I haven't read through all of the posts on this thread, but here is my input.
Some women seem to go for men who appear to be "fixer uppers". Maybe they get some sort of satisfaction from helping such a man improve? Maybe these women like to be in a position of power in a relationship, and in order to do so intentionally date down knowing that these men probably won't leave or cheat. Maybe men like this are all women have access to in the first place?
There could be a vast number of complex reasons for this and while it is an interesting idea I don't think it's really all that complicated.
Most women generally get into relationships with men that mirror them in some manner or fashion.
I know of a guy in my area that is a couple years older than me, around 32ish, and is for real one of the biggest douchebags I have ever met. He associates with these real estate scam artists, I'm talking like those bogus seminars and such, is friends with nightlife promoters out here, one in particular I know sells coke. Besides that the dude just comes across as a poser, fake, etc.
Anyway, he has a live in girlfriend, who is not only very attractive but college educated and has a decent job at a hospital, came from an upper middle class background, etc. This guy actively cheats on her and yet despite all of this and his characteristics she sticks with him. Most normal and well adjusted women would leave but the reason she stays with him is BECAUSE on a deeper level she is just as messed up as he is.