Hello Jishnu, and thanks for your thoughtful and interesting response. I am not sure I see the appeal of positivism as a response to the deep methodological concerns you raise - although nothing hangs on this for the basic position in your blog, I agree. To start with the bit I am most certain about, it is not clear that an appeal to the consent of those affected or representation of those whose interests are at stake is a satisfactory response to the relativist worry. After all, all these ideas - the value of consent, what representation means and requires, the nature of democracy, are all themselves morally loaded, and hence are themselves either universal or relative (I prefer this over absolute/relative, for complicated reasons I won't go in to).
Note that democracy, to confer legitimacy on outcomes, requires an extensive set of individual rights; consent must be free and unforced (whatever that means); and there is the question of whose interests are legitimately affected. I suspect there is enough diversity in the world over these questions that they do not offer an escape from concerns about relativism. I'm not sure, also, how you get to democracy or representation from positivism alone (but then I don't have to be ;-) )
If this seems a bit remote from economic positivism, let me try to bridge the gap, though here I am outside my comfort zone. If you're committed to counting preferences as mere preferences, and weighing those of individuals equally, then it is not clear how this escapes a charge of relativism: there are plenty of worldviews that see our social world, instead, as a realm of obligation and community, for example. In other words, to make morality largely absent from economic thinking is itself to take a moral position, and a controversial one at that.
It seems like a lot of work is done on the positivist account by the notion of market failure. I am interested to know how far you think this gets you? To be crude, if the parent really wants that crate of beer, and the child's schooling is compromised, but not heavily so, is there a point at which the parent spending the money on beer is the optimal outcome, and so there is no market failure here? I can see scope, of course, to resist aggregation, insist on diminishing returns, discount some preferences compared to others etc. How much filtering and weighting work can you do with the preferences at issue, before an account starts measuring welfare "objectively"?