In my area they have a paper list of all registered voters in the district. You walk in, they ask your name, you tell them, they cross off your name, you go vote.
Works great.
John Jones walks in: "hello, I'm Dave Davidson, and I'm here to vote"
"OK Mr Davidson, we got you on the list"
A few hours later...
John Jones walks in "hello, I'm John Jones, and I'm here to vote"
"OK Mr Jones, we got you on the list"
A few hours later....
Dave Davidson walks in: "hello, I'm Dave Davidson, and I'm here to vote"
"I'm sorry, Mr Davidson, we show that you have already voted, I'm afraid you can't vote because we have no way of proving you didn't vote"