 Any function \(u\) that assigns a larger number to \(A\) than to \(B\) will work as such a representation. Consequently, the function \(u\) can be replaced with any function u’ as long as u’ is a positive monotone transformation of \(u\). As this transformation property is the defining characteristic of ordinal scales, we call this an ordinal preference representation (See the entry on  measurement in science.)