College is supposed to be society’s great leveler. But the college admissions process is not on the level. And Americans are right to be cynical about the way it favors the wealthy and well-connected.

When I applied to college, I didn’t have any connections, and my parents didn’t have enough money to send me. My father never made more than $6,000 a year, but I was able to get government loans with a low-interest rate (only 1.5 percent), and I worked a job at a campus parking lot to help pay tuition, room and board. I don’t know where I would’ve ended up if I hadn’t gone to college, but life would’ve turned out very different.

I’m running for president to make sure that every student in America has the same opportunity I did, to get a good education that opens the door to career opportunities they never dreamed of. That starts with making college more affordable and accessible, issues I have worked on for years through my foundation.

Today, I am proposing a plan to make community college free for all students—and to make four-year public colleges and universities free for lower-income students. We’ll do that in part by doubling the size of Pell grants and giving students funding to cover non-tuition expenses like books, transportation, food and child care. My plan will also significantly reduce the burden of undergraduate student loans and guarantee no one owes more than they can afford to pay.

But affordability isn’t the only obstacle to a college degree. And so my plan will invest in completion strategies, informed by proven models, like the one I launched as mayor that helps community college students and achieves graduation rates nearly 30 points higher than comparison group students.

Helping more students graduate starts with helping more of them get into school. But as the recent scandals have shown, students aren’t competing on a level playing field for spots at top colleges.

America is one of the only countries with legacy admissions—the practice of giving an advantage to children or relatives of alumni. Over 80 percent of the most selective colleges use legacy status as a factor in admissions. Studies have found that legacy applicants receive an advantage worth the equivalent of 160 additional points on the SAT (out of 1600). Giving preference to legacy applicants is part of a flawed higher education system that too often benefits wealthy, white students. Their advantage comes at the expense of qualified students who are minority, low-income or middle class and whose parents did not attend college. Legacy preferences are one reason why 38 top colleges in America had more students enrolled from the top 1 percent of household incomes than from the bottom 60 percent.

Neither tradition nor the purported need to fundraise from alumni should sustain this practice, especially as income inequality grows worse—and as generational racial inequalities persist. As president, I will work to end the practice and eliminate the unfair advantage some students receive by chance of being born into a well-educated, and often affluent, family.

My plan will require all institutions receiving federal aid, which include our most elite colleges, to make public their admissions, enrollment and graduation rates for legacy and non-legacy applicants. Colleges that create equity between these groups will be rewarded.

The idea of making information about legacy students more transparent is neither new nor my own; the late Senator Edward Kennedy pursued a similar system in 2003. He approached the issue with personal experience: He was a legacy.

Education is the key to fulfilling the promise of America as a land of opportunity for all, because of its power to drive economic mobility. Harnessing that power requires us to extend opportunity for all—on more equal footing.

Together, we can end legacy preferences and create a more equitable system of higher education.

Michael Bloomberg is a Democratic candidate for president of the United States.

The views expressed in this article are the writer’s own.