  and the state \(\omega(a) = \omega(b) = \omega(c) = \frac{1}{2}\), \(\omega(x) = \omega(y) = \omega(z) = 0\). It is a simple exercise to show that \(\omega\) cannot be expressed as a weighted average of \(\{0,1\}\)-valued states on \(\mathcal{A}\). For further examples and discussion of this point, see Wright [1980].