It's a parallel to how the Trinity decides their League
That's why it's hilarious. Nevertheless, Minerva doesn't fit that role. Box explains quite masterfully upthread why this kind of thing is completely up Lex's alley; Joker makes a certain amount of sense because, while he doesn't actually care about whether these things work, or have any goals he wants to accomplish, he thinks it's a lark and enjoys being included. Cheetah can't be justified, any more than Sinestro. Certainly Circe very easily could - she'd be there for very nearly the same reasons as Lex, and both of them would go nuts trying to successfully manipulate the other - but then, she's not Diana's archenemy, Cheetah is. It's a bit of a mess either way really.