Earlier quoted context omitted.
Unless you're driving in a place known for courtesy like Canada or Hawaii ಠ_ಠ... People often stop late and won't move until you go first...
My father taught me this trick -- if you're going to arrive simultaneously, just make sure you stop clearly second (especially if the other car is on your right). I find it is usually pretty efficient and have yet to notice someone doing the same to me at the same time.
When I was road tripping in the US, I also attempted to prevent unclear situations at 4-way stops by intentionally slowing down just a bit so it is clear that I'm not first to drive. Since I couldn't prevent the stop anyway I was usually much more comfortable with letting other people drive first, or at least with having a clear order and knowing about my position in that order.