I had initially thought that it would be something along the lines of "here is a vector, each component of which represents one thing you could want, take the inner product in the usual way, length has to always be 1." Gains from trade would be represented as "I don't want this thing as much as you do." I am now coming to the conclusion that this is at best incomplete, and that the suggestion of a weighted integral over a domain is probably better, if still incomplete.