiction with Savage’s Sure-Thing principle. These preferences also violate Machina &amp; Schmeidler’s Strong Comparative Probability principle, on the natural assumption that the subjects strictly prefer the outcome \(\$100\) to the outcome \(\$0\). And indeed it is easy to see that the Ellsberg preferences are inconsistent with probabilistic sophistication. More specifically, they are incompatible with its being the case that both (i) the decision maker’s preferences over acts are reducible to preferences over corresponding lotteries over outcomes, generated by an assignment of subjective probabilities to the set of events and (ii) he or she partially orders these lotteries by first-order stochastic dominance. To see why, assume that these conditions hold. Note first that \(P_{g_1}\) would stochastically dominate \(P_{f_1}\) if and only if \(P(\{b\})\geq P(\{r\})\) and that \(P_{f_2}\) would stochastically dominate \(P_{g_2}\) if and only if \(P(\{r\})\geq P(\{b\})\). \(f_1\succ g_1\) would entail that \(P_{g_1}\) does not stochastically dominate \(P_{f_1}\), and hence that \(P(\{r\}) &gt; P(\{b\})\). But \(g_2\succ f_2\) would entail that \(P_{f_2}\) does not stochastically dominate \(P_{g_2}\), and hence that \(P(\{b\})&gt; P(\{r\})\). Contradiction.