Voter ID and Universal Background Check for Guns
One of the proposals some have made to close the so-called gun show loophole is called "universal background check". I'm not sure how they plan to impose such checks without making it very difficult for private citizens to sell guns to others. But I've got a solution that kills two birds with one bullet.
We don't need crazy, sociopathic, or dangerous people buying guns. We don't need them voting either. If you can't be trusted to exercise your right to bear arms, you can't be trusted to vote as far as I'm concerned. What we need is a system where you apply for a Trusted Citizen ID, a background check is performed, and if you pass, a picture ID is issued. Use this ID to buy guns anywhere (Cabella's, gun show, or private sale) and to vote in your designated precinct.
Non-citizens who want to buy a gun would get the version of the ID that doesn't enable them to vote.