I can see some good in this-like a previous poster said, maybe people will think twice before down-voting something, or it will curb emotion driven vote bombing. As a whole though, I'm not so sure this is such a good idea.
Not everyone's an open book-we all express opinions in private, it's an emotional well being necessity. Some people will always be apprehensive about voicing their opinions openly for various reasons; the anonymity thing lets people have that freedom without fear of repercussion, lets them "get it out". Of course that has a downside, which we already discussed (vote-bombing, petty vendettas, etc.), but I think the good of anonymity outweighs the bad. As A-Yty said, I feel this will lead to uniform voting, which will lead to resentment/discontent, OR, on the flip-side, possible calling out of "the offender" & then a flame war, and just general not-gonna-end-well-ness for the forum.