The American Enterprise Institute recently published a paper, authored by eight economists, detailing the alternative health care system they prefer to Obamacare. I disagree with much of what they have to say, but I want to focus here on one crucial problem: The paper tries to achieve the impossible. It is titled “Best of Both Worlds: Uniting Universal Coverage and Personal Choice in Health Care.” But those two goals can’t be united—they’re, in fact, contradictory.

The authors want to construct a health care system in which, if someone — let’s call him Joe — wants insurance (or health care more broadly) and he can’t pay, it’s someone else’s responsibility — let’s call her Sandra — to foot the bill.

On the other hand, the authors want a system which “allow[s] people to spend as much of their own money on health care and health insurance — to buy access to better technologies and better doctors—as they want.”

But if Sandra is required to pay for Joe’s health care, her choices when it comes to her own medical care are inevitably limited — a portion of the income she’s earned and needs to pursue the best care for herself is being funneled into Joe’s pockets.

Something’s got to give.

Either Sandra has a moral right to pursue the best health care for herself, a principle which is incompatible with the system of redistribution the authors idealize—or her responsibility is to sacrifice for others, in which case we shouldn’t pretend that Sandra is free to make the choices that most benefit her.

Only a free market is truly compatible with personal choice.