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.
Oh, thou clear spirit, of thy fire thou madest me, and like a true child of fire, I breathe it back to thee.