And in addition, seeing as this is an anonymous (I'm assuming) vote, then I could lie to you and vote my way (to get more votes for Y), but then if everyone will do it, the colluding wouldn't work, so we need to be able to trust each other and work together, which is exactly what we in the end, for people to work together and not against each other.
Then the other side should also coordinate tightly in this manner, and now you have a new problem: polarization.
X and Y need not be alternatives for the same problem, X might be about financial deregulation and Y about privacy deregulation.
Anonymous voting doesn’t help when independent thought itself is trained away from an early age.
There's nothing wrong with persuading people.