[Retric]

Fast breaking removes energy from the collision and if someone is not paying attention there going to hit you anyway.

If your going to respond the the car behind you then it's much better to simply slow down if your being tailgated. Doing anything else is counter productive.

PS: Even a long line of tailgating cars can stop because you can only use the space between you and the obstacle, but the car behind you get's that same distance plus the distance between you at them. This space keeps stacking as you go further back so by 10 cars or so it's a long slow break.

[zo1]

Though the "buffer" gets eaten-away with every added car that has to wait for the one in front of them before they can "react". Assuming they don't see past the car in front of them.

[Retric]

Your model suggests we should get thousands of car pileups if anyone does heavy breaking in bumper to bumper traffic. Clearly that does not happen.

The reason is the buffer between you and the car in front of you is eaten by the difference in your speeds. Going from 80MPH to 70 MPH takes ~0.7 seconds, where starting to break takes ~0.2 seconds. Even if there is just 5 feet between cars the signal propagates plenty fast.

[zo1]

What do you mean by difference in speeds? The assumption I made, simplifying the thought experiment, was that the cars had a fixed-length between them, and they were all going at the same speed.