I would tend to disagree with you here. Anonymous polls offer the best way for people to give truthful answers. While there are those people who will lie and pick the opposite from the truth, I would think that for most people, there would be no need to lie, as long as it stays anonymous. Of course we could start a poll to find out how many people lie when they post in a poll.
you should've put an option on for negative. people will vote just to participate and see the results easily.