This approach could lead to free college in some states, but probably not all. The Affordable Care Act’s Medicaid expansion is instructive, with many states declining to participate despite the federal government’s promise to cover 90 percent of the cost.

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How many states would participate in a free college partnership with the federal government? It would probably depend on how much federal money is on the line; how much states are required to contribute; and the politics of college affordability.

The design of a free college policy matters not just for how many states participate, but also for which students in those states benefit — and which might be hurt. States that stretch their budget to adopt free college might lack the resources to provide high-quality instruction or support services for students who need them most. These states might fund their institutions inadequately, inequitably or both.

Eliminating tuition as a revenue source could also constrain states’ ability to expand popular institutions and programs. A low-income student might find the promise of a free college education dashed by a rejection letter from a local public college, grown more selective as the lure of free tuition pulls students away from private colleges and into public ones.

To avoid such unintended consequences would require the federal government to do far more than just provide funding to states. Existing free college proposals count on federal requirements and oversight.

A bolder approach to free college would make participating in a federal-state partnership the only way a state could get federal money for higher education. A 2016 proposal from New America would do this by eliminating Pell grants, student loans and education tax credits. This plan would instead fund colleges through formula-based grants to institutions and states that meet federal requirements.

Putting all federal money on the line could get all states to participate but would be an enormous expansion of the federal role in higher education.