In the specific case of a one-law referendum, which is what the question was asking about, what would be the purpose?
Let's pick a subject that will be polarizing and motivate people strongly, abortion for example. Now we have a referendum to allow it (Ireland did that recently, IIRC). Could be a referendum to forbid it, doesn't matter.
What does it mean to be 67% for abortion rights? Your brain is saying "well, I am 33% against too"? If you were voting on two different laws or two different political offices, then yes, you might "spend" 67% of your voting power to have your way on your most important subject, and 33% on your second important choice.
This logic might even work for 1 office and 5 candidates. 67% to your favorite candidate, 33% on your second-best choice. That makes sense.
But, again, for voting on one law and one law only, with a binary yes-no, what is the purpose of this quantified vote system? (please don't use quantum, it means quantified in discrete steps, not just quantified and poor word is overused ;-). You either want something or you do not. If you don't care - don't vote at all.
p.s. One valid reason for a quantified vote would be places that have laws forcing you to vote, even if you didn't care: voting 50/50 would essentially spoil your ballot, assuming there was no other way (such as voting blank or checking off both Yes and No). But that's a special case at best.