 Preferences can be represented numerically. \(A\succ B\) is then expressed by a set if numerical utility functions \(\{u_i\}\), each of which assigns a higher value to \(A\) than to \(B\), while \(A\sim B\) is represented by assigning the same value to the two. Such numerical representations might serve different purposes, one being that utility functions can be analysed with the tools of maximisation under constraints, as done in economics. It is important, however, to stress the limitations of such representations. First, not all preferences can be represented numerically. Second, there are different scales by which preferences can be represented, which require premises of different strengths. Third, the resulting utility representation must be clearly distinguished from the older hedonistic concept of utility. 