 This property states that if some element of a subset \(\mathcal{B}\) of \(\mathcal{A}\) is chosen from \(\mathcal{A}\), then it is also chosen from \(\mathcal{B}\). According to property \(\alpha\), removing some of the alternatives that are not chosen does not influence choice. This property has often been assumed to hold, but counterarguments have been raised against it. Consider the following example. Erna is invited to an acquaintance’s house for dinner. Her choice for dessert is between an apple (which is the last piece of fruit in the fruit basket) \((X)\) and nothing instead \((Y)\). Because Erna is polite, she chooses \(Y\). Had she faced a choice between an apple \((X)\), nothing \((Y)\) and an orange \((Z)\), she would have taken the apple. Thus her choices are: