Background checks aren't going to be allowed to disclose what kind of anti-depressants a dating site participant has been prescribed, so the whole thing remains a big gamble. There is no way to legislate the risk out of an inherently risky activity.
Sure there is. Require men to be given injections of estrogen until they're married. That'd probably do the trick.
Of course, then we'd end up acting like a bunch of French pusses...but that's the ultimate objective of these POS nanny-state legislators anyway.
Not just anti-depressants. I would also be looking at serial divorces, serial restraining orders (either directions), membership in radical organizations, etc. BTW, what I have listed are of course disqualifying criteria. After one very bad experience (she went extreme psycho), I would almost prefer running a background check of the same magnitude of a Q clearance.