White considers dilation to be a problem since learning \(Y\) doesn’t seem to be relevant to \(H\). That is, since you are ignorant about \(X\), learning whether or not the coin landed \(X\) up doesn’t seem to tell you anything about whether the coin landed heads up. It seems strange to argue that your belief in \(H\) should dilate from \(1/2\) to \([0,1]\) upon learning \(Y\). It feels as if this should just be irrelevant to \(H\). However, \(Y\) is only really irrelevant to \(H\) when \(p(X)=1/2\). Any other precise belief you might have in \(X\) is such that \(Y\) now affects your posterior belief in \(H\). Figure 2 shows the situation for one particular belief about how likely \(X\) is; for one particular \(p\in P\). The horizontal line can shift up or down, depending on what the committee member we focus on believes about \(X\). \(p(H\mid Y)\) is a half only if the prior in \(X\) is also a half. However, the imprecise probabilist takes into account all the ways \(Y\) might affect belief in \(H\).