What if two cars arrive simultaneously at opposite sides of the 4-way and are both turning left? This could easily deadlock two self-driving cars if not considered.
Your situation is a bit ambiguous. Do you mean they turn to their respective left (in that case their trajectories should not intersect), or to the same left? Not sure about USA, but where I am from the right of the way belongs to the driver who turns to the same side as the side of the road they are on, i.e. to his right (we drive on the right side).
What if two cars arrive simultaneously at opposite sides of the 4-way and are both turning left? This could easily deadlock two self-driving cars if not considered.