SchoolChoice145

# SchoolChoice145 - School Choice Mechanism Ichiro Obara UCLA...

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School Choice Mechanism Ichiro Obara UCLA January 31, 2010 Obara (UCLA) School Choice January 31, 2010 1 / 27

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Boston Public School Match Boston Public School Match Obara (UCLA) School Choice January 31, 2010 2 / 27
Boston Public School Match Boston Mechanism Boston Public School Match Boston Public School (BPS) system assigns about 60000 students to elementary schools, middle schools, and high schools every year. BPS used to use the mechanism called Boston Mechanism . Obara (UCLA) School Choice January 31, 2010 3 / 27

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Boston Public School Match Boston Mechanism Boston Mechanism Boston public schools need to respect the following priorities of students. 1 students with younger sibling and within walk-zone 2 students with younger sibling 3 students within walk-zone 4 other students Within each priority class, students are prioritized by randomly generated numbers. Obara (UCLA) School Choice January 31, 2010 4 / 27
Boston Public School Match Boston Mechanism Boston Mechanism Given this priority order, BM works as follows. 1 Students submit the list of their favorite schools (best three in practice). 2 Assign students to their ﬁrst best choice according to the above priority order up to the capacity of each school. 3 Assign all unassigned students to their second best choice according to the priority order up to the capacity of each school ······ 4 Student who were not assigned to any school (likely to happen if students list only their best three) are assigned to some school by BPS. Obara (UCLA) School Choice January 31, 2010 5 / 27

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Boston Public School Match Boston Mechanism Boston Mechanism BM respects the ﬁrst choice of students and generates a stable matching. One problem is that students may not reveal their true preferences. Example Your best school is p 1 and second best is p 2 . The capacity of p 1 and p 2 is 100. Suppose that there are more than 100 students who prefer p 1 most and has a higher priority in p 1 than you. Also suppose that there are more than 100 students who prefers s 2 most. If you list p 1 as your ﬁrst choice, then you can’t get either p 1 or p 2 . If you pretend that p 2 is your ﬁrst choice, then you can get p 2 if your priority is high enough in p 2 . Obara (UCLA) School Choice January 31, 2010 6 / 27
Boston Public School Match Boston Mechanism Here is another example. Example 4 schools and 5 students. q 1 = q 2 = 1, q 3 = q 4 = 2. The preferences are as follows. p

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## This note was uploaded on 04/25/2010 for the course ECON 145 taught by Professor Obara during the Winter '10 term at UCLA.

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SchoolChoice145 - School Choice Mechanism Ichiro Obara UCLA...

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