It’s not unusual in Ontario to see a cross intersection with four-way stop signs. 

That’s right.

Everyone has to stop, look at each other, smile, and say, “After you…” before proceeding on their way.

The first car to arrive gets to drive off first. In the rare event that you arrive in a dead heat, the driver to the left gets to go first.  This makes me wonder, though… if the drivers are across the intersection from one another, are they not technically on each other’s left?  I can just picture an “Ontario Stand Off”.

Driver A: “After you…”

Driver B: “No, after you…”

Driver A: “No, really, after you…” and so on. 

In theory, this could continue for some time, given how nice and polite Canadians generally are. 
On reflection, I can see why this has not been attempted in Australia.