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Healthcare: Look anywhere you like for answers, just not the US
America’s healthcare Clusterf**k offers no solutions
The subtle assurance/insurance difference
We also need to bring in one more idea, a rather archaic differentiation between assurance and insurance. Assurance is really a way of saving for something that's probably going to happen. Burial, for example, other than those lost at sea or devoured by wolverines, as we're all going to need a box and either a plot or a burning.
So, rationally, we might as well save a bit over the years to do so.
Insurance is about something unlikely to happen but which would be devastating if it did. The house burning down is unlikely, devastating if it did and yes, please go check your house insurance policy right now. At which point we need to have risk pooling.
We might now apply this distinction to healthcare. Assurance is things like getting the blood pressure checked, the 'flu shot, vaccines, contraception perhaps. There's no risk pooling here so insurance isn't the way to deal with it (which is one of the things that makes the US system so insane).
Being scraped up off the road, treating that vicious cancer – these are rare mishaps and risk pooling is appropriate. It can cost millions to properly deal with such incidents so we need to be paying some sum into a pot to pay for the treatment if we are unlucky enough to need it. Buying a reverse lottery ticket if you like, the one you hope you don't win.
These differences are still there whether you decide to have taxpayer financing or some variation of out-of-pocket, private insurance or whatever. Assurance and insurance just are not the same thing. The biggest difference being that we can use market processes to make that assurance side of things more efficient while equity means that we're just not going to do that on the insurance side of things.
Armed with this, the path dependence, our three goals, and our distinctions between assurance and insurance, we can now ponder extant healthcare systems.

Under WHO healthcare rankings, France was top, the NHS pretty good, and the US nowhere
There's been two major sets of rankings over the years. The WHO used to do one and France was top, the NHS pretty good, and the US nowhere. But do note that only 25 per cent was actually efficacy, and 12.5 per cent of the ranking points responsiveness - the rest was some variation on equity. The Commonwealth Fund is a more recent evaluator and its rankings are even more equity based.
There's nothing actually wrong with such an insistence, it's just that one ought to be aware that any such measurement system is going to be shaped by the prejudices of those building the ranking system. You're all engineers around here and you know that you get what you measure and if what you're measuring is how fair a healthcare system is then you'll be measuring that equity, not the efficacy or efficiency.
So, given our laying out of the principles we can try to design a healthcare system we can all be proud of. Insurance, by its very definition, is going to have to be something that has a wide pool over which we can share risks.