Who are you kidding?
The cars would have to be completely enclosed, with no view to the outside. They would have to be built like brick :censored::censored::censored::censored:houses so that people would even contemplate getting into one.
Why?
Because no one is going to be able to look out of a car window careening into an intersection like that with all them cars doing the jitterbug within inches of each other without getting a heart attack of major proportions!
One look at that intersection and you know, if you get hit you're mincemeat, so I'm all for it, as long as the vehicle I ride in is a tank!!
For this to work it would take a city of people insensitive to the possibility of losing their lives, or a people that have attained the ultimate trust of technology.
Your ambulance would absolutely have to play by the same rules and you'd have zero control. But then both of you WOULD be busy in the back!
http://player.vimeo.com/video/37751380?title=0&byline=0&portrait=0
I put this in because it's trippy to contemplate!
And you know what else? Each and every one of those cars would have to be completely DEFECT FREE, all the time, without fail; anything that mechanically slows the car down in the middle of that intersection for even a millisecond would cause a fatal encounter!