In the early 1980s, a couple of weeks after the first election in El Salvador, I met a woman who had voted there. She showed us the ink that was still on her finger and my first thought was: Why don’t they do it that way in Chicago? It wouldn’t eliminate fraud but it would at least make multiple voting much more difficult.
The reason they don’t do it, I am speculating, is that for any given election one party primarily benefits from fraud, the other party usually doesn’t think the battle is worth fighting (and either wants to retain the fraud option or fears the anti-fraud rules could be used against it in the future), many voters also benefit from the fraud, and the voters who don’t benefit are not well enough organized or even aware of the problem. So while voting fraud is a serious problem in the aggregate, it is difficult, at any particular moment, to get a big enough constituency together to do anything about it.
Perhaps the Internet, by facilitating the flow of information and political organization, is increasing political incentives in the USA to do something systematic about election fraud. I hope so.