In 1997, while investigating what makes a great public high school, I stumbled across an interesting — I would say disturbing — situation on a pleasant cul-de-sac called Summit Avenue in suburban New York. Two nearly identical Dutch colonials sat side by side, yet one was valued at $540,000 and the other $350,000.

Everyone on that block knew why. Anyone who has ever shopped for a home can guess the reason. The two houses shared a prestigious line on their return address stickers: Bronxville, N.Y. 10708. But the lower-priced was in the Tuckahoe school district, where about a quarter of the students were from low-income families. The higher-priced was in the Bronxville school district, with the number of low-income families close to zero.

This situation has not changed much since. The richest communities have the most desirable schools, thus the most valuable real estate. Tim DeRoche’s new book “A Fine Line: How Most American Kids Are Kept Out of the Best Public Schools” makes that clear.

But DeRoche and other experts have begun to illuminate ways that those with average or below-average incomes might enroll their children in such prized institutions, if policymakers used their imaginations.

DeRoche cited a 1992 concurring opinion by Supreme Court Justice Antonin Scalia in the Freeman v. Pitts desegregation case. Scalia imagined an education system “in which parents are free to disregard neighborhood-school assignment, and to send their children (with transportation paid) to whichever school they choose.”

The justice made the suggestion just before the charter school movement began to blossom into what is now 3 million children attending public schools their parents choose. They may have to win a randomized lottery to get into an oversubscribed charter, but DeRoche said that was an improvement over the past. So why not have lotteries for all schools in a district, charter or otherwise?

“All the residents of a district deserve an equal opportunity to enroll in the best schools in the district,” DeRoche said. “The results may seem frustrating or even tragic. But a lottery gives every district family a fair chance — an equal opportunity — to enroll their child in a coveted school that could dramatically change her life trajectory.”

Such ideas are often unpopular with teachers unions, who oppose nonunion charters. Some school boards see lotteries as hard to administer. Also, DeRoche’s idea would not have equalized the two houses on Summit Avenue, since each was in a different district.

DeRoche proposed that states adopt the language of a 1987 California law that ended geographic assignment for one kind of school. It mandated “the unrestricted enrollment and attendance of students in community colleges, thereby providing each resident of the state an equal opportunity to attend the community college of his or her choice.”

Richard D. Kahlenberg is a senior fellow at the Century Foundation in Washington and a leading advocate of increasing racial and economic diversity in public schools. He said random lotteries don’t do enough to give low-income children more access to good schools.

He favors programs like the system for elementary and middle school choice in Cambridge, Mass., which weights a lottery to provide a more even mix of low-income and middle-class children in each school. He also likes the enrollment system he helped design for the Charlotte-Mecklenburg, N.C., magnet schools. It seeks a mix of low, medium and high socioeconomic status families on each campus.

An approach that has impressed many advocates of school choice, including me, is the My School D.C. enrollment system, which is used to match family preferences with nearly all public traditional and charter schools in Washington. Thomas Toch, director of FutureEd, an independent think tank at Georgetown University’s McCourt School of Public Policy, explained in The Washington Post Magazine in 2019 how the system grew from discussions between D.C. schools chancellor Kaya Henderson, D.C. Public Charter School Board Scott Pearson and a Nobel-winning economist named Alvin Roth.

In 1995, Roth wrote a mathematical algorithm that improved the efficiency of the system for matching medical school graduates with hospital residencies. Roth similarly helped New York City rewrite its dysfunctional high school enrollment system. Henderson was rare among school district leaders in supporting charter schools. So she endorsed, along with deputy mayor for education Abigail Smith, throwing both regular and charter schools into a big bowl and letting Roth match family preferences and school slots for nearly everybody.

Toch said he was surprised that the D.C. scramble for seats before Roth got involved vexed charter schools as much as regular ones, and their parents. “Common lotteries greatly reduce the problem,” he told me.

Realtors still print colorful brochures noting how many more students attend the Ivy League from one high school compared to others. Big price differences still characterize neighborhoods like Summit Avenue. But the rise of charters, nonselective magnet schools and clever algorithms have scrambled preferences enough to give families more freedom of choice, if the politicians in charge will let them have it.