Boston Mechanism (Immediate Acceptance)

About

The Boston Mechanism assigns students to schools using immediate acceptance: once a school fills its seats, those seats are permanently taken. This creates strong incentives for strategic misreporting.

Algorithm Pseudocode

Round k (k = 1, 2, 3, ...):
  For each unmatched student s:
    s applies to their k-th choice school
  For each school with new applicants:
    School PERMANENTLY accepts top
    applicants up to remaining quota
    Rejects the rest (forever)
  Repeat until all matched or
  all choices exhausted.

Controls

Manipulation Finder

Select a student to find their optimal strategic report under Boston:

Properties of Boston Mechanism

✗ NOT Strategy-proof — students benefit from misreporting

✗ NOT Stable — can produce blocking pairs

✗ NOT Fair — penalizes honest students

✓ Simple to understand and implement

✓ Respects stated first choices

Under DA, truthful play is ALWAYS optimal. Under Boston, strategic play is necessary to avoid being hurt. Boston was replaced in Boston in 2005 after research by Abdulkadiroglu, Pathak, Roth & Sonmez showed its manipulability harmed disadvantaged families.

Event Log

Setup

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

School Priorities (quota):

A[2]: s3 > s1 > s4 > s2 > s5
B[2]: s2 > s5 > s1 > s3 > s4
C[1]: s4 > s3 > s1 > s5 > s2
D[1]: s5 > s4 > s2 > s1 > s3

Truthful Boston

s2 reports: A > B > C > D

Strategic Boston

s2 reports: B > A > C > D

Why Strategic Play Matters

Under Boston, listing a competitive school first is risky: if rejected in Round 1, you lose access to schools that filled their seats. Savvy families learn to "play it safe" by listing less competitive schools first. This disproportionately harms families who lack information about school popularity, typically lower-income families.