I don't think of myself as poorly informed (though nobody does)

I do! (Think of myself as poorly informed.)

(More seriously, the sense in which you use "poorly informed" is unclear, obviously on most topics one is poorly informed, but perhaps in the context where a person thinks themselves to be well-informed, they don't simultaneously think themselves poorly informed. Belief in belief type situations might enable that though, where you believe that you believe to be well-informed, but you know that you aren't.)