The model you present here is semi-quantitative, in that it has an example value of $1000 for insurance premiums, another of $X for liability, but "small chance" is not introduced as a variable, and neither are "lot larger" and the change in premiums as a function of change in safety spending. I suspect that if this model were completed in accordance with your premise of equality, it would imply there is no rational case for insurance.

This seems moot, however, as this is not shaping up to be a plausible model for how things actually went since Winterbottom's unfortunate accident. Road transport vehicles have become a great deal safer since then, even as the potential for them to do harm has increased enormously. For your argument to be pertinent, it would have to be likely that, in the alternative reality where Rolf's ruling remained the law and liability insurance did not come about, they would be safer than they are now.

> The model you present here is semi-quantitative, in that it has an example value of $1000 for insurance premiums, another of $X for liability, but "small chance" is not introduced as a variable, and neither are "lot larger" and the change in premiums as a function of change in safety spending.

All of the numbers are obviously made up examples because in practice they depend on what the risky behavior is and the value of the dollar etc. But we can make up more of the numbers, if you like example numbers.

A 1% chance of a million dollar liability has an expected value of -$10,000. A 1% chance of a premium increase with a net present cost of $1000 has an expected value of -$10. Therefore, the resources the party would rationally expend to prevent the harm is $10,000 in the first case and $10 in the second case. That difference is a lot.

> I suspect that if this model were completed in accordance with your premise of equality, it would imply there is no rational case for insurance.

Insurance is a net loss to the average insured, even before the moral hazard, because the sum of the premiums is necessarily more than the sum of the claims since premiums also have to cover the insurance company's overhead (or the insurance company becomes insolvent).

Its only purpose is to pool risk. Many people prefer a 100% chance of a $1050 loss to a 1% chance of a $100,000 loss. But pooling risk introduces moral hazard -- that's one of the reasons people like to be insured. "Peace of mind" = don't have to worry because the insurance will cover it.

> For your argument to be pertinent, it would have to be likely that, in the alternative reality where Rolf's ruling remained the law and liability insurance did not come about, they would be safer than they are now.

The market wants cars that are safer for their occupants because insurance can't bring you back from the dead.

The market doesn't care if cars are less safe for pedestrians or other motorists, because that cost is on the other party or the insurance company. And so we see cars getting heavier over time, as expected from that set of incentives.

> Its only purpose is to pool risk.

Precisely - there is a rational case for insurance despite your analysis.

The fact that cars have, on average, become heavier lately is at most a cherry-picked second-order effect that is far from sufficient to refute either what I wrote in my previous post, or in my original post in this thread. Despite your analysis, it is plausible, and IMHO extremely likely, that the same forces that have led to the improved situation since Winterbottom v. Wright will continue to improve the situation for pedestrians and other motorists, as they have in the past.