Did the Nobel Prize Committee choose this year’s economics laureates to influence the growing debate in Boston about how to assign students to public schools? I know we’re the hub of the universe and all that, but the Scandinavians can’t possibly be so focused on our issues. Still, the awards to economists Lloyd Shapley and Alvin Roth shouldn’t just shine a spotlight on their work on assignment mechanisms. It should also make us pause before embracing changes that restrict the school choices of Boston’s parents — especially those with less means.
Boston has struggled for decades to find an equitable way to assign students to schools. The current system for elementary- and middle-school children splits the city up into three zones. Children entering the system generate a list of their preferred schools, which can be within their zone, or within a mile of their home, or one of the city’s few “city-wide” schools. High school students can apply anywhere. Students with siblings in a school or who live within walking distance of a school have a better chance of getting in. But beyond those factors, a lottery determines which child goes where.
Motivated in part by concerns about the high cost of transporting students around, Boston Public Schools have put five potential reforms on the table. One proposal eschews lotteries and choice altogether and simply assigns students to the nearest possible school. The other proposals would keep the basic outline of the current system, but increase the number of zones from three to six, nine, 11, or 23.
Of course, a lot of thinking went into the current rules, and even subtle tweaks can change how well the results reflect the city’s values.
The current system owes much to Roth, a professor at UCLA, and Shapley, a Harvard colleague of mine (who, sadly, is leaving for Stanford). Most of the time, economists argue for allocating things based on prices; cars and cabbages go to the buyers willing to pay most, who presumably value the goods most highly. But in some cases, ethical considerations preclude that; Roth worked to develop kidney exchanges to address the fact that we don’t like auctioning off life-saving organs. In other situations, both the people seeking an item and the people providing it have certain preferences that need to be honored. Prospective spouses, except perhaps for Scarlett O’Hara, don’t just sell themselves to the highest bidder. They want to find the right match. In a similar spirit, Boston declines to sell admissions to its prestigious Boston Latin School, both to ensure opportunity and to maintain the high quality of the student body.
Without prices, we need an alternative system to make matches that reflect individual preferences. Shapley proposed such an approach: Suitors propose to their ideal mate. Those mates tentatively select their favorite suitor, and the rejected suitors try again. Rejected suitors can present themselves either to an unmatched person, or to a mate who already has a prospective spouse, who then decides whether to dump him or her for the new beau. The process continues until all the suitors have the best mate that they can get. It sounds strange to say, but Shapley’s algorithm ultimately provided the basis for Boston’s current assignment system.
In practice, this complex system isn’t perfect, but it is much better than a simpler one that makes the first choices permanent. When your first pick determines your outcome, there is a huge incentive to initially choose a less-popular, less-attractive option. Boston used to have such a system. When Roth helped redesign it in 2005, the new system encouraged families to try for the schools they really want.
Four of the new proposals don’t monkey with this core algorithm, but they do restrict parental choice by making zones smaller. This will benefit parents in zones with good schools, and hurt parents in the often poorer districts with weaker schools. Smaller zones will reduce kids’ travel distances and the school system’s transit costs, but we can instead tinker with the algorithm to nudge towards this outcome without radically restricting parental choice.
A good school assignment system seeks to merge the great benefit of the free market — providing abundant choices — with more social equity. Shrinking the school zones provides less choice and less equity, which seems far from what the city needs, and far from the spirit of the pioneering work of Shapley and Roth.