We have already moved on, and a case like this would no longer be regarded as unusual, let alone difficult. In the process, something like what you propose arose, in the form of liability insurance. The system works reasonably well, in that there are a lot fewer hard cases without creating a crippling burden in the average case.

If anything, this case, together with the way things have changed since then, demonstrates that there is often a good deal of subjectivity in what constitutes a 'hard' case.

But that only moves the problem somewhere else, because insurance is a moral hazard. Someone who would otherwise be cautious to prevent harm has less incentive to do it because when the harm comes the insurance pays.

Insurance is not free, and it generally gets more expensive the more reckless you are (or seem) to be (which is not to say this is the only factor in whether this is a zero-sum game, but it is arguably the most objectively quantifiable.)

The moral hazard is the difference between the insurance payout and the amount your future rates change as a result of the claim. If this amount is zero, there is no insurance. If it isn't, there is that much less incentive to avoid the harm.

Much less? Can you explain this immediate threshold as soon as the moral hazard is non-zero?

"That much less" meaning equal to the difference between the amount of the harm and what they'd expect to pay in increased premiums.

If spending $X would avoid a 2% chance of a million dollars in damage, the X you're inclined to spend is a lot larger if the potential loss is the full million dollars than if it would increase your insurance premiums by a net present cost of $1000.

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.

Not necessarily. In the case of accidents, liability insurance presents no moral hazard. The ordinary person is not going to leave a broken railing in his house that could cause a guest to fall and injure himself just because he has homeowner's insurance.

Similarly, the ordinary person doesn't seek out automobile accidents on account of having mandatory automobile insurance.

Perhaps most strikingly, the moral hazard theory would suggest that life insurance policy holders are more likely to commit suicide, but in reality they are less likely to![1]

Sure, there are probably vanishingly rare exceptions to the above, but the moral hazard concern is wildly overblown for consumer insurance products purchased by ordinary people.

[1] https://www.munichre.com/us-life/en/perspectives/suicide-mor...

> In the case of accidents, liability insurance presents no moral hazard. The ordinary person is not going to leave a broken railing in his house that could cause a guest to fall and injure himself just because he has homeowner's insurance.

Maybe not if repairing the railing costs $15, but what if the safety repairs would cost $15,000? When not doing it could cause someone who gets hurt to render you bankrupt and homeless, you find the money. When you're insured, you may have other priorities.

> Similarly, the ordinary person doesn't seek out automobile accidents on account of having mandatory automobile insurance.

It's not about seeking them out. You don't want an accident, but you do want to read that text you just got, and you're more likely to wait until you're stationary if an at fault accident could ruin you instead of just raising your insurance premiums.

> Perhaps most strikingly, the moral hazard theory would suggest that life insurance policy holders are more likely to commit suicide, but in reality they are less likely to!

Isn't suicide an exception to nearly all life insurance polices, among other reasons to remove that very incentive?

> You don't want an accident, but you do want to read that text you just got, and you're more likely to wait until you're stationary if an at fault accident could ruin you instead of just raising your insurance premiums.

Literally no one ever has thought “self, I’m going to look at this text while I drive because I’m insured!” In the real world they’re doing it because they’re addicted and not because of some rational calculus. That might make a good scenario for a comedic skit though.

I don’t feel like looking it up on my phone, but I’d bet at worse than even odds that drunk drivers are in fact less likely to be insured, when the moral hazard theory would predict they’re more likely to be.

> Isn't suicide an exception to nearly all life insurance polices, among other reasons to remove that very incentive?

The answer is either not really or even an outright no. Individual policies usually have a 1-2 year no suicides clause and after that they pay. Group policies like employer offered ones usually have no wait period and will just pay out.

> Literally no one ever has thought “self, I’m going to look at this text while I drive because I’m insured!”

It works the other way. If you have no insurance, you think, "self, I'm not going to look at this text while I drive because I'm not insured, and if I hit someone it could cause me to lose my house."

Same reason undocumented immigrants follow the speed limit.

> I don’t feel like looking it up on my phone, but I’d bet at worse than even odds that drunk drivers are in fact less likely to be insured, when the moral hazard theory would predict they’re more likely to be.

There are obvious reasons for this to be the case independently. People with a DUI record are more likely to drive drunk, but people with a DUI record may not be able to get or afford insurance. Drunk driving and not having insurance might both be correlated with poverty. Things like that. Is it your argument that not having insurance causes you to be less likely to drive drunk, all else equal?

> The answer is either not really or even an outright no. Individual policies usually have a 1-2 year no suicides clause and after that they pay. Group policies like employer offered ones usually have no wait period and will just pay out.

But the 1-2 year clause is there specifically because of the moral hazard. Otherwise not only would anyone planning to commit suicide have the incentive to take out life insurance first, anyone who needed a quick big payout for their loved ones would have the incentive to take out a policy and then commit suicide.

And the general trend in the opposite direction is caused by both the removal of that incentive, and the same kind of confounders as in the DUI case. People with stable employer-provided insurance coverage or with the financial stability to afford premiums for >2 years are the sort of people less likely to take their own lives.