Each of these cases has something in common: everyone knows and can agree upon the price of the thing being insured. But sometimes, you want to insure against something that you know will be very expensive, but whose actual cost you don’t know ahead of time — say, the liability insurance on your car, which is insuring against the medical bills of someone injured in an accident. How does an insurer know how much to charge? And what if it’s a “catastrophic” event, one that ends up being so expensive that the total premiums that the person buying the insurance would never pay that much over their entire lives?

It turns out that you can meaningfully insure these too, so long as the actuaries can figure out the average costs, and figure out the odds of different possible expenses; you just spread these costs over the whole pool of insured people. If you know that one person out of every thousand will have a million-dollar expense, and you’ve got 10,000 customers, then you can expect to make $10M in payouts over the years, and price your premiums at $1,000 apiece plus a fee. This works out even though none of those ten people will ever pay $1M in premiums; the lucky ones pay, the unlucky ones get paid back.

At first glance, this kind of “catastrophic event insurance” works a lot like ordinary insurance; by spreading risk over the entire pool of insured people, it lets people insure not just against events which they could pay for if the cost were spread out over their entire lifetime (like ordinary insurance), but even against events which you couldn’t pay for.

But catastrophic insurance is only sort-of insurance: it has a fundamental problem. Imagine that one day, someone figures out that the one-in-1,000 odds above aren’t as simple as we thought: there are actually two groups of people (maybe good and bad drivers, or maybe people with different risks for some disease) that have different odds. That one-in-1,000 actually breaks down to 90% of people having a one-in-10,000 chance, and 10% of people having a one-in-100 chance. If you were charging people based on their odds, like ordinary insurance does, then 90% of people would be paying $100 instead of $1,000, and the other 10% would be paying $10,000.

What this means is that, when everyone is paying the same rate, the “safe” people are really subsidizing the “unsafe” people. And so long as nobody can tell which pool anyone is in, that’s how all insurance works. But as soon as people get a better understanding of risk, things change. If catastrophic insurance is being sold on the free market, things change quickly: even if one insurer decided to ignore it and keep charging everyone $1,000, someone else could show up and insure 90% of their customers for only $100. Pretty soon they’d have all of those customers, and the original insurer would be left with just the 10% with higher risk; they’d have to raise their rate to $10,000 just to avoid going bankrupt!

That is, everyone would end up charging the same rates that they would if this were ordinary insurance; there’s no way (in the free market) for the insurers to spread the costs around. It becomes impossible to insure against events which cost more than any one person could afford.

The only way to prevent this is to move away from a perfectly free market. If insurers were forbidden to change their rates or refuse customers based on this criterion, then you could keep everyone paying the same $1,000, and everyone would still be insured against this risk.

Of course, this doesn’t come for free; what you’ve effectively done is say that we will cover this risk, and everyone has to pony up to cover it. That is, this is a kind of tax; it can happen the way described above, with insurers required to cover something and the cost being spread across everyone insured, or it could be done as a literal tax, with everyone paying in and some central service paying out and no private companies involved, or as anything in between. Whether this is a good or bad idea depends on the situation.

The upshot is this: catastrophic insurance (which spreads people’s costs across the whole population) is unstable as a free-market good, because as knowledge of risks improves, it turns into “ordinary” insurance (which spreads an individual’s costs across time). If its cost as ordinary insurance is more than people can afford — that is, if the thing being insured against is something which people simply couldn’t pay for if it happened, like cancer treatment or accident liability — then that risk becomes uninsurable. The alternative is to make a social decision that payment for this (we can’t really call it “insurance” anymore) is going to be made out of a fund that everyone chips in to; which is to say, a tax, which pays for the benefit that people are now protected from a risk which can’t be protected against via insurance. That decision amounts to saying “everyone is chipping in to pay for X when it happens to people.”

So whenever there’s a kind of catastrophic event that people might want to insure against, we should think about it the same way we do about a tax. Is it worth it? How will the costs be distributed among people? How will the benefits be distributed? Is it better to do this with insurance rates or a literal tax? This is the question we have to ask about any kind of catastrophic insurance, whenever we either have figured out a way to split up the risk pool, or when we think that’s likely to happen in the near future.