A big-name college drops legacy admissions. Will others follow?

How should U.S. colleges convey fairness and gain the public’s trust? As they look for ways to have more inclusive campuses, some schools are considering whether to keep legacy admissions.

For nearly a year, the “Varsity Blues” college admissions scandal has sparked a public backlash against perks for the wealthy and well connected. One main target: legacy preferences. But until January, Johns Hopkins University had been staying mum about a major shift in its policy: Since 2014, it has admitted applicants without regard to any family alumni ties.

President Ronald...