Considering the amount of airtime that politicians get I have yet to see any evidence that we require them to be attractive. Here are our congressmen with last names beginning with A. Not that there's anything hideous about them but any beauty pageant that produces these winners has a serious flaw.

I don't know... Number 3 might be sleepingbaggable, if you're into daddies.

Reviewing those pictures again I think I may have found the actual common link that predicts electability:

Lots of real estate in the forehead region.