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School Choice: DA vs Boston vs TTC

Three mechanisms, identical preferences — fundamentally different outcomes

Setup: 6 Students, 4 Schools

Student True Preferences:
s1: A>B>C>D | s2: A>B>C>D | s3: B>A>C>D
s4: B>C>A>D | s5: A>C>B>D | s6: C>B>A>D
School Priorities [quota]:
A[2]: s3>s1>s5>s2>s4>s6 | B[2]: s2>s4>s6>s1>s3>s5
C[1]: s5>s6>s3>s2>s4>s1 | D[1]: s4>s1>s6>s3>s5>s2
Boston mode:

Deferred Acceptance (DA)

Student-proposing Gale-Shapley

Boston Mechanism

Immediate Acceptance

Top Trading Cycles

Cycle-based allocation