Medaka's tensai-dere-ness in the manga could also be viewed as "idealism on steroids", imho. She sort of thinks that problems would be solved through her ideal means, no matter how unusual they sound to other people, as long as she thinks the method is still ideal. You could also view that as being overly naive… but maybe not.

It seems like she does enjoy persuading other people when Zenkichi's around… or persuading him in the process…

Lastly, Medaka is hot, no exceptions.