The subject of welfare economics suffered a major blow in the 1930s when economists came to be persuaded by Lionel Robbins and others (influenced by 'logical positivist' philosophy) that interpersonal comparisons of utility have no scientific basis and cannot sensibly be made. One person's happiness, it was argued, could not be compared, in any way, with the happiness of another.
..However, since economists came, by and large, to be convinced - far too rapidly - that there was indeed something methodologically wrong in using interpersonal comparisons of utilities, the fuller version of the utilitarian tradition soon gave way, in the 1940s and 1950s, to an informationally impoverished version of relying on utility or happiness. It came to be known as 'the new welfare economics'. This took the form of continuing to rely on utilities only ( this is often called 'welfarism'), but of dispensing with interpersonal comparisons altogether. .. welfarism without interpersonal comparisons is, in fact, a very restrictive informational basis for social judgement. (p277-278)
Sen later disputes that we need to reduce everything to a single measure or source of importance in the first place:
There are indeed schools of thought which insist, explicitly or by implication, that all the distinct values must be reduced ultimately to a single source of importance. To some extent that search is fed by fear and panic about what is called non-commensurability - that is irreducible diversity between distinct sources of value. This anxiety, based on the presumption of some alleged barriers to judging the relative importance of distinct objects, overlooks the fact that nearly all appraisals undertaken as a part of normal living involve prioritization and weighting of distinct concerns, and that there is nothing particularly special in the recognition that evaluation has to grapple with competing priorities.
The fact that we understand perfectly clearly that apples are not oranges, and that their virtues as food vary in different dimensions - from pleasure to nutrition - does not keep us transfixed with indecision every time we face a choice between the two in deciding what to eat. Those who are insistent that human beings cannot cope with determining what to do unless all values are somehow reduced to no more than one, are evidently comfortable with counting ("is it more or less?") but not with judgement ("is this more important than the other?").