 Given an alternative set \(\mathcal{A}\), we can represent (hypothetical) choice as a function \(\mathbf{C}\) that, for any given subset \(\mathcal{B}\) of \(\mathcal{A}\), delivers those elements of \(\mathcal{B}\) that a deliberating agent has not ruled out for choice. For brevity’s sake we will call them ‘chosen elements’. The formal definition of a choice function is as follows: