Group fairness in dynamic refugee assignment

TL;DR

This work introduces a principled approach to group fairness in the dynamic refugee assignment problem, modeling sequential arrivals, location capacities, and an ex-post fairness rule that imposes minimum average employment per group. It then develops two online algorithms, Amplified Bid Price Control (ABP) and Conservative Bid Price Control (CBP), with provable guarantees: ABP achieves distribution-dependent vanishing regret for ex-post feasible, low-sensitivity fairness rules, while CBP attains distribution-independent vanishing regret under slackness, with explicit bounds on global and group-specific regret. The authors validate the framework and algorithms on real-world US and Netherlands data, showing that substantial group fairness gains can be achieved with only small reductions in total employment (roughly 1–5%), supporting practical deployment in GeoMatch-like decision-support systems. The results connect to online packing and offer insights into trade-offs between fairness and efficiency, highlighting the value of tunable fairness rules (Random, Proportional Optimized, MaxMin) and addressing the challenges posed by small groups. The work also discusses limitations, such as the handling of intersectional groups and families, and outlines avenues for future research in non-stationary arrivals and broader public-policy applications.

Abstract

Ensuring that refugees and asylum seekers thrive (e.g., find employment) in their host countries is a profound humanitarian goal, and a primary driver of employment is the geographic location within a host country to which the refugee or asylum seeker is assigned. Recent research has proposed and implemented algorithms that assign refugees and asylum seekers to geographic locations in a manner that maximizes the average employment across all arriving refugees. While these algorithms can have substantial overall positive impact, using data from two industry collaborators we show that the impact of these algorithms can vary widely across key subgroups based on country of origin, age, or educational background. Thus motivated, we develop a simple and interpretable framework for incorporating group fairness into the dynamic refugee assignment problem. In particular, the framework can flexibly incorporate many existing and future definitions of group fairness from the literature (e.g., Random, Proportionally Optimized within-group, and MaxMin). Equipped with our framework, we propose two bid-price algorithms that maximize overall employment while simultaneously yielding provable group fairness guarantees. Through extensive numerical experiments using various definitions of group fairness and real-world data from the U.S. and the Netherlands, we show that our algorithms can yield substantial improvements in group fairness compared to an offline benchmark fairness constraints, with only small relative decreases ($\approx$ 1%-5%) in global performance.

Figures (8)

• Figure 2: Minimum requirements for each group and scenario over bootstrapped arrival sequences.
• Figure 3: $\textsf{FR}_{g}(\boldsymbol{\omega})$ of Rand and BP with respect to the three fairness rules in each scenario.
• Figure 4: Distribution of FR$(\boldsymbol{\omega})$ under the three fairness rules for each scenario across 50 bootstrapped arrival sequences. The labels show FR---the average value of FR$(\boldsymbol{\omega})$. We note that, unlike ABP and CBP, the Random, OPT, and BP algorithms are independent of the chosen fairness rule.
• Figure 5: Slackness for each fairness rule, shown at the group-level. Specifically, each bar corresponds to a value of $\epsilon_{g,\mathcal{F}}(\mathcal{P})$ where $\mathcal{P}$ is the true distribution of 2016 arrivals.
• Figure 6: $\textsc{FR}_g(\boldsymbol{\omega})$ achieved by OPT with respect to the three fairness targets for each scenario.

Theorems & Definitions (100)

• Remark 1: Discussion on assumptions
• Example 1: Random Fairness Rule
• Example 2: Proportionally Optimized Fairness Rule
• Example 3: MaxMin Fairness Rule
• Definition 1
• Definition 2
• Proposition 1
• Proposition 2
• Theorem 1
• Lemma 4.1