You can put more than one order on a set. For example, regarding salsas from the set {mild, medium, hot}:
- mild < medium < hot, where < means the predicate “is less spicy than”
- medium ≻ hot ≻ mild, where x≻y means the predicate “She prefers x to y”.
One could launch off into defining ≻ᵢ’s for every ᵢ of the population. (This is the kind of thing one needs to do in talking about Arrow’s Theorem.) That’s when notation begins to suck.
