When Americans are asked whether they support a “Medicare for all” system that would replace all current insurance with a generous government program, a majority often say yes. But when they’re asked follow-up questions, they often reveal that they’re not familiar with the details of that plan — or that they would also be happy with other Democratic policy proposals.

In a new survey from The New York Times as well as the Commonwealth Fund and the Harvard T.H. Chan School of Public Health, we forced the issue. We asked a panel of 2,005 adults to pick their favorite plan from three choices. One resembled the Medicare for all proposal; one was like more incremental Democratic proposals; and one was like a plan proposed by congressional Republicans, which would reduce federal involvement in the health system and give more money and autonomy to states.