Also, mine covers non-Archimedean orders. The IOC's ranking system, for instance, is a lexicographic order in which one gold beats any number of silvers; that can't be expressed at all as an additive scheme with a positive real score for each of gold, silver and bronze, because for any additive scheme there must be some number of silvers large enough to beat one gold.

Good point. I think I assumed x,y and z would be rational numbers (equivalent to integers), and ignored tie-breaking as some extra step that might or might not involve counting red-haired witch-doctors in each team :)

(Although, I could retrospectively pretend that I intended the domain to include infinite ordinals.)