Why is a codomain of [0,1] more general than a preorder?
The function only uses the preorders on candidates implied by the utility functions.
The (implicit, as OP says “obvious/not matter”) measurability of a compact set seems like more structure than a preorder, to me, and I’m not thinking of “generalization” as imposing more structure.
Yeah, preorder is misleading. I was only trying to say with as few characters as possible that they are only considering a ranking of candidates possibly with ties. (Which is a preorder, but is less general.)
Why is a codomain of
[0,1]more general than a preorder?The (implicit, as OP says “obvious/not matter”) measurability of a compact set seems like more structure than a preorder, to me, and I’m not thinking of “generalization” as imposing more structure.
Yeah, preorder is misleading. I was only trying to say with as few characters as possible that they are only considering a ranking of candidates possibly with ties. (Which is a preorder, but is less general.)