 It turns out that as long as the set of prospects/options, \(S\), is finite, any weak order of the options in \(S\) can be represented by an ordinal utility function. To be precise, let us say that \(u\) is a utility function with domain \(S\). We say that the function \(u\) represents the preference \(\preceq\) between the options in \(S\) just in case: