Public Service Announcement:
I've found that, in 90% of the cases I've seen the Dunning-Kruger effect mentioned as a way to put down a debating partner, the speaker considers her own cognitive ability beyond the ken of her target, mistaken in much the same way as the target supposedly misoverestimates his own. I hereby christen this phenomenon, a relative of simple "projection", as the Meta-Dunning-Kruger Effect. © ® ™ &c.