Let the probabilities for red, blue and yellow marbles be \(r\), \(b\) and \(y\) respectively. If you were an expected utility maximiser and preferred I to II, then \(r &gt; b\) and a preference for IV over III entails that \(r+y &lt; y +b\). No numbers can jointly satisfy these two constraints. Therefore, no probability function is such that an expected utility maximiser with that probability would choose in the way described above. While by no means universal, these preferences are a robust feature of many experimental subjects’ response to this sort of example (Camerer and Weber 1992; Fox and Tversky 1995). Some experiments suggest that Ellsberg-type patterns of preference are rarer than normally recognised (Binmore et al. 2012; Voorhoeve et al. 2016). For more on ambiguity attitudes, see Trautmann and van der Kuilen (2016).