← Gallery

Incomplete Preference Lists

When agents only list schools/people they find acceptable, some participants may remain unmatched. This is preferable to an unacceptable assignment.

List Mode

Students submit their full acceptable preference lists.

Algorithm Pseudocode 
DA with Incomplete Lists:
while ∃ free student s with
  remaining acceptable schools:
    sch ← s's top remaining school
    if s is acceptable to sch:
      if sch has vacant slot:
        tentatively match (s, sch)
      else if sch prefers s to worst:
        displace worst, match (s, sch)
      else: reject s
    else: s finds sch unacceptable

Preference Lists

Strategy-Proofness of DA

Under DA, submitting a complete honest list is always weakly dominant. There is no strategic reason to omit acceptable schools. Truncating can only hurt or have no effect.

Event Log

Click "Run DA" to begin.

Matching Visualization

Real-World Systems with Limited Lists

🇬🇧
UCAS (UK): Students limited to 5 university choices. Strategic list construction matters when lists are artificially short.
🇺🇸
NYC High Schools: Students rank up to 12 schools from 700+ options. Short lists cause many students to go unmatched in early rounds.
🇧🇷
Brazil SISU: Students can only list 2 programs. This extreme truncation makes strategic behavior significant.

Truncation Strategy

Under Deferred Acceptance: Truncating your list can only HURT you. Under Boston Mechanism: Truncating can actually HELP (by gaming priorities).