Q is random and inexplicable, the rules he operates by are random and inexplicable, when he can't act, it is random and inexplicable. The writer makes it up as they go along.

There isn't any real system to how he operates, he is just there to play the role of this "higher and superior" being in random episodes.

That's what I kind of think. They probably could have fleshed his character out more, his system out more, but I guess that undermines being unfathomable.