Last spring I got rear ended twice. The first offender cajoled me into not calling the police, then hid like a rat when I tried to make a claim on her for the $746 repair. I figured that this woman (who was not wealthy) saw an Asian male and a rich looking WASP in a late model SUV and though she could safely avoid liability. Fortunately, she had left her insurance card and I finally called her agency (a high risk agency) and they believed my story even though they couldn't contact her. So I got my $746 repair. And her insurance premiums probably exploded.
The second time was better since I called the cops and got a police report and the other driver got cited. It was OK, but I was still worried about getting hurt and going through the hassle of getting paid back if I did get hurt or some damage was found on my car.
It was OK since the other driver began to cry like a baby because she thought I was hurt. That was a nice thing to do that made me not particularly angry.
I think that it should be a state law that when you're at fault in an accident, you should not only be forced to pay for the repairs to the vehicle, you should be forced to pay the other an "aggravation payment" according to a sliding scale. And it should be a damn generous curve- say $.25 for each $1.00 in damage.
Either that, or after the police find out who's at fault, the person who suffered the damages gets to punch the person at fault once for every $100 in damage. For every $300 in damage, the person who suffered gets to use an instrument like a jack, baseball bat, or 2 X 4.
Or the person who suffered damages could write a waiver if the person who caused them was sufficiently regretful.
That way people like me wouldn't get violently mad. We'd get the compensation we really NEEDED.