 Ordinal numerical representations of preference are just a convenient tool – they do not represent any information that cannot be represented by the relation \(\succ\) itself. However, there is relevant information about preferences that is not represented by the relation \(\succ\) itself. For example, when an agent expresses two preferences, say \(A\succ B\) and \(C\succ B\), one might ask how much the agent prefers \(A\) to \(B\), in particular in comparison to how much she prefers \(C\) to \(B\). To answer this question, one needs to determine both a measurement procedure for measuring preference intensities and a measurement scale for representing these measurements. 