You then imply a universal or societal "overall" utility function of the form V(x) = ∑( Uₐ(x) ) over all a.

I wasn't intending to imply that the society had homogeneous or even transferable utility functions--that was the substance of my clarification from the previous post.

Your fallacy is in applying the log transform to the individual Uₐ(x) functions rather than to the top-level function V(x) as a whole.

Insofar as there is no decision-maker at the top level, it wouldn't make much sense to do so. The transform is just used (by economists) to compute individuals' decisions in a mathematically simpler format, typically by separating a Cobb-Douglas function into two terms.

The point is that for economists, the two functions produce the same results--people buy the same things, make the same decisions, etc. You cannot aggregate economists' utility functions outside of using a proxy like money. For ethicists, the exact form of the utility function is important, and aggregation is possible--and that's the problem I'm trying to identify.