How Game Theory Helped Improve New York City's High School Application Process - NYTime... - 0 views
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“It was an allocation problem,” explained Neil Dorosin, the director of high-school admissions at the time of the redesign. The city had a scarce resource — in this case, good schools — and had to work out an equitable way to distribute it. “But unlike a scarce resource like Rolling Stones tickets, where whoever’s willing to pay the most gets the tickets, here we can’t use price,”
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In the early 1960s, the economists David Gale and Lloyd Shapley proved that it was theoretically possible to pair an unlimited number of men and women in stable marriages according to their preferences.In game theory, “stable” means that every player’s preferences are optimized; in this case, no man and no woman matched with another partner would both prefer to be with each other.
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Here is how it works: Each suitor proposes to his first-choice mate; each woman has her own list of favorites. (The economists worked from the now-quaint premise that men only married women, and did the proposing.) She rejects all proposals except her favorite — but does not give him a firm answer. Each suitor rejected by his most beloved then proposes to his second choice, and each woman being wooed in this round again rejects all but her favorite.
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Professor Abdulkadiroglu said he had fielded calls from anguished parents seeking advice on how their children could snare the best match. His advice: “Rank them in true preference order.”
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The deferred acceptance algorithm, Professor Pathak said, is “one of the great ideas in economics.” It quickly became the basis for a standard lesson in graduate-level economics courses.
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In the case of rejection, the algorithm looks to make a match with a student’s second-choice school, and so on. Like the brides and grooms of Professors Gale and Shapley, students and schools connect only tentatively until the very end of the process.
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The courting continues until everyone is betrothed. But because each woman has waited to give her final answer (the “deferred acceptance”), she has the opportunity to accept a proposal later from a suitor whom she prefers to someone she had tentatively considered earlier. The later match is preferable for her, and therefore more stable.
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It seems that most students prefer to go to school close to home, and if nearby schools are underperforming, students will choose them nevertheless. Researching other options is labor intensive, and poor and immigrant children in particular may not get the help they need to do it.