 As noted, a SWFL respects a given assumption about measurability and interpersonal comparability if, for any two profiles \(\langle W_1, W_2 , \ldots ,W_n\rangle\) and \(\langle W^*_1, W^*_2,\ldots, W^*_n\rangle\) that are deemed to contain the same information, we have \(F(W_1, W_2 , \ldots ,W_n) = F(W^*_1, W^*_2,\ldots, W^*_n)\). Arrow’s conditions and theorem can be restated as follows: