 Arrow’s view, as noted, is that only intrapersonal level comparisons are meaningful, while all other kinds of comparisons are not. Sen (1970b) formalized various assumptions about measurability and interpersonal comparability of welfare by (i) defining an equivalence relation on welfare profiles that specifies when two profiles count as ‘containing the same information’, and (ii) requiring any profiles in the same equivalence class to generate the same social preference ordering. Of the three kinds of comparison statements introduced above, the meaningful ones are those that are invariant in each equivalence class. Arrow’s ordinalist assumption can be expressed as follows: