Refugee Resettlement Matching
Two-sided matching · capacity constraints · integration outcomes
A country admits a quarterly cohort of refugee families. Each family is assigned to one locality — a city, a county, a municipality — where they'll start their new life. The assignment shapes everything that follows: employment outcomes, children's schooling, health, social integration. Jones & Teytelboym (2017)'s local refugee match formalised the problem as two-sided matching with capacity constraints. Bansak, Ferwerda, Hainmueller et al. (2018)'s Science paper showed that data-driven assignment could raise employment outcomes by 40–75% over the status quo in both US and Swiss contexts — a striking demonstration of market-design in humanitarian practice.
Problem context
Matching families to places, under capacity and for integration
Global refugee numbers have reached historic highs; by UNHCR figures, the number of forcibly displaced people worldwide exceeded 110 million by the mid-2020s. Of those, a small fraction enter formal resettlement programmes in third countries — the US, Canada, UK, EU member states, Australia. Each host country runs its own programme; within the country, a central resettlement agency (in the US, the State Department Refugee Admissions Program; in the UK, the Home Office UK Refugee Resettlement Scheme) assigns incoming families to local resettlement affiliates.
Historically, the assignment was ad hoc — based on available housing, local capacity, and caseworker judgement. Jones & Teytelboym (2017) proposed a market-design framework: treat families as one side, localities (with capacities) as the other, elicit family preferences and locality priorities, and run a deferred-acceptance-style mechanism. Bansak et al. (2018) showed the Annie system (for Annie MOORE: Matching Outcome Optimisation Engine) using machine-learning-predicted employment probabilities as integration scores, deployed jointly with US resettlement agency HIAS and Swiss authorities.
Delacrétaz, Kominers & Teytelboym (2019) extended the theory with slot-specific priorities and compound capacity constraints (language services, housing types, sibling-reunion). The algorithmic core is a deferred-acceptance variant over a bipartite structure — closely related to school-choice mechanism and kidney exchange in the matching-market family.
Multi-stakeholder framing
Mathematical formulation
Two-sided matching with outcome objective
| Symbol | Definition | Domain |
|---|---|---|
| F | Set of refugee families | |F| = n |
| L | Set of localities (resettlement sites) | |L| = m |
| ql | Capacity of locality l (families it can host) | ℕ⁺ |
| sfl | Predicted integration score (e.g., employment prob) for family f at locality l | [0, 1] |
| ≻f | Preference order of family f over localities (if elicited) | total order |
| ≻l | Priority of locality l over family types (language, composition) | total order |
| xfl | Binary: 1 if family f matched to locality l | {0, 1} |
| LANGl | Language-service capacity of l | ℕ⁺ |
s.t. Σl xfl = 1 ∀ f // each family placed
Σf xfl ≤ ql ∀ l // locality capacity
Σf: lang(f)=k xfl ≤ LANGl,k ∀ l, k // language-service cap per locality
family-composition · housing-type constraints
xfl ∈ {0, 1}
Deferred-acceptance variant (Jones-Teytelboym 2017) Elicit family preferences ≻f and locality priorities ≻l.
Run family-proposing DA: iteratively families propose to best locality, localities tentatively accept top ql by priority; iterate until no rejections. Produces stable match (no family-locality pair both prefer deviating).
Slot-specific priorities (Delacrétaz-Kominers-Teytelboym 2019) handle language / housing-type constraints without losing strategy-proofness.
Complexity Outcome-max is LP-assignment (Hungarian O(n3), polynomial). DA is O(nm). Real instances: n ~ 1000 families / year per affiliate, m ~ 30-100 localities.
Interactive solver
Match families to localities under capacity; compare algorithms
Resettlement Matching Solver
Solution interpretation
Outcome vs stability vs fairness
Outcome-maximising assigns every family to the locality where their predicted integration score is highest — subject to capacity. It maximises aggregate success but can produce matches that no family would have requested voluntarily.
Deferred acceptance respects family preferences and produces stable matchings (no family-locality pair both prefer deviating). Aggregate outcome score may be lower, but the match is procedurally fair and strategy-proof for families.
Random baseline approximates the historical non-optimised practice. Both DA and outcome-max substantially outperform it on predicted integration — the Bansak et al. paper's core result is that even modest data-driven assignment recovers large benefits.
The tradeoff: outcome-max says “the algorithm knows best”; DA says “families have preferences that matter, even if the algorithm's employment prediction is higher somewhere else.” Both are defensible; the choice is not technical.
Limitations & Critique
What the matching does not see
Predicted integration scores are uncertain and contested
The sfl scores come from a ML model trained on past outcomes — which reflect historical programme conditions, local labour markets, and who was already placed there. Over-reliance on predictions can entrench past patterns and miss population-level shifts.
Family preferences are rarely elicited in practice
DA requires preference lists, but eliciting useful preferences from families in transit, with limited information about potential localities, is operationally hard. Most deployments use proxies (language, family-reunion) rather than full preferences.
Community consent is procedurally weak
Receiving communities are often not consulted before arrivals. Positive reception predicts better integration, but the model treats localities as passive capacity units. Formalised community-voice mechanisms are an open design question.
Post-arrival mobility is common and underdocumented
Many resettled families relocate within the first 1-2 years to join family networks or seek better opportunities. Assignment optimisation that scores only initial placement misses medium-term outcomes. Models accounting for secondary migration are a newer frontier.
Programme scope is very small relative to need
Formal resettlement places less than 1% of displaced refugees annually. The overwhelming majority remain in countries of first asylum indefinitely. Optimising a 1% slice cannot substitute for broader policy response.
Political volatility shifts admissions sharply
Annual refugee admission numbers fluctuate by orders of magnitude with political climate — the US quota dropped from 85,000 (2016) to 15,000 (2020) within four years, then rebounded. Optimisation cannot compensate for volume instability.
Extensions & variants
Theory and practice converging
Slot-specific priorities
Delacrétaz-Kominers-Teytelboym (2019) — compound capacity constraints preserving strategy-proofness.
Joint optimisation of capacity and assignment
Plan where to expand locality capacity while optimising within-period assignments.
Dynamic / multi-period matching
Rolling arrival cohorts; capacity fills and refreshes; look-ahead optimisation. Ahani-Andersson-Martinello-Teytelboym-Trapp (2021).
Preference-integration hybrid
Weighted combination of predicted outcomes + family preferences in a single objective.
Stochastic integration scores
Confidence intervals on sfl; robust / risk-averse matching.
Post-arrival learning
Use realised outcome data to update scoring model (online learning). Care with feedback loops (cf. predictive-policing critique).
Family-composition constraints
Keep nuclear families together; co-locate extended family networks; UNHCR family-unity principle as hard constraint.
Cross-country assignment
EU-level proposals to allocate quota by Dublin-style framework; inherently more political than single-country.
Key references
Cited above
Related applications
Sister matching-market problems