In You Call This Health Insurance?, Arnold Kling distinguishes between true insurance and “split the check” plans:
One of the most serious impediments to rational debate on health care is the misuse of the term ‘health insurance.’ What we call health ‘insurance’ in this country was never designed to insure the consumer. Instead, its purpose is to insure steady, reliable incomes for health care providers. True health insurance is the economist’s equivalent of a unicorn — we can describe it, but none of us has actually seen it.
What Blue Cross and Blue Shield pioneered was a “split-the-check” approach to health care. An equivalent plan for restaurant meals would be that instead of paying for your meal, you would pay an annual premium to “Blue Eats,” which would in turn reimburse restaurants for their costs, plus a profit margin. Every individual member of “Blue Eats” would have an incentive to eat out a lot and order the most expensive items on the menu, because the cost is shared among all of the members of “Blue Eats.”
“Blue Eats” would be a great marketing ploy by restaurants, because it would get people to eat out more and spend more at restaurants. Similarly, John C. Goodman argues that what we call “health insurance” originated as a marketing ploy by physicians and hospitals. It worked really well, too.
Insurable events are unlikely events.