 Cardinal measurability with no interpersonal comparability (CNC): 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 \(i \in N\), \(W^*_i = a_i W_i + b_i\), where the \(a_i\)s and \(b_i\)s are real numbers (with \(a_i \gt 0)\), possibly different for different individuals.