I think we are all ineluctably attracted to our animus or anima so we choose the complementary gender as our avatar.
So Julia or the Queen are plainly my anima, while your avatar is plainly your animus.
Or at a simple level you could be my anima while I could be your animus. All we need to do is make you my avatar and me your avatar. A simple, economical solution.
This would bypass the Australian people trying to make up their minds, and perhaps start a trend on Typology Central.
And perhaps a trend for the whole world where people would simple ask, "Would you be my avatar?".
It would avoid this whole complicated and involved process of voting and take us back to our roots.