The Brady Bunch is proposing, in the wake of the two recent mass shootings, that greater effort be put into "preventing dangerous people from buying guns on their own".
They're pretty nebulous as to who exactly shouldn't be allowed to buy a gun since including everybody right up front gets you laughed at. The suggestions they do make include people who are already prohibited, so no gain there.
The DHS has a list of qualifiers that includes military vets, constitutionalists, Tea Partiers and the like, but the list lacks provenience. What is needed here is a study of the political beliefs of all the mass shooters since 1950 to see what really should be looked at. Most of the ones that I remember who actually had any expressed political beliefs were leftists. Oswald, Fromme, etc. Based on this, we should probably prohibit registered Democrats and anyone expressing political beliefs to the left of the party platform from owning guns. Given the very modest amount of light between Debbie Wasserman-Schultz and Joseph Stalin, this should inconvenience the smallest number of people.
Of course the quickest way to eliminate gun violence would be to make violent crime illegal. In the ensuing pax judicus* guns would have no use and therefore be peacefully abandoned, right?
*I don't care what my friends say, when I was younger, Latin was NOT the language of the army, and it was not necessary to learn it. That was from my fathers time.