if you can get registered, you can vote. That's a problem with same-day registration. I don't think anybody compares records to see if you voted in two states or two cities in the same state, unless maybe after the election if a witness comes forward. Even then, it's too late to invalidate the ballot.

SSNs aren't used for identification anymore. It left too many numbers in porous hands, so states stopped using them. At one time, the Virginia drivers license number was your SSN, leaving a lot of sensitive information in the hands of people who took checks at their businesses.

I was registered in Michigan and Florida at the same time. Florida told me they would contact Michigan to cancel my registration when I signed up for a drivers license in FLA. For some reason the message didn't get through. After a couple years I got a post card from Michigan (forwarded to me despite the passage of time) that basically said "we heard you moved, so we're going to remove you unless you object"