The very reasonable and very logical assumption for the program to make is simply stop the vehicle, or reverse course until it finds a path it can take forward again.
Why would a car take into account the amount of human lives? If something is going cause the car to collide with something else it will decide if it can avoid that obstacle and do so, either by swerving or stopping.
Are we holding machines to different standards than we hold each other?
Not too long ago I had the opportunity to have a surgery performed by a robot controlled by a human surgeon. My wife was adamantly against it since there had been accidents previously with the robot other places in the world. Overall, the rate of incident was lower than the rate of incident for human surgeons, but to her that was not the important point.
There are people who will definitely hold machines to higher standards, and if they don't meet them, to them they are clearly inferior.
I've talked to a few hospital executives and all have said that in most cases, these robots only cost them money and decrease the quality of the surgical procedures.
http://www.dailymail.co.uk/sciencetech/article-2526934/Surge...
http://www.wsj.com/articles/robotic-surgery-brings-higher-co...
And another from a relatively reputable healthcare company/journal:
http://www.healthline.com/health-news/is-da-vinci-robotic-su...
The only way to enforce the limited choice domain you presented is for the automated drivers to be operating the vehicles unsafely prior to the collision event. In that case, never mind the other car, because either car could be forced off the cliff due to a goat standing in the middle of the road.
Also, I'll program my driver to believe that its car always contains MAXINT passengers.
How do you know the kids would be saved by your sacrifice? How do you know they would die from your selfishness? How do you know that bus isn't actually filled with violent and dangerous felons being transferred to supermax while awaiting execution, and the guards on it aren't also corrupt to the core?
You don't have that extra information at the time the decision would need to be made.
The logical and ethical thing for the computer to do would be to switch over to emergency collision avoidance mode, and try to avoid damage to the one vehicle it can actually control. The authority to instruct a driver to put its passengers at risk would have to be vested in some sort of traffic control program capable of recognizing when the selfish behavior of individual driver programs might result in more damage and injury overall.
And that's a whole new can of worms.
Why would it do anything else?
There are 3 possible outcomes:
The cars can communicate with each other. The logical resolution would be to drive the car with the least passengers off the cliff to save as many lives as mathematically possible.I don't know how I would feel about my car killing me although logically I wouldn't have a chance of survival anyways.