I want to repeatably (i.e. in deterministic way) select 10% (or K%, $K \in (0,100]$) of elements in a set S.
The only way to do so I can imagine, is having an $order(S)$, which is a sequence. Then (assuming |S| = 100) simply select every 100/K-th element. Or first K elements, etc.
I wonder how generic can be this deterministic choose operation? Can something different than order be used? My aim is to denote all possible deterministic methods, to then prove a property that I think holds, if only the selection is deterministic.