 Cardinal measurability with interpersonal unit comparability (CUC): Two profiles \(\langle W_1, W_2 , \ldots ,W_n\rangle\) and \(\langle W^*_1, W^*_2,\ldots, W^*_n\rangle\) contain the same information whenever, for each \(i \in N\), \(W^*_i = aW_i + b_i\), where \(a\) is the same real number for all individuals \((a \gt 0)\) and the \(b_i\)s are real numbers.