Quote by JDoolin
So, hypothetically, what if they changed the election rules so instead of voting yes/no, each voter would turn an analog dial to determine how much they liked each candidate, yielding some real number between zero and one?

It still wouldn't be a vector space because no candidate can have a negative result so the axioms of a vector space are not satisfied. I.e. if A is a nonnull election result then there is no election result B such that A+B=0 where 0 is the null election vector.