but not necessarily an unsolvable one.

Really? Every use of utilities I have seen either uses a real world measure (such as money) with a notation that it isn't really utilities or they go directly for the unfalsifiable handwaving. So far I haven't seen anything to suggest "aggregating utility functions" is even theoretically possible. For that matter most of what I have read suggests that even an individual's "utility function" is usually unmanageably fuzzy, or even unfalsifiable, itself.