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My thought experiment would be to offer chronically ill elderly the choice of some vey large amount of money if they should to let the illness run its course.
I published a related proposal in 1994: Buy Health Not Health Care.
The knowledge asymmetry here I think makes the hole thing impractical.
For example, the Dr. might know that the median survival for the procedure is rather low, say 3 months, but, because when someone does well they do real well, the average might be 2 years, even though it is only 10% of the patients that achieve it. (Think cancer treatment.)
So the Dr. might say, the average person survives 2 years or more, and of the people that survive for 2 years or more, the recurrence rate is nearly zero. You'd think that sounded great, and be ready to pay a lot for it (50/50 chance of cure! you'd think). Then, the Dr. might go on to talk you into a 3 month payoff (meaning if you survive for 3 months, you pay). For example, he might say, "I can't possibly wait 2 years to get paid for a procedure that costs $200,000 - I just got out of med school, and my loans are due now." And the patient doesn't have the background to read and understand the medical and statistical details, and signs up.
So he thinks he's paying for the average outcome of 2 years or more survival and low recurrence rates, but in reality is going to be paying for median outcome, which is 3 months and then dead.
And of course we could write things into the contract about how the doctor has to refund if the patient is dead within two years, etc, but good luck with that. Consumers get their clocks cleaned with stuff simpler than this all the time. (And who's to say Dr. is still going to have the money then anyway.)
A successful Dr. is going to be the best business man, rather than the best practitioner.
Also, I have to say that negotiating on the spot for life saving treatments is pretty unrealistic in its own right. Most people can't negotiate successfully for a car, forget about their lives.