 Counterexamples have been offered to show that these properties are not plausible in all situations. Consider an agent who chooses to stay at a friend’s house for a cup of tea \((T)\) rather than to go home \((H)\), but who leaves in a hurry when the friend offers a choice between tea and cocaine \((C)\) at his next visit. Then \(\mathbf{C}(\{T,H\}) =\{T\}\) and \(\mathbf{C}(\{T,H,C\}) =\{H\}\), and hence the visitor violates both properties \(\alpha\) and \(\beta\). 