 To exemplify property \(\beta\), suppose that we have three restaurants, \(X, Y\) and \(Z\), within walking distance, and two additional restaurants, \(V\) and \(W\), that we can reach by car. Furthermore, suppose that we begin by choosing among the restaurants within walking distance. We agree that the choice is between \(X\) and \(Y\), but we find no reasons to choose one of them rather than the other, i.e. \(\mathbf{C}(\{X, Y, Z\})=\{X,Y\}\).  Then we find out that we do in fact have access to a car. Property \(\beta\) says that if \(X\) is one of the chosen restaurants in this situation, then so is \(Y\), and vice versa.  In other words: \(X\in \mathbf{C}(\{X, Y, Z, V, W\})\) holds if and only if \(Y \in \mathbf{C}(\{X, Y, Z, V, W\})\). 