  Classical Utilitarianism, as reflected in equation (3), requires that if \(U\) is a numerical measure of well-being, then so is \(\alpha U+\beta\), where \(\alpha\) is a positive number and \(\beta\) is a number of either sign. Formally, we say that \(U\) is unique up to “positive affine transformations.” We confirm presently that the theory’s recommendations are invariant under such transformations.