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Lotteries in Student Assignment: An Equivalence Result

How Are Lotteries Used in Student Assignment?

School Assignment, June 2010

Parag Pathak and Jay Sethuraman inves­ti­gate a sim­pli­fied method for under­stand­ing how lot­ter­ies are used in assign­ing stu­dents to schools.  This work stems from design of new stu­dent assign­ment mech­a­nisms cou­pled with inter­ests by pol­i­cy­mak­ers from author­i­ties such as the NYC Department of Education.  Here Pathak and Sethuraman uncover that sin­gle and mul­ti­ple lot­tery mech­a­nisms are equiv­a­lent for the prob­lem of allo­cat­ing stu­dents to schools in which stu­dents have strict pref­er­ences and the schools are indifferent.

School dis­tricts around the world employ cen­tral­ized mech­a­nisms to assign stu­dents to schools.  These processes of assign­ing stu­dents con­sider fac­tors such as stu­dent pri­or­i­ties at indi­vid­ual schools (such as geo­graphic prox­im­ity) along with appli­cants rank order­ing of schools.  Upon con­sid­er­a­tion of this model, a key ques­tion is raised: if many stu­dents rank the same school as their top choice, which of these stu­dents should be assigned to that school?  A lot­tery mech­a­nism is a way to achieve fair­ness in the assign­ment process.  Pathak and Sethuraman exam­ine sin­gle ver­sus mul­ti­ple lot­tery mech­a­nisms with con­sid­er­a­tion of assign­ment prob­lems moti­vated by DOE discussion.