 Ordinal measurability with no interpersonal comparability (ONC): 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 \(i \in N\), \(W^*_i = \phi_i (W_i)\), where \(\phi_i\) is some positive monotonic transformation, possibly different for different individuals.