 This provides Ramsey with the resources needed to sketch a representation theorem, which forms the centrepiece of his paper. According to this theorem, the subject’s preferences will satisfy eight relatively simple conditions only if there exists at least one function, \(\mathcal{U}\), such that the difference in utility between \(\omega_1\) and \(\omega_2\) is at least as great as that between \(\omega_3\) and \(\omega_4\) if and only if