Here in Israel voting is very organized and it's pretty hard to cheat, other than those who arrive with an Identity Card of a similar looking dead person who hasn't been registered as dead, or the same sort of thing with someone hospitalized. As long as nobody in the polling station staff realizes it or "squeals," it can be done.
In Shiloh and other small communities, there's pretty much always a neighbor on the "staff" who can easily vouch. Also, we're all sent notices telling us exactly where we are supposed to vote. And we must vote there. If there was a mistake by the clerk in the Ministry of Interior, which happens --such as sending someone to Shilat, rather than Shiloh-- one can get free public transportation.
Now, in the United States, there aren't required Identity Cards, and from what I've read, there is no longer an assigned place to vote. So how does it work? Besides just trusting people...