Russ Roberts muses about applying Coase to traffic accidents while he's in California. Pedestrians, he notes, run wild in a way they wouldn't in DC because in traffic accidents the driver of the car is usually to blame. What a wonderful coincidence that we covered Coase on Monday in my principles of microeconomics course.
Coase notes the problem is not (in the case of traffic accidents) the car when it hits the pedestrian. The problem is that both the pedestrian and the car tried to occupy the same space at the same time. Remove one of these elements and you remove the problem (like all externality issues).
In brief, the question we should focus on is who is the least cost avoider--who is in the better position to avoid a collusion? Given the car extends well beyond what most grew up maneuvering in (ie, their body) and cars move much faster than people, pedestrians are the least cost avoider. The legal action should be to make pedestrians liable for being hit by cars.
This is not, of course, meant to be a hard fast rule. If you're hit while on the sidewalk or curb or crosswalk, that would still be the drivers fault. Again, the least cost avoider holds: it's less costly for drivers to stay in the street and watch lights than for pedestrians to be forever vigilant about where every car in the vicinity is. But in cases where a pedestrian crosses the street without warning, blame should lie with them.
Remember, economics is not about good guys and bad guys. It's about a bunch of people facing costs and benefits.