because there are ``orderings'' of the world's population that would fool your algorithm

So don't use those orderings. That randomness isn't buying you power. It's acting as though you know nothing about the distribution of red-headed people. If you do, in fact, know something about the distribution of red-headed people (i.e. there are more red-headed people than average in Ireland and fewer in Africa, therefore make sure each sample draws proportionally from Ireland, Africa, and non-Ireland-non-Africa), then you can exploit that to make your prediction more reliable.