Interpersonal Comparisons

Ratio-scale utility Suppose u is a utility function for a weak order > 0 on X that satisfies one or more additional conditions in a set including positivity: u(x) > 0 for all x e X. We say that u is a ratio-scale utility function (with respect to <£) if, for every utility function v for > 0, v satisfies % if and only if there is a positive number a such that, for all x e X }

v(x) = au(x).