Democratic presidential hopeful Mike Bloomberg is promising that, if elected, he will stop colleges and universities from giving preferential treatment to legacy students. It’s part of an effort, he said Tuesday, to “restore fairness” to the college-admissions process — and he is threatening to limit access to federal funds if schools do not end legacy admissions.

This new campaign promise from the 78-year-old former New York mayor, who has been rising in polls of Democratic voters, is spelled out in his newly released higher education plan, one of three he has issued on education. The other two on his campaign website address early childhood learning and career and technical education.

Legacy admissions are preferences schools give to relatives of graduates, a practice that colleges and universities say helps them stay connected to former students and raise money. Critics say it gives an unfair advantage to students from wealthy families whose relatives attended a school — and takes slots that could go to deserving students of lesser means.

Most highly selective private colleges and universities provide preference to some legacy applicants, and some classes have sizable percentages of legacies. The student newspaper at Harvard University, the Crimson, reported that at least 14 percent of the Class of 2022 was made up of legacy admissions. It also reported that 36.3 percent of students with at least one parent who attended Harvard said their family income was $500,000 or more.

Bloomberg’s plan says he “will call for an end to giving children of alumni advantages in the college admissions process, to level the playing field for all students.” He would do this, it says, by supporting legislation to require all institutions receiving federal aid to make public their comparative rates of admission for legacy and non-legacy candidates. They would also be required to report enrollment and completion rates broken out by race, income and legacy status.

Bloomberg said he would “consider stronger measures if progress isn’t made toward ending legacy preferences, including limiting schools’ access to federal funds.” The threat suggests Bloomberg would be an activist president on education issues.

Bloomberg is a 1964 electrical engineering graduate of Johns Hopkins University, which last month announced it had quietly dropped legacy preferences a few years earlier and found it helped create a more diverse student body.

My Washington Post colleague Nick Anderson, who wrote about the policy change here, reported that not long ago, freshmen at Hopkins who had legacy connections outnumbered students who qualified for Pell Grants, given to those from low-income families. For the Class of 2023, the opposite is true, with substantially fewer students having family ties to graduates. Anderson quoted Hopkins President Ronald J. Daniels as saying legacy preference is “deeply perplexing given the country’s deep commitments to merit and equal opportunity.”

Bloomberg, who has spent more money on TV ads than all the other candidates put together, gave the university $1.8 billion in 2018 to support financial aid for low- and medium-income students. He was chairman of the university’s board of trustees from 1996 to 2002.

In 2018, a report from the Harvard Committee to Study Race-Neutral Alternatives in admissions supported legacy preference. It said:

The practice of considering, among many other factors, whether an applicant’s parent attended Harvard College or Radcliffe College as an undergraduate also helps to cement strong bonds between the university and its alumni. Harvard hopes that its alumni will remain engaged with the College for the rest of their lives, and this consideration is one way that it encourages them to do so. Harvard also relies to an unusual degree on the participation of its alumni in the admissions process. In every state and almost every country around the world, Harvard graduates volunteer their time to serve as alumni interviewers. Harvard alumni also offer generous financial support to their alma mater. That financial support is essential to Harvard’s position as a leading institution of higher learning; indeed, it helps make the financial aid policies possible that help the diversity and excellence of the College’s student body. Although alumni support Harvard for many reasons, the committee is concerned that eliminating any consideration of whether an applicant’s parent attended Harvard or Radcliffe would diminish this vital sense of engagement and support. In addition, giving consideration to whether an applicant’s parent attended the College serves a community-building function, and contributes to a sense among all undergraduates that they are part of a lifelong educational engagement. Finally, the committee notes that children of Harvard alumni tend to be very strong applicants.

In a 2018 letter to Congress, however, Richard D. Kahlenberg, a senior fellow at the Century Foundation who has spent decades researching and writing about inequality in education, wrote:

Legacy preferences are often justified as a fundraising tool, but there is no convincing evidence that the existence of favorable treatment for the children of alumni is tied to increased giving.

Bloomberg’s plan also calls for eliminating tuition for all students at two-year public colleges. For students from low-income families, tuition at four-year schools would be eliminated, too. His proposal, which would cost about $700 billion, is not as broad as some plans advanced by other Democratic candidates who have called for tuition-free public higher education for all.