I'm fine with it. I like the idea of the voter being in a bubble with nothing but the ballot and himself. I think you get a more honest response that way, and electioneering at the balloting location becomes less likely. If you want to tell everyone afterwards who/what you voted for...go for it.
"As I walked out the door toward the gate that would lead to my freedom, I knew if I didn't leave my bitterness and hatred behind I'd still be in prison."