 Theorem 4 (Bolker)  Let \(\Omega\) be a complete and atomless Boolean algebra of propositions, and \(\preceq\) a continuous, transitive and complete relation on \(\Omega \setminus \bot \), that satisfies Averaging and Impartiality. Then there is a desirability measure on \(\Omega \setminus \bot \) and a probability measure on \(\Omega\) relative to which \(\preceq\) can be represented as maximising desirability.